Finite Group Databasebeta

← #13178286

Subgroups — #13178286

Order 1728.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×C4⋊#1113C211yesmaximal, characteristic, complemented
3C3×#64093C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C3×#64091C211yesmaximal, characteristic, complemented
6#11723729C211yesmaximal, characteristic, complemented
7#11723727C211yesmaximal, characteristic, complemented
8#11723725C211yesmaximal, characteristic, complemented
9#11723701C211yesmaximal, characteristic, complemented
10#11723700C211yesmaximal, characteristic, complemented
11#11723696C211yesmaximal, characteristic, complemented
12#11723694C211yesmaximal, characteristic, complemented
13#11723690C211yesmaximal, characteristic, complemented
14#11723687C211yesmaximal, characteristic, complemented
15#11723686C211yesmaximal, characteristic, complemented
16#10594264—31nomaximal
17#10594263—31nomaximal
18#10594262—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic, complemented
20C22×#1113C2211yescharacteristic
21C22×#1113C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
30C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
31#89049—24no—
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic
34C2×#6295C2211yescharacteristic, complemented
35C2×#6295C2211yescharacteristic, complemented
36C2×#6295C2211yescharacteristic, complemented
37C2×#6294C2211yescharacteristic, complemented
38C2×#6294C2211yescharacteristic, complemented
39C4⋊#1113—24no—
40C33×C22⋊C4C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C3×#3750C2211yescharacteristic, complemented
48C3×#3750C2211yescharacteristic, complemented
49#88815C2211yescharacteristic, complemented
50#88814C2211yescharacteristic, complemented
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88814C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3802—31no—
60C2×D3×D12—31no—
61C2×D3×D12—31no—
62#64093D311yescharacteristic, complemented
63#64092D311yescharacteristic, complemented
64#64091D311yescharacteristic, complemented
65C3×#884—31no—
66C3×#884—31no—
67C3×#884—61no—
68C3×#883—31no—
69C3×#883—31no—
70C3×#883—61no—
71C3×#882—31no—
72C3×#882—31no—
73C3×#882—61no—
74#63983—31no—
75#63983—31no—
76#63983—31no—
77#63981—31no—
78#63977—31no—
79#63976—31no—
80#63971—31no—
81#63970—31no—
82#63958—31no—
83#63923—31no—
84#63922—31no—
85#63922—31no—
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63916—31no—
90#63910—31no—
91#63909—31no—
92#63908—31no—
93#63905—31no—
94#63897—31no—
95#63891—31no—
96#63890—31no—
97#63886—31no—
98#63885—31no—
99#63884—31no—
100#63884—31no—
101#63854—31no—
102#63853—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C22×C3×C3⋊D3C2311yescharacteristic
114C2×#1113—22no—
115C2×#1113—41no—
116C2×#1113—41no—
117C2×#1113—41no—
118C2×#1113—41no—
119C2×#1113D414yescomplemented
120C2×C33×C4C2311yescharacteristic
121C2×C33×C4C2311yescharacteristic
122C3×#638—22no—
123C3×#638—22no—
124C3×#638—41no—
125C3×#638—41no—
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C2×C3×C3⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊Dic3C2311yescharacteristic
130C2×C3×C3⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊Dic3C2311yescharacteristic
132C3×C4⋊(C3⋊D3)—22no—
133C3×C4⋊(C3⋊D3)—22no—
134C3×C4⋊(C3⋊D3)—41no—
135C3×C4×C3⋊D3—22no—
136C3×C4×C3⋊D3—41no—
137#6295—22no—
138#6295—22no—
139#6295—22no—
140#6295—22no—
141#6295—41no—
142#6294—22no—
143#6294—41no—
144#5653—91no—
145#5605—91no—
146#5589—91no—
147C23×C3⋊D3C2×D311yescharacteristic, complemented
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—61no—
151C22×D32—31no—
152C22×D32—31no—
153C22×D32—31no—
154C22×D32—31no—
155C22×D32—31no—
156C22×D32—31no—
157C2×#638C2×D311yescharacteristic
158C2×#638C2×D311yescharacteristic, complemented
159C2×#638C2×D311yescharacteristic, complemented
160C2×#638C2×D311yescharacteristic, complemented
161C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
162C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
163C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
164C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
165C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—61no—
175C2×C3×#67—61no—
176C2×C3×#67—61no—
177C2×C3×#67—61no—
178C2×C3×D12—31no—
179C2×C3×D12—31no—
180C2×C3×D12—31no—
181C2×C3×D12—31no—
182C2×C3×D12—31no—
183C2×C3×D12—31no—
184C2×C3×D12—61no—
185C2×C3×D12—61no—
186C2×C3×D12—61no—
187C2×C3×C4×D3—31no—
188C2×C3×C4×D3—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191C2×C3×C4×D3—61no—
192C2×C3×C4×D3—61no—
193#3811—64no—
194D3×#67—64no—
195D3×#67—64no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—31no—
204C2×#626—31no—
205C2×#626—31no—
206C2×#625—31no—
207C2×#625—31no—
208C2×#625—31no—
209C2×#625—31no—
210C2×#625—31no—
211C2×#624—31no—
212C2×#624—31no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—31no—
216C2×D3×Dic3—31no—
217#3802—64no—
218D3×D12—64no—
219D3×D12—64no—
220C32×C22⋊C4—21no—
221C32×C22⋊C4—21no—
222C32×C22⋊C4—21no—
223C32×C22⋊C4—41no—
224C32×C22⋊C4C2×D311yescharacteristic, complemented
225C32×C22⋊C4C2×D311yescharacteristic, complemented
226C32×C22⋊C4C2×D311yescharacteristic, complemented
227#3757C2×D311yescharacteristic, complemented
228#3752C2×D311yescharacteristic, complemented
229#3752C2×D311yescharacteristic, complemented
230#3752C2×D311yescharacteristic, complemented
231#3752C2×D311yescharacteristic, complemented
232C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
233#3750C2×D311yescharacteristic, complemented
234#3750C2×D311yescharacteristic, complemented
235C3×#217—31no—
236C3×#217—31no—
237C3×#217—61no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—31no—
246C3×(C2×D3)⋊C4—61no—
247C3×(C2×D3)⋊C4—61no—
248C3×(C2×D3)⋊C4—61no—
249C3×(C2×D3)⋊C4—61no—
250C3×C4⋊Dic3—31no—
251C3×C4⋊Dic3—31no—
252C3×C4⋊Dic3—61no—
253C3×Dic3⋊C4—31no—
254C3×Dic3⋊C4—31no—
255C3×Dic3⋊C4—31no—
256C3×Dic3⋊C4—31no—
257C3×Dic3⋊C4—61no—
258C3×Dic3⋊C4—61no—
259#3724—31no—
260Dic3⋊Dic3—31no—
261Dic3⋊Dic3—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—31no—
267#3722—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—31no—
276(C2×D3)⋊Dic3—31no—
277(C2×D3)⋊Dic3—31no—
278(C2×D3)⋊Dic3—31no—
279(C2×D3)⋊Dic3—31no—
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3—21no—
296C2×C3×C3⋊D3—21no—
297C2×C3×C3⋊D3—21no—
298C2×C3×C3⋊D3—21no—
299C2×C3×C3⋊D3—44no—
300C2×C3×C3⋊D3C2×D412yes—
301C2×C3×C3⋊D3C2×D412yes—
302C2×C3×C3⋊D3C2×D412yes—
303#1113—44no—
304#1113—44no—
305C33×C4—21no—
306C33×C4—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3—21no—
309C3×C3⋊Dic3—21no—
310C3×C3⋊Dic3—21no—
311C3×C3⋊Dic3—21no—
312C3×C3⋊Dic3—21no—
313C22×#67—91no—
314C2×D3×D4—91no—
315C2×D3×D4—91no—
316C2×D3×D4—91no—
317C2×D3×D4—91no—
318C22×D12—91no—
319C3×#123—91no—
320C3×#121—91no—
321C3×#120—91no—
322#953—91no—
323#939—91no—
324#939—91no—
325#938—91no—
326#938—91no—
327#937—91no—
328#937—91no—
329#937—91no—
330#937—91no—
331#937—91no—
332#935—91no—
333#930—91no—
334#929—91no—
335C2×(C2×D3)⋊C4—91no—
336#895—91no—
337#895—91no—
338#894—91no—
339#894—91no—
340#894—91no—
341#894—91no—
342#886—91no—
343#884—31no—
344#884—31no—
345#884—61no—
346#884—91no—
347#884—91no—
348#883—31no—
349#883—31no—
350#883—61no—
351#883—91no—
352#883—91no—
353#882—31no—
354#882—31no—
355#882—61no—
356#882—91no—
357#882—91no—
358#882—91no—
359D3×C22⋊C4—91no—
360D3×C22⋊C4—91no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—21no—
364C23×C32—41no—
365C23×C32C22×D311yescharacteristic
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C22×C3⋊D3—22no—
369C22×C3⋊D3—41no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3C22×D311yescharacteristic
372C22×C3⋊D3C22×D311yescharacteristic
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3⋊D3C22×D311yescharacteristic
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—61no—
390C22×C3×D3—61no—
391C22×C3×D3—61no—
392C22×C3×D3—61no—
393C22×C3×D3—61no—
394C22×C3×D3—61no—
395C22×C3×D3—62no—
396C22×C3×D3—62no—
397C22×C3×D3—122no—
398C22×C3×D3—121no—
399C22×C3×D3—121no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—122no—
403C22×C3×D3—122no—
404C2×D32—34no—
405C2×D32—34no—
406C2×D32—34no—
407C2×D32—62no—
408C2×D32—62no—
409C2×D32—62no—
410C2×D32—121no—
411C2×D32—121no—
412C2×D32—121no—
413C2×D32—121no—
414C2×D32—121no—
415C2×D32—121no—
416C2×D32—121no—
417C2×D32—121no—
418C2×D32—121no—
419C2×D32—121no—
420C2×D32—121no—
421C2×D32—121no—
422C2×C32×C4—21no—
423C2×C32×C4—21no—
424C2×C32×C4—21no—
425C2×C32×C4—21no—
426C2×C32×C4—21no—
427C2×C32×C4—21no—
428C2×C32×C4—41no—
429C2×C32×C4—41no—
430C2×C32×C4C22×D311yescharacteristic
431C2×C32×C4C22×D311yescharacteristic
432C2×C32×C4C22×D311yescharacteristic
433C2×C32×C4C22×D311yescharacteristic
434C2×C32×C4C22×D311yescharacteristic
435C2×C32×C4C22×D311yescharacteristic
436#638—22no—
437#638—22no—
438#638—41no—
439#638—41no—
440C2×C3⋊Dic3C22×D311yescharacteristic
441C2×C3⋊Dic3C22×D311yescharacteristic
442C2×C3⋊Dic3C22×D311yescharacteristic
443C2×C3⋊Dic3C22×D311yescharacteristic
444C2×C3⋊Dic3C22×D311yescharacteristic
445C2×C3⋊Dic3C22×D311yescharacteristic
446C4⋊(C3⋊D3)—22no—
447C4⋊(C3⋊D3)—22no—
448C4⋊(C3⋊D3)—41no—
449C4×C3⋊D3—22no—
450C4×C3⋊D3—41no—
451C3×#67—62no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—62no—
455C3×#67—122no—
456C3×#67—122no—
457C3×#67—121no—
458C3×#67—121no—
459C3×#67—121no—
460C3×#67—121no—
461C3×#67—122no—
462C3×#67—122no—
463C2×C3×Dic3—31no—
464C2×C3×Dic3—31no—
465C2×C3×Dic3—31no—
466C2×C3×Dic3—31no—
467C2×C3×Dic3—31no—
468C2×C3×Dic3—31no—
469C2×C3×Dic3—31no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—31no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—61no—
476C2×C3×Dic3—61no—
477C2×C3×Dic3—61no—
478C2×C3×Dic3—61no—
479C2×C3×Dic3—61no—
480C2×C3×Dic3—61no—
481C3×D12—62no—
482C3×D12—62no—
483C3×D12—62no—
484C3×D12—62no—
485C3×D12—122no—
486C3×D12—122no—
487C3×D12—121no—
488C3×D12—121no—
489C3×D12—122no—
490C3×C4×D3—62no—
491C3×C4×D3—62no—
492C3×C4×D3—122no—
493C3×C4×D3—121no—
494C3×C4×D3—121no—
495C3×C4×D3—122no—
496#626—62no—
497#626—62no—
498#626—62no—
499#626—62no—
500#626—62no—
501#626—62no—
502#626—62no—
503#626—62no—
504#626—121no—
505#626—121no—
506#625—62no—
507#625—62no—
508#625—62no—
509#625—62no—
510#625—121no—
511#624—62no—
512#624—121no—
513D3×Dic3—62no—
514D3×Dic3—62no—
515D3×Dic3—121no—
516D3×Dic3—121no—
517#534—271noSylow
518C2×C33—41no—
519C2×C33C22×D411yescharacteristic
520C2×C33H(5,𝔽2)11yescharacteristic
521C2×C33H(5,𝔽2)11yescharacteristic
522C3×C3⋊D3—22no—
523C3×C3⋊D3—22no—
524C3×C3⋊D3—22no—
525C3×C3⋊D3—41no—
526C3×C3⋊D3—41no—
527C3×C3⋊D3—41no—
528C24×C3—91no—
529C23×D3—31no—
530C23×D3—31no—
531C23×D3—61no—
532C23×D3—91no—
533C23×D3—91no—
534C23×D3—91no—
535C23×D3—91no—
536C23×D3—91no—
537C23×D3—91no—
538C2×C3×D4—91no—
539C2×C3×D4—91no—
540C2×C3×D4—91no—
541C2×C3×D4—91no—
542C2×C3×D4—91no—
543C2×C3×D4—91no—
544C2×C3×D4—91no—
545C22×C3×C4—91no—
546C22×C3×C4—91no—
547C2×#67—31no—
548C2×#67—31no—
549C2×#67—31no—
550C2×#67—31no—
551C2×#67—31no—
552C2×#67—31no—
553C2×#67—31no—
554C2×#67—31no—
555C2×#67—61no—
556C2×#67—61no—
557C2×#67—61no—
558C2×#67—61no—
559C2×#67—91no—
560C2×#67—91no—
561C2×#67—91no—
562C2×#67—91no—
563C2×#67—91no—
564C2×#67—91no—
565C2×#67—91no—
566C2×#67—91no—
567C2×#67—91no—
568C2×#67—91no—
569C2×#67—184no—
570C22×Dic3—91no—
571C22×Dic3—91no—
572D3×D4—184no—
573D3×D4—184no—
574D3×D4—184no—
575D3×D4—184no—
576C2×D12—31no—
577C2×D12—31no—
578C2×D12—31no—
579C2×D12—31no—
580C2×D12—31no—
581C2×D12—31no—
582C2×D12—61no—
583C2×D12—61no—
584C2×D12—61no—
585C2×D12—91no—
586C2×D12—91no—
587C2×D12—91no—
588C2×D12—91no—
589C2×D12—91no—
590C2×D12—184no—
591C2×C4×D3—31no—
592C2×C4×D3—31no—
593C2×C4×D3—31no—
594C2×C4×D3—31no—
595C2×C4×D3—61no—
596C2×C4×D3—61no—
597C2×C4×D3—91no—
598C2×C4×D3—91no—
599C2×C4×D3—91no—
600C2×C4×D3—91no—
601C3×C4⋊C4—91no—
602C3×C4⋊C4—91no—
603C3×C4⋊C4—91no—
604C3×C22⋊C4—21no—
605C3×C22⋊C4—21no—
606C3×C22⋊C4—21no—
607C3×C22⋊C4—41no—
608C3×C22⋊C4—91no—
609C3×C22⋊C4—91no—
610C3×C22⋊C4—91no—
611C3×C22⋊C4—91no—
612C3×C22⋊C4—91no—
613C3×C22⋊C4D3211yescharacteristic, complemented
614C3×C22⋊C4D3211yescharacteristic, complemented
615C3×C22⋊C4D3211yescharacteristic, complemented
616#217—31no—
617#217—31no—
618#217—61no—
619#217—91no—
620#217—91no—
621#217—91no—
622#217—91no—
623#217—91no—
624#217—91no—
625(C2×D3)⋊C4—31no—
626(C2×D3)⋊C4—31no—
627(C2×D3)⋊C4—31no—
628(C2×D3)⋊C4—31no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—61no—
634(C2×D3)⋊C4—61no—
635(C2×D3)⋊C4—61no—
636(C2×D3)⋊C4—61no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—91no—
647(C2×D3)⋊C4—91no—
648(C2×D3)⋊C4—91no—
649C4⋊Dic3—31no—
650C4⋊Dic3—31no—
651C4⋊Dic3—61no—
652C4⋊Dic3—91no—
653Dic3⋊C4—31no—
654Dic3⋊C4—31no—
655Dic3⋊C4—31no—
656Dic3⋊C4—31no—
657Dic3⋊C4—61no—
658Dic3⋊C4—61no—
659Dic3⋊C4—91no—
660Dic3⋊C4—91no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—21no—
664C22×C32—21no—
665C22×C32—21no—
666C22×C32—21no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—41no—
675C22×C32—41no—
676C22×C32—41no—
677C22×C32—42no—
678C22×C32—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—81no—
685C22×C32—81no—
686C22×C32C23×D311yescharacteristic
687C22×C32C23×D311yescharacteristic
688C22×C32C23×D311yescharacteristic
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—21no—
693C2×C3⋊D3—21no—
694C2×C3⋊D3—21no—
695C2×C3⋊D3—21no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C2×C3⋊D3—21no—
700C2×C3⋊D3—21no—
701C2×C3⋊D3—21no—
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—44no—
705C2×C3⋊D3D3×D412yes—
706C2×C3⋊D3D3×D412yes—
707C2×C3⋊D3D3×D412yes—
708C2×C3×D3—32no—
709C2×C3×D3—32no—
710C2×C3×D3—32no—
711C2×C3×D3—32no—
712C2×C3×D3—32no—
713C2×C3×D3—32no—
714C2×C3×D3—62no—
715C2×C3×D3—62no—
716C2×C3×D3—62no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—62no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—61no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—121no—
749C2×C3×D3—121no—
750C2×C3×D3—121no—
751C2×C3×D3—121no—
752C2×C3×D3—121no—
753C2×C3×D3—121no—
754C2×C3×D3—121no—
755C2×C3×D3—121no—
756C2×C3×D3—121no—
757C2×C3×D3—121no—
758C2×C3×D3—121no—
759C2×C3×D3—121no—
760C2×C3×D3—121no—
761C2×C3×D3—121no—
762C2×C3×D3—124no—
763C2×C3×D3—124no—
764C2×C3×D3—128no—
765D32—124no—
766D32—124no—
767D32—124no—
768D32—124no—
769D32—124no—
770D32—124no—
771C32×C4—21no—
772C32×C4—21no—
773C32×C4—21no—
774C32×C4—21no—
775C32×C4—21no—
776C32×C4—21no—
777C32×C4—41no—
778C32×C4—41no—
779C32×C4—41no—
780C32×C4—41no—
781C32×C4—41no—
782C32×C4—41no—
783C32×C4—81no—
784C32×C4—81no—
785C3⋊Dic3—21no—
786C3⋊Dic3—21no—
787C3⋊Dic3—21no—
788C3⋊Dic3—21no—
789C3⋊Dic3—21no—
790C3⋊Dic3—21no—
791C3×Dic3—62no—
792C3×Dic3—61no—
793C3×Dic3—61no—
794C3×Dic3—61no—
795C3×Dic3—61no—
796C3×Dic3—61no—
797C3×Dic3—61no—
798C3×Dic3—61no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—61no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—121no—
805C3×Dic3—121no—
806C3×Dic3—121no—
807C3×Dic3—121no—
808C3×Dic3—121no—
809C22×D4—271no—
810C22×D4—271no—
811#123—91no—
812#123—271no—
813#123—271no—
814#123—271no—
815#121—91no—
816#121—271no—
817#121—271no—
818#121—271no—
819#120—91no—
820#120—271no—
821#120—271no—
822#120—271no—
823C2×C22⋊C4—271no—
824C33#53411yescharacteristic, complemented, Sylow
825C23×C3—21no—
826C23×C3—21no—
827C23×C3—21no—
828C23×C3—41no—
829C23×C3—91no—
830C23×C3—91no—
831C23×C3—91no—
832C23×C3—91no—
833C23×C3—91no—
834C23×C3—91no—
835C23×C3—182no—
836C23×C3—361no—
837C23×C3—361no—
838C23×C3C2×D3211yescharacteristic
839C23×C3C2×D3211yescharacteristic
840C23×C3C2×D3211yescharacteristic
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—31no—
847C22×D3—31no—
848C22×D3—31no—
849C22×D3—31no—
850C22×D3—31no—
851C22×D3—31no—
852C22×D3—31no—
853C22×D3—61no—
854C22×D3—61no—
855C22×D3—61no—
856C22×D3—61no—
857C22×D3—61no—
858C22×D3—61no—
859C22×D3—62no—
860C22×D3—62no—
861C22×D3—94no—
862C22×D3—94no—
863C22×D3—94no—
864C22×D3—122no—
865C22×D3—121no—
866C22×D3—121no—
867C22×D3—121no—
868C22×D3—121no—
869C22×D3—122no—
870C22×D3—122no—
871C22×D3—182no—
872C22×D3—182no—
873C22×D3—182no—
874C22×D3—361no—
875C22×D3—361no—
876C22×D3—361no—
877C22×D3—361no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—361no—
883C22×D3—361no—
884C22×D3—361no—
885C22×D3—361no—
886C3×D4—182no—
887C3×D4—182no—
888C3×D4—182no—
889C3×D4—182no—
890C3×D4—361no—
891C3×D4—361no—
892C3×D4—361no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—21no—
899C2×C3×C4—41no—
900C2×C3×C4—41no—
901C2×C3×C4—91no—
902C2×C3×C4—91no—
903C2×C3×C4—91no—
904C2×C3×C4—91no—
905C2×C3×C4—91no—
906C2×C3×C4—91no—
907C2×C3×C4—182no—
908C2×C3×C4—361no—
909C2×C3×C4C2×D3211yescharacteristic
910C2×C3×C4C2×D3211yescharacteristic
911C2×C3×C4C2×D3211yescharacteristic
912C2×C3×C4C2×D3211yescharacteristic
913C2×C3×C4C2×D3211yescharacteristic
914C2×C3×C4C2×D3211yescharacteristic
915#67—62no—
916#67—62no—
917#67—62no—
918#67—62no—
919#67—122no—
920#67—122no—
921#67—121no—
922#67—121no—
923#67—121no—
924#67—121no—
925#67—122no—
926#67—122no—
927#67—182no—
928#67—182no—
929#67—182no—
930#67—182no—
931#67—182no—
932#67—182no—
933#67—182no—
934#67—182no—
935#67—361no—
936#67—361no—
937C2×Dic3—31no—
938C2×Dic3—31no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—31no—
943C2×Dic3—31no—
944C2×Dic3—31no—
945C2×Dic3—31no—
946C2×Dic3—31no—
947C2×Dic3—31no—
948C2×Dic3—31no—
949C2×Dic3—61no—
950C2×Dic3—61no—
951C2×Dic3—61no—
952C2×Dic3—61no—
953C2×Dic3—61no—
954C2×Dic3—61no—
955C2×Dic3—182no—
956C2×Dic3—361no—
957D12—62no—
958D12—62no—
959D12—62no—
960D12—62no—
961D12—122no—
962D12—122no—
963D12—121no—
964D12—121no—
965D12—122no—
966D12—182no—
967D12—182no—
968D12—182no—
969D12—182no—
970D12—361no—
971C4×D3—62no—
972C4×D3—62no—
973C4×D3—122no—
974C4×D3—121no—
975C4×D3—121no—
976C4×D3—122no—
977C4×D3—182no—
978C4×D3—182no—
979C4×D3—361no—
980C4×D3—361no—
981C2×C32—21no—
982C2×C32—21no—
983C2×C32—21no—
984C2×C32—21no—
985C2×C32—21no—
986C2×C32—21no—
987C2×C32—21no—
988C2×C32—21no—
989C2×C32—21no—
990C2×C32—41no—
991C2×C32—41no—
992C2×C32—41no—
993C2×C32—41no—
994C2×C32—42no—
995C2×C32—41no—
996C2×C32—41no—
997C2×C32—81no—
998C2×C32—81no—
999C2×C32—82no—
1000C2×C32C2×D3×D411yescharacteristic
1001C2×C32C2×D3×D411yescharacteristic
1002C2×C32C2×D3×D411yescharacteristic
1003C2×C32#100411yescharacteristic
1004C2×C32#100411yescharacteristic
1005C2×C32#100411yescharacteristic
1006C2×C32#100911yescharacteristic
1007C2×C32#100911yescharacteristic
1008C2×C32#100911yescharacteristic
1009C3⋊D3—22no—
1010C3⋊D3—22no—
1011C3⋊D3—22no—
1012C3⋊D3—41no—
1013C3⋊D3—41no—
1014C3⋊D3—41no—
1015C3×D3—62no—
1016C3×D3—62no—
1017C3×D3—62no—
1018C3×D3—62no—
1019C3×D3—62no—
1020C3×D3—62no—
1021C3×D3—122no—
1022C3×D3—122no—
1023C3×D3—122no—
1024C3×D3—122no—
1025C3×D3—121no—
1026C3×D3—121no—
1027C3×D3—121no—
1028C3×D3—121no—
1029C3×D3—121no—
1030C3×D3—121no—
1031C3×D3—241no—
1032C3×D3—241no—
1033C24—91no—
1034C24—271no—
1035C24—271no—
1036C2×D4—91no—
1037C2×D4—91no—
1038C2×D4—91no—
1039C2×D4—91no—
1040C2×D4—91no—
1041C2×D4—91no—
1042C2×D4—91no—
1043C2×D4—271no—
1044C2×D4—271no—
1045C2×D4—271no—
1046C2×D4—271no—
1047C2×D4—271no—
1048C2×D4—544no—
1049C2×D4—544no—
1050C22×C4—91no—
1051C22×C4—91no—
1052C22×C4—271no—
1053C22×C4—271no—
1054C4⋊C4—91no—
1055C4⋊C4—91no—
1056C4⋊C4—91no—
1057C4⋊C4—271no—
1058C22⋊C4—91no—
1059C22⋊C4—91no—
1060C22⋊C4—91no—
1061C22⋊C4—91no—
1062C22⋊C4—91no—
1063C22⋊C4—271no—
1064C22⋊C4—271no—
1065C22⋊C4—271no—
1066C22⋊C4—271no—
1067C22⋊C4—271no—
1068C22⋊C4—271no—
1069C22⋊C4#111311yescharacteristic, complemented
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—21no—
1073C22×C3—21no—
1074C22×C3—21no—
1075C22×C3—21no—
1076C22×C3—21no—
1077C22×C3—21no—
1078C22×C3—21no—
1079C22×C3—21no—
1080C22×C3—21no—
1081C22×C3—21no—
1082C22×C3—21no—
1083C22×C3—41no—
1084C22×C3—41no—
1085C22×C3—41no—
1086C22×C3—41no—
1087C22×C3—41no—
1088C22×C3—41no—
1089C22×C3—41no—
1090C22×C3—41no—
1091C22×C3—42no—
1092C22×C3—41no—
1093C22×C3—81no—
1094C22×C3—81no—
1095C22×C3—92no—
1096C22×C3—92no—
1097C22×C3—92no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—181no—
1101C22×C3—181no—
1102C22×C3—181no—
1103C22×C3—181no—
1104C22×C3—181no—
1105C22×C3—181no—
1106C22×C3—181no—
1107C22×C3—181no—
1108C22×C3—181no—
1109C22×C3—181no—
1110C22×C3—181no—
1111C22×C3—181no—
1112C22×C3—181no—
1113C22×C3—364no—
1114C22×C3C22×D3211yescharacteristic
1115C22×C3C22×D3211yescharacteristic
1116C22×C3C22×D3211yescharacteristic
1117C2×D3—32no—
1118C2×D3—32no—
1119C2×D3—32no—
1120C2×D3—32no—
1121C2×D3—32no—
1122C2×D3—32no—
1123C2×D3—62no—
1124C2×D3—62no—
1125C2×D3—62no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—61no—
1129C2×D3—61no—
1130C2×D3—61no—
1131C2×D3—61no—
1132C2×D3—61no—
1133C2×D3—61no—
1134C2×D3—61no—
1135C2×D3—61no—
1136C2×D3—61no—
1137C2×D3—61no—
1138C2×D3—62no—
1139C2×D3—61no—
1140C2×D3—61no—
1141C2×D3—61no—
1142C2×D3—61no—
1143C2×D3—61no—
1144C2×D3—61no—
1145C2×D3—61no—
1146C2×D3—61no—
1147C2×D3—61no—
1148C2×D3—61no—
1149C2×D3—61no—
1150C2×D3—61no—
1151C2×D3—61no—
1152C2×D3—61no—
1153C2×D3—61no—
1154C2×D3—61no—
1155C2×D3—61no—
1156C2×D3—61no—
1157C2×D3—121no—
1158C2×D3—121no—
1159C2×D3—121no—
1160C2×D3—121no—
1161C2×D3—121no—
1162C2×D3—121no—
1163C2×D3—121no—
1164C2×D3—121no—
1165C2×D3—121no—
1166C2×D3—121no—
1167C2×D3—121no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—124no—
1172C2×D3—124no—
1173C2×D3—128no—
1174C2×D3—364no—
1175C2×D3—364no—
1176C2×D3—364no—
1177C2×D3—364no—
1178C2×D3—364no—
1179C2×D3—364no—
1180C3×C4—21no—
1181C3×C4—21no—
1182C3×C4—21no—
1183C3×C4—21no—
1184C3×C4—21no—
1185C3×C4—21no—
1186C3×C4—41no—
1187C3×C4—41no—
1188C3×C4—41no—
1189C3×C4—41no—
1190C3×C4—41no—
1191C3×C4—41no—
1192C3×C4—81no—
1193C3×C4—81no—
1194C3×C4—181no—
1195C3×C4—181no—
1196C3×C4—181no—
1197C3×C4—181no—
1198C3×C4—181no—
1199C3×C4—181no—
1200Dic3—62no—
1201Dic3—61no—
1202Dic3—61no—
1203Dic3—61no—
1204Dic3—61no—
1205Dic3—61no—
1206Dic3—61no—
1207Dic3—61no—
1208Dic3—61no—
1209Dic3—61no—
1210Dic3—61no—
1211Dic3—61no—
1212Dic3—61no—
1213Dic3—121no—
1214Dic3—121no—
1215Dic3—121no—
1216Dic3—121no—
1217Dic3—121no—
1218C32—21no—
1219C32—21no—
1220C32—21no—
1221C32—41no—
1222C32#558911yescharacteristic, complemented
1223C32#560511yescharacteristic, complemented
1224C32#565311yescharacteristic, complemented
1225C23—91no—
1226C23—91no—
1227C23—91no—
1228C23—91no—
1229C23—91no—
1230C23—91no—
1231C23—182no—
1232C23—274no—
1233C23—361no—
1234C23—361no—
1235C23—542no—
1236C23—1081no—
1237C23—1081no—
1238C23—1081no—
1239C23—1081no—
1240C23C2×#111311yescharacteristic
1241D4—182no—
1242D4—182no—
1243D4—182no—
1244D4—182no—
1245D4—361no—
1246D4—361no—
1247D4—361no—
1248D4—542no—
1249D4—542no—
1250D4—542no—
1251D4—542no—
1252D4—1081no—
1253C2×C4—91no—
1254C2×C4—91no—
1255C2×C4—91no—
1256C2×C4—91no—
1257C2×C4—91no—
1258C2×C4—91no—
1259C2×C4—182no—
1260C2×C4—361no—
1261C2×C4—542no—
1262C2×C4—1081no—
1263C2×C4C2×#111311yescharacteristic
1264C2×C4C2×#111311yescharacteristic
1265C2×C3—21no—
1266C2×C3—21no—
1267C2×C3—21no—
1268C2×C3—21no—
1269C2×C3—21no—
1270C2×C3—21no—
1271C2×C3—21no—
1272C2×C3—21no—
1273C2×C3—21no—
1274C2×C3—42no—
1275C2×C3—41no—
1276C2×C3—41no—
1277C2×C3—41no—
1278C2×C3—41no—
1279C2×C3—41no—
1280C2×C3—41no—
1281C2×C3—81no—
1282C2×C3—81no—
1283C2×C3—82no—
1284C2×C3—182no—
1285C2×C3—182no—
1286C2×C3—182no—
1287C2×C3—361no—
1288C2×C3—361no—
1289C2×C3—361no—
1290C2×C3#6430711yescharacteristic
1291C2×C3#6430711yescharacteristic
1292C2×C3#6430811yescharacteristic
1293C2×C3D32×D411yescharacteristic
1294C2×C3D32×D411yescharacteristic
1295C2×C3D32×D411yescharacteristic
1296C2×C3#6431311yescharacteristic
1297C2×C3#6431411yescharacteristic
1298C2×C3#6431411yescharacteristic
1299D3—62no—
1300D3—62no—
1301D3—62no—
1302D3—62no—
1303D3—62no—
1304D3—62no—
1305D3—122no—
1306D3—122no—
1307D3—122no—
1308D3—122no—
1309D3—121no—
1310D3—121no—
1311D3—121no—
1312D3—121no—
1313D3—121no—
1314D3—121no—
1315D3—241no—
1316D3—241no—
1317C22—21no—
1318C22—21no—
1319C22—21no—
1320C22—92no—
1321C22—92no—
1322C22—92no—
1323C22—181no—
1324C22—181no—
1325C22—181no—
1326C22—181no—
1327C22—181no—
1328C22—181no—
1329C22—181no—
1330C22—181no—
1331C22—181no—
1332C22—181no—
1333C22—181no—
1334C22—181no—
1335C22—181no—
1336C22—181no—
1337C22—181no—
1338C22—364no—
1339C22—1084no—
1340C22—1084no—
1341C22C22×#111311yescharacteristic
1342C4—21no—
1343C4—21no—
1344C4—181no—
1345C4—181no—
1346C4—181no—
1347C4—181no—
1348C4—181no—
1349C4—181no—
1350C3—21no—
1351C3—21no—
1352C3—21no—
1353C3—41no—
1354C3#1059426211yescharacteristic, complemented
1355C3#1059426311yescharacteristic, complemented
1356C3#1059426411yescharacteristic, complemented
1357C2—41no—
1358C2—182no—
1359C2—182no—
1360C2—182no—
1361C2—361no—
1362C2—361no—
1363C2—361no—
1364C2#1172461911yescharacteristic
1365C2D4×#111311yescharacteristic
1366C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×C4⋊#1113C2semidirect
3. C3×#64093C2semidirect
4. C3×#64092C2semidirect
5. C3×#64091C2semidirect
6. #11723729C2semidirect
7. #11723727C2semidirect
8. #11723725C2semidirect
9. #11723701C2semidirect
10. #11723700C2semidirect
11. #11723696C2semidirect
12. #11723694C2semidirect
13. #11723690C2semidirect
14. #11723687C2semidirect
15. #11723686C2semidirect
19. C23×C3×C3⋊D3C22semidirect
21. C22×#1113C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C3×#638C22semidirect
27. C2×C3×C4⋊(C3⋊D3)C22semidirect
28. C2×C3×C4⋊(C3⋊D3)C22semidirect
29. C2×C3×C4×C3⋊D3C22semidirect
30. C2×C3×C4×C3⋊D3C22semidirect
34. C2×#6295C22semidirect
35. C2×#6295C22semidirect
36. C2×#6295C22semidirect
37. C2×#6294C22semidirect
38. C2×#6294C22semidirect
40. C33×C22⋊C4C22semidirect
41. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C3×#3752C22semidirect
45. C3×#3752C22semidirect
46. C3×C4⋊(C3⋊Dic3)C22semidirect
47. C3×#3750C22semidirect
48. C3×#3750C22semidirect
49. #88815C22semidirect
50. #88814C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88814C22semidirect
62. #64093D3semidirect
63. #64092D3semidirect
64. #64091D3semidirect
119. C2×#1113D4semidirect
147. C23×C3⋊D3C2×D3semidirect
158. C2×#638C2×D3semidirect
159. C2×#638C2×D3semidirect
160. C2×#638C2×D3semidirect
162. C2×C4⋊(C3⋊D3)C2×D3semidirect
163. C2×C4⋊(C3⋊D3)C2×D3semidirect
164. C2×C4×C3⋊D3C2×D3semidirect
165. C2×C4×C3⋊D3C2×D3semidirect
224. C32×C22⋊C4C2×D3semidirect
225. C32×C22⋊C4C2×D3semidirect
226. C32×C22⋊C4C2×D3semidirect
227. #3757C2×D3semidirect
228. #3752C2×D3semidirect
229. #3752C2×D3semidirect
230. #3752C2×D3semidirect
231. #3752C2×D3semidirect
232. C4⋊(C3⋊Dic3)C2×D3semidirect
233. #3750C2×D3semidirect
234. #3750C2×D3semidirect
613. C3×C22⋊C4D32semidirect
614. C3×C22⋊C4D32semidirect
615. C3×C22⋊C4D32semidirect
824. C33#534semidirect
1069. C22⋊C4#1113semidirect
1222. C32#5589semidirect
1223. C32#5605semidirect
1224. C32#5653semidirect
1354. C3#10594262semidirect
1355. C3#10594263semidirect
1356. C3#10594264semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#890492
C2×C4⋊#11132
C3×#640932
C3×#640922
C3×#640912
#117237292
#117237272
#117237252
#117237012
#117237002
#117236962
#117236942
#117236902
#117236872
#117236862
#105942643
#105942633
#105942623