Finite Group Databasebeta

← #13178236

Subgroups — #13178236

Order 1728.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89042C211yesmaximal, characteristic, complemented
3C3×#64093C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6#11723727C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723718C211yesmaximal, characteristic, complemented
9#11723701C211yesmaximal, characteristic, complemented
10#11723700C211yesmaximal, characteristic, complemented
11#11723696C211yesmaximal, characteristic, complemented
12#11723694C211yesmaximal, characteristic, complemented
13#11723692C211yesmaximal, characteristic, complemented
14#11723684C211yesmaximal, characteristic, complemented
15#11723684C211yesmaximal, characteristic, complemented
16#10594279—31nomaximal
17#10594278—31nomaximal
18#10594272—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29#89049—24no—
30C2×#6296C2211yescharacteristic, complemented
31C2×#6295C2211yescharacteristic
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic
34C2×#6295C2211yescharacteristic, complemented
35C2×#6295C2211yescharacteristic, complemented
36C2×#6294C2211yescharacteristic
37C2×#6294C2211yescharacteristic, complemented
38#89042—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic
43C3×#3752C2211yescharacteristic
44C3×#3752C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47C3×#3750C2211yescharacteristic, complemented
48C3×#3750C2211yescharacteristic, complemented
49#88815C2211yescharacteristic, complemented
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic, complemented
52#88814C2211yescharacteristic, complemented
53#88814C2211yescharacteristic, complemented
54#88814C2211yescharacteristic, complemented
55#88813C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3798—31no—
60C2×#3798—31no—
61C2×#3798—31no—
62#64093D311yescharacteristic, complemented
63#64092D311yescharacteristic, complemented
64C22⋊C4×C3⋊D3D311yescharacteristic, complemented
65C3×#884—31no—
66C3×#884—31no—
67C3×#884—61no—
68C3×#883—31no—
69C3×#883—31no—
70C3×#883—61no—
71C3×D3×C22⋊C4—31no—
72C3×D3×C22⋊C4—31no—
73C3×D3×C22⋊C4—61no—
74#63981—31no—
75#63977—31no—
76#63976—31no—
77#63971—31no—
78#63970—31no—
79#63959—31no—
80#63959—31no—
81#63958—31no—
82#63953—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#63909—31no—
91#63908—31no—
92#63905—31no—
93#63904—31no—
94#63904—31no—
95#63899—31no—
96#63895—31no—
97#63893—31no—
98#63881—31no—
99#63881—31no—
100#63879—31no—
101#63879—31no—
102#63853—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
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
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C2×C33×C4C2311yescharacteristic
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C3×C4⋊(C3⋊D3)—41no—
129C3×C4×C3⋊D3—22no—
130C3×C4×C3⋊D3—22no—
131C3×C4×C3⋊D3—22no—
132C3×C4×C3⋊D3—41no—
133#6296—22no—
134#6295—22no—
135#6295—22no—
136#6295—22no—
137#6295—22no—
138#6295D414yescomplemented
139#6294—22no—
140#6294—41no—
141#5654—91no—
142#5612—91no—
143#5490—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×#638C2×D311yescharacteristic
152C2×#638C2×D311yescharacteristic
153C2×#638C2×D311yescharacteristic, complemented
154C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
155C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
158C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×#67—61no—
168C2×C3×D12—31no—
169C2×C3×D12—31no—
170C2×C3×D12—61no—
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—61no—
180C2×C3×C4×D3—61no—
181C2×C3×C4×D3—61no—
182C2×C3×C4×D3—61no—
183#3811—64no—
184D3×#67—64no—
185D3×#67—64no—
186C2×#627—31no—
187C2×#627—31no—
188C2×#627—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—31no—
193C2×#626—31no—
194C2×#626—31no—
195C2×#626—31no—
196C2×#626—31no—
197C2×#626—31no—
198C2×#626—31no—
199C2×#625—31no—
200C2×#625—31no—
201C2×#625—31no—
202C2×#625—31no—
203C2×#625—31no—
204C2×#624—31no—
205C2×#624—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210#3798—64no—
211#3798—64no—
212#3798—64no—
213C32×C22⋊C4—21no—
214C32×C22⋊C4—21no—
215C32×C22⋊C4—21no—
216C32×C22⋊C4—41no—
217C32×C22⋊C4C2×D311yescharacteristic, complemented
218C32×C22⋊C4C2×D311yescharacteristic, complemented
219C32×C22⋊C4C2×D311yescharacteristic, complemented
220#3757C2×D311yescharacteristic, complemented
221#3757C2×D311yescharacteristic, complemented
222#3752C2×D311yescharacteristic
223#3752C2×D311yescharacteristic
224#3752C2×D311yescharacteristic, complemented
225#3752C2×D311yescharacteristic, complemented
226C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
227#3750C2×D311yescharacteristic, complemented
228#3750C2×D311yescharacteristic, complemented
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—61no—
234C3×#217—61no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
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—61no—
244C3×(C2×D3)⋊C4—61no—
245C3×(C2×D3)⋊C4—61no—
246C3×(C2×D3)⋊C4—61no—
247C3×C4⋊Dic3—31no—
248C3×C4⋊Dic3—31no—
249C3×C4⋊Dic3—61no—
250C3×Dic3⋊C4—31no—
251C3×Dic3⋊C4—31no—
252C3×Dic3⋊C4—31no—
253C3×Dic3⋊C4—31no—
254C3×Dic3⋊C4—61no—
255C3×Dic3⋊C4—61no—
256#3724—31no—
257Dic3⋊Dic3—31no—
258Dic3⋊Dic3—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—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—
274Dic32—31no—
275Dic32—31no—
276Dic32—31no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2411yescharacteristic
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
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—44no—
294C2×C3×C3⋊D3C2×D412yes—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C3×C3⋊D3#4112yescomplemented
297#1113—44no—
298C33×C4—21no—
299C33×C4—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3C2×D412yes—
307C22×#67—91no—
308C2×D3×D4—91no—
309C2×D3×D4—91no—
310C2×#235—91no—
311C2×#235—91no—
312C2×#235—91no—
313C3×#123—91no—
314C3×#121—91no—
315C2×C3×C22⋊C4—91no—
316#953—91no—
317#939—91no—
318#938—91no—
319#938—91no—
320#937—91no—
321#937—91no—
322#936—91no—
323#930—91no—
324#929—91no—
325C4×#67—91no—
326C4×#67—91no—
327C2×(C2×D3)⋊C4—91no—
328#897—91no—
329#896—91no—
330#895—91no—
331#894—91no—
332#893—91no—
333#893—91no—
334#885—91no—
335#885—91no—
336#884—31no—
337#884—31no—
338#884—61no—
339#884—91no—
340#883—31no—
341#883—31no—
342#883—61no—
343#883—91no—
344#882—91no—
345#882—91no—
346#882—91no—
347#67⋊C4—91no—
348#67⋊C4—91no—
349D3×C22⋊C4—31no—
350D3×C22⋊C4—31no—
351D3×C22⋊C4—61no—
352D3×C22⋊C4—91no—
353D3×C22⋊C4—91no—
354#878—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—41no—
359C23×C32C22×D311yescharacteristic
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C22×C3⋊D3—22no—
363C22×C3⋊D3—22no—
364C22×C3⋊D3—41no—
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
388C22×C3×D3—62no—
389C22×C3×D3—64no—
390C22×C3×D3—122no—
391C22×C3×D3—121no—
392C22×C3×D3—121no—
393C22×C3×D3—122no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—121no—
401C2×D32—121no—
402C2×D32—121no—
403C2×C32×C4—21no—
404C2×C32×C4—21no—
405C2×C32×C4—21no—
406C2×C32×C4—21no—
407C2×C32×C4—21no—
408C2×C32×C4—21no—
409C2×C32×C4—41no—
410C2×C32×C4—41no—
411C2×C32×C4C22×D311yescharacteristic
412C2×C32×C4C22×D311yescharacteristic
413C2×C32×C4C22×D311yescharacteristic
414C2×C32×C4C22×D311yescharacteristic
415C2×C32×C4C22×D311yescharacteristic
416C2×C32×C4C22×D311yescharacteristic
417#638—22no—
418#638—22no—
419#638—41no—
420C2×C3⋊Dic3C22×D311yescharacteristic
421C2×C3⋊Dic3C22×D311yescharacteristic
422C2×C3⋊Dic3C22×D311yescharacteristic
423C2×C3⋊Dic3C22×D311yescharacteristic
424C2×C3⋊Dic3C22×D311yescharacteristic
425C2×C3⋊Dic3C22×D311yescharacteristic
426C2×C3⋊Dic3C22×D311yescharacteristic
427C4⋊(C3⋊D3)—41no—
428C4×C3⋊D3—22no—
429C4×C3⋊D3—22no—
430C4×C3⋊D3—22no—
431C4×C3⋊D3—41no—
432C3×#67—62no—
433C3×#67—62no—
434C3×#67—62no—
435C3×#67—62no—
436C3×#67—122no—
437C3×#67—122no—
438C3×#67—121no—
439C3×#67—121no—
440C3×#67—122no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—31no—
449C2×C3×Dic3—31no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—31no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—61no—
456C2×C3×Dic3—61no—
457C2×C3×Dic3—61no—
458C2×C3×Dic3—61no—
459C2×C3×Dic3—61no—
460C2×C3×Dic3—61no—
461C2×C3×Dic3—61no—
462C3×D12—121no—
463C3×D12—121no—
464C3×D12—122no—
465C3×C4×D3—62no—
466C3×C4×D3—62no—
467C3×C4×D3—62no—
468C3×C4×D3—62no—
469C3×C4×D3—62no—
470C3×C4×D3—62no—
471C3×C4×D3—122no—
472C3×C4×D3—122no—
473C3×C4×D3—122no—
474C3×C4×D3—121no—
475C3×C4×D3—121no—
476C3×C4×D3—122no—
477#627—62no—
478#627—62no—
479#627—62no—
480#626—34no—
481#626—34no—
482#626—62no—
483#626—62no—
484#626—62no—
485#626—62no—
486#626—62no—
487#626—62no—
488#626—62no—
489#626—62no—
490#625—34no—
491#625—62no—
492#625—62no—
493#625—62no—
494#625—62no—
495#624—62no—
496#624—121no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—121no—
500D3×Dic3—121no—
501#546—271noSylow
502C2×C33—41no—
503C2×C33C22×D411yescharacteristic
504C2×C33C2×#4111yescharacteristic
505C2×C33H(5,𝔽2)11yescharacteristic
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—22no—
509C3×C3⋊D3—41no—
510C3×C3⋊D3—41no—
511C24×C3—91no—
512C23×D3—31no—
513C23×D3—31no—
514C23×D3—61no—
515C23×D3—91no—
516C23×D3—91no—
517C23×D3—91no—
518C2×C3×D4—91no—
519C2×C3×D4—91no—
520C2×C3×D4—91no—
521C2×C3×D4—91no—
522C22×C3×C4—91no—
523C22×C3×C4—91no—
524C22×C3×C4—91no—
525C22×C3×C4—91no—
526C2×#67—31no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—31no—
531C2×#67—31no—
532C2×#67—61no—
533C2×#67—61no—
534C2×#67—61no—
535C2×#67—91no—
536C2×#67—91no—
537C2×#67—91no—
538C2×#67—91no—
539C2×#67—91no—
540C2×#67—91no—
541C2×#67—91no—
542C2×#67—91no—
543C2×#67—91no—
544C2×#67—91no—
545C2×#67—184no—
546C22×Dic3—91no—
547C22×Dic3—91no—
548D3×D4—184no—
549D3×D4—184no—
550#235—184no—
551#235—184no—
552#235—184no—
553C2×D12—31no—
554C2×D12—31no—
555C2×D12—61no—
556C2×D12—91no—
557C2×D12—91no—
558C2×D12—91no—
559C2×D12—91no—
560C2×D12—91no—
561C2×C4×D3—31no—
562C2×C4×D3—31no—
563C2×C4×D3—31no—
564C2×C4×D3—31no—
565C2×C4×D3—31no—
566C2×C4×D3—31no—
567C2×C4×D3—31no—
568C2×C4×D3—31no—
569C2×C4×D3—61no—
570C2×C4×D3—61no—
571C2×C4×D3—61no—
572C2×C4×D3—61no—
573C2×C4×D3—91no—
574C2×C4×D3—91no—
575C2×C4×D3—91no—
576C2×C4×D3—91no—
577C2×Dic6—91no—
578C2×Dic6—91no—
579C2×Dic6—91no—
580C3×C4⋊C4—91no—
581C3×C4⋊C4—91no—
582C3×C4⋊C4—91no—
583C3×C22⋊C4—21no—
584C3×C22⋊C4—21no—
585C3×C22⋊C4—21no—
586C3×C22⋊C4—41no—
587C3×C22⋊C4—91no—
588C3×C22⋊C4—91no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593C3×C22⋊C4D3211yescharacteristic, complemented
594C3×C22⋊C4D3211yescharacteristic, complemented
595C3×C22⋊C4D3211yescharacteristic, complemented
596#217—31no—
597#217—31no—
598#217—31no—
599#217—31no—
600#217—61no—
601#217—61no—
602#217—91no—
603#217—91no—
604#217—91no—
605#217—91no—
606#217—91no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—61no—
616(C2×D3)⋊C4—61no—
617(C2×D3)⋊C4—61no—
618(C2×D3)⋊C4—61no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629C4⋊Dic3—31no—
630C4⋊Dic3—31no—
631C4⋊Dic3—61no—
632C4⋊Dic3—91no—
633Dic3⋊C4—31no—
634Dic3⋊C4—31no—
635Dic3⋊C4—31no—
636Dic3⋊C4—31no—
637Dic3⋊C4—61no—
638Dic3⋊C4—61no—
639Dic3⋊C4—91no—
640Dic3⋊C4—91no—
641C4×Dic3—91no—
642C4×Dic3—91no—
643C4×Dic3—91no—
644C22×C32—21no—
645C22×C32—22no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—41no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—42no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—41no—
667C22×C32—81no—
668C22×C32—81no—
669C22×C32C23×D311yescharacteristic
670C22×C32C23×D311yescharacteristic
671C22×C32C23×D311yescharacteristic
672C2×C3⋊D3—21no—
673C2×C3⋊D3—21no—
674C2×C3⋊D3—21no—
675C2×C3⋊D3—21no—
676C2×C3⋊D3—21no—
677C2×C3⋊D3—21no—
678C2×C3⋊D3—21no—
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—44no—
685C2×C3⋊D3#23512yescomplemented
686C2×C3⋊D3D3×D412yes—
687C2×C3⋊D3D3×D412yes—
688C2×C3×D3—32no—
689C2×C3×D3—32no—
690C2×C3×D3—32no—
691C2×C3×D3—32no—
692C2×C3×D3—32no—
693C2×C3×D3—32no—
694C2×C3×D3—62no—
695C2×C3×D3—62no—
696C2×C3×D3—62no—
697C2×C3×D3—62no—
698C2×C3×D3—62no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—62no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
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—121no—
725C2×C3×D3—121no—
726C2×C3×D3—121no—
727C2×C3×D3—121no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—121no—
733C2×C3×D3—124no—
734C2×C3×D3—124no—
735C2×C3×D3—128no—
736D32—124no—
737D32—124no—
738D32—124no—
739C32×C4—21no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—21no—
745C32×C4—41no—
746C32×C4—41no—
747C32×C4—41no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—41no—
751C32×C4—81no—
752C32×C4—81no—
753C3⋊Dic3—21no—
754C3⋊Dic3—21no—
755C3⋊Dic3—21no—
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3D3×D412yes—
760C3×Dic3—32no—
761C3×Dic3—32no—
762C3×Dic3—62no—
763C3×Dic3—61no—
764C3×Dic3—61no—
765C3×Dic3—61no—
766C3×Dic3—61no—
767C3×Dic3—61no—
768C3×Dic3—61no—
769C3×Dic3—61no—
770C3×Dic3—61no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—61no—
774C3×Dic3—61no—
775C3×Dic3—121no—
776C3×Dic3—121no—
777C3×Dic3—121no—
778C3×Dic3—121no—
779C3×Dic3—121no—
780C3×Dic3—121no—
781C2×#41—271no—
782C22×D4—271no—
783#124—271no—
784#123—91no—
785#123—271no—
786C22⋊Q8—271no—
787#121—91no—
788#121—271no—
789#121—271no—
790#120—271no—
791#120—271no—
792C4×D4—271no—
793C4×D4—271no—
794C2×C22⋊C4—91no—
795C2×C22⋊C4—271no—
796C33#54611yescharacteristic, complemented, Sylow
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—21no—
800C23×C3—41no—
801C23×C3—91no—
802C23×C3—91no—
803C23×C3—91no—
804C23×C3—91no—
805C23×C3—91no—
806C23×C3—182no—
807C23×C3—182no—
808C23×C3—361no—
809C23×C3C2×D3211yescharacteristic
810C23×C3C2×D3211yescharacteristic
811C23×C3C2×D3211yescharacteristic
812C22×D3—31no—
813C22×D3—31no—
814C22×D3—31no—
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—61no—
827C22×D3—62no—
828C22×D3—62no—
829C22×D3—62no—
830C22×D3—62no—
831C22×D3—64no—
832C22×D3—122no—
833C22×D3—121no—
834C22×D3—121no—
835C22×D3—122no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—361no—
843C22×D3—361no—
844C22×D3—361no—
845C3×D4—182no—
846C3×D4—182no—
847C3×D4—361no—
848C3×D4—361no—
849C2×C3×C4—21no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—41no—
856C2×C3×C4—41no—
857C2×C3×C4—91no—
858C2×C3×C4—91no—
859C2×C3×C4—91no—
860C2×C3×C4—91no—
861C2×C3×C4—91no—
862C2×C3×C4—91no—
863C2×C3×C4—91no—
864C2×C3×C4—182no—
865C2×C3×C4—182no—
866C2×C3×C4—182no—
867C2×C3×C4—361no—
868C2×C3×C4C2×D3211yescharacteristic
869C2×C3×C4C2×D3211yescharacteristic
870C2×C3×C4C2×D3211yescharacteristic
871C2×C3×C4C2×D3211yescharacteristic
872C2×C3×C4C2×D3211yescharacteristic
873C2×C3×C4C2×D3211yescharacteristic
874#67—62no—
875#67—62no—
876#67—62no—
877#67—62no—
878#67—94no—
879#67—94no—
880#67—122no—
881#67—122no—
882#67—121no—
883#67—121no—
884#67—122no—
885#67—182no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—182no—
893C2×Dic3—31no—
894C2×Dic3—31no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—31no—
903C2×Dic3—31no—
904C2×Dic3—31no—
905C2×Dic3—31no—
906C2×Dic3—31no—
907C2×Dic3—61no—
908C2×Dic3—61no—
909C2×Dic3—61no—
910C2×Dic3—61no—
911C2×Dic3—61no—
912C2×Dic3—61no—
913C2×Dic3—61no—
914C2×Dic3—182no—
915C2×Dic3—361no—
916D12—94no—
917D12—121no—
918D12—121no—
919D12—122no—
920D12—182no—
921D12—182no—
922D12—182no—
923D12—182no—
924C4×D3—62no—
925C4×D3—62no—
926C4×D3—62no—
927C4×D3—62no—
928C4×D3—62no—
929C4×D3—62no—
930C4×D3—122no—
931C4×D3—122no—
932C4×D3—122no—
933C4×D3—121no—
934C4×D3—121no—
935C4×D3—122no—
936C4×D3—182no—
937C4×D3—182no—
938C4×D3—361no—
939C4×D3—361no—
940Dic6—182no—
941Dic6—182no—
942Dic6—182no—
943C2×C32—21no—
944C2×C32—21no—
945C2×C32—21no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—21no—
951C2×C32—21no—
952C2×C32—41no—
953C2×C32—41no—
954C2×C32—41no—
955C2×C32—41no—
956C2×C32—42no—
957C2×C32—41no—
958C2×C32—41no—
959C2×C32—81no—
960C2×C32—81no—
961C2×C32—82no—
962C2×C32C2×#23511yescharacteristic
963C2×C32C2×D3×D411yescharacteristic
964C2×C32C2×D3×D411yescharacteristic
965C2×C32C2×D3×D411yescharacteristic
966C2×C32#100411yescharacteristic
967C2×C32#100411yescharacteristic
968C2×C32D3×#4111yescharacteristic
969C2×C32D3×#4111yescharacteristic
970C2×C32#100911yescharacteristic
971C3⋊D3—22no—
972C3⋊D3—22no—
973C3⋊D3—22no—
974C3⋊D3—41no—
975C3⋊D3—41no—
976C3×D3—64no—
977C3×D3—62no—
978C3×D3—62no—
979C3×D3—62no—
980C3×D3—62no—
981C3×D3—62no—
982C3×D3—62no—
983C3×D3—122no—
984C3×D3—122no—
985C3×D3—122no—
986C3×D3—121no—
987C3×D3—121no—
988C3×D3—121no—
989C3×D3—121no—
990C3×D3—241no—
991C24—91no—
992C24—271no—
993#41—544no—
994C2×Q8—271no—
995C2×D4—91no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—91no—
999C2×D4—271no—
1000C2×D4—271no—
1001C2×D4—271no—
1002C2×D4—271no—
1003C2×D4—271no—
1004C2×D4—544no—
1005C22×C4—91no—
1006C22×C4—91no—
1007C22×C4—91no—
1008C22×C4—91no—
1009C22×C4—271no—
1010C22×C4—271no—
1011C4⋊C4—91no—
1012C4⋊C4—91no—
1013C4⋊C4—91no—
1014C4⋊C4—271no—
1015C22⋊C4—91no—
1016C22⋊C4—91no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—91no—
1020C22⋊C4—91no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4—271no—
1025C22⋊C4—271no—
1026C22⋊C4#111311yescharacteristic, complemented
1027C42—271no—
1028C22×C3—22no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—21no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—21no—
1038C22×C3—21no—
1039C22×C3—21no—
1040C22×C3—21no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—42no—
1050C22×C3—41no—
1051C22×C3—81no—
1052C22×C3—81no—
1053C22×C3—92no—
1054C22×C3—92no—
1055C22×C3—92no—
1056C22×C3—181no—
1057C22×C3—181no—
1058C22×C3—181no—
1059C22×C3—181no—
1060C22×C3—181no—
1061C22×C3—181no—
1062C22×C3—181no—
1063C22×C3—181no—
1064C22×C3—181no—
1065C22×C3—181no—
1066C22×C3—181no—
1067C22×C3—181no—
1068C22×C3—364no—
1069C22×C3C22×D3211yescharacteristic
1070C22×C3C22×D3211yescharacteristic
1071C22×C3C22×D3211yescharacteristic
1072C2×D3—32no—
1073C2×D3—32no—
1074C2×D3—32no—
1075C2×D3—32no—
1076C2×D3—32no—
1077C2×D3—32no—
1078C2×D3—62no—
1079C2×D3—62no—
1080C2×D3—62no—
1081C2×D3—62no—
1082C2×D3—62no—
1083C2×D3—61no—
1084C2×D3—61no—
1085C2×D3—61no—
1086C2×D3—61no—
1087C2×D3—61no—
1088C2×D3—61no—
1089C2×D3—61no—
1090C2×D3—61no—
1091C2×D3—61no—
1092C2×D3—61no—
1093C2×D3—61no—
1094C2×D3—61no—
1095C2×D3—62no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—124no—
1118C2×D3—124no—
1119C2×D3—128no—
1120C2×D3—364no—
1121C2×D3—364no—
1122C2×D3—364no—
1123C3×C4—21no—
1124C3×C4—21no—
1125C3×C4—21no—
1126C3×C4—21no—
1127C3×C4—21no—
1128C3×C4—21no—
1129C3×C4—41no—
1130C3×C4—41no—
1131C3×C4—41no—
1132C3×C4—41no—
1133C3×C4—41no—
1134C3×C4—41no—
1135C3×C4—81no—
1136C3×C4—81no—
1137C3×C4—92no—
1138C3×C4—181no—
1139C3×C4—181no—
1140C3×C4—181no—
1141C3×C4—181no—
1142C3×C4—181no—
1143C3×C4—181no—
1144Dic3—32no—
1145Dic3—32no—
1146Dic3—62no—
1147Dic3—61no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—61no—
1151Dic3—61no—
1152Dic3—61no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—61no—
1157Dic3—61no—
1158Dic3—61no—
1159Dic3—121no—
1160Dic3—121no—
1161Dic3—121no—
1162Dic3—121no—
1163Dic3—121no—
1164Dic3—121no—
1165C32—21no—
1166C32—21no—
1167C32—21no—
1168C32—41no—
1169C32#549011yescharacteristic, complemented
1170C32#561211yescharacteristic, complemented
1171C32#565411yescharacteristic, complemented
1172C23—91no—
1173C23—91no—
1174C23—91no—
1175C23—91no—
1176C23—91no—
1177C23—182no—
1178C23—182no—
1179C23—361no—
1180C23—542no—
1181C23—542no—
1182C23—1081no—
1183C23C2×#111311yescharacteristic
1184Q8—542no—
1185D4—182no—
1186D4—182no—
1187D4—274no—
1188D4—361no—
1189D4—361no—
1190D4—542no—
1191D4—542no—
1192D4—542no—
1193D4—542no—
1194C2×C4—91no—
1195C2×C4—91no—
1196C2×C4—91no—
1197C2×C4—91no—
1198C2×C4—91no—
1199C2×C4—91no—
1200C2×C4—91no—
1201C2×C4—182no—
1202C2×C4—182no—
1203C2×C4—182no—
1204C2×C4—361no—
1205C2×C4—542no—
1206C2×C4—1081no—
1207C2×C4C2×#111311yescharacteristic
1208C2×C4C2×#111311yescharacteristic
1209C2×C3—21no—
1210C2×C3—21no—
1211C2×C3—21no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—21no—
1217C2×C3—21no—
1218C2×C3—42no—
1219C2×C3—41no—
1220C2×C3—41no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—41no—
1224C2×C3—41no—
1225C2×C3—81no—
1226C2×C3—81no—
1227C2×C3—82no—
1228C2×C3—182no—
1229C2×C3—182no—
1230C2×C3—182no—
1231C2×C3—361no—
1232C2×C3—361no—
1233C2×C3D3×#23511yescharacteristic
1234C2×C3D3×#23511yescharacteristic
1235C2×C3#6430611yescharacteristic
1236C2×C3D32×D411yescharacteristic
1237C2×C3D32×D411yescharacteristic
1238C2×C3D32×D411yescharacteristic
1239C2×C3#6431311yescharacteristic
1240C2×C3#6431411yescharacteristic
1241C2×C3#6431411yescharacteristic
1242D3—64no—
1243D3—62no—
1244D3—62no—
1245D3—62no—
1246D3—62no—
1247D3—62no—
1248D3—62no—
1249D3—122no—
1250D3—122no—
1251D3—122no—
1252D3—121no—
1253D3—121no—
1254D3—121no—
1255D3—121no—
1256D3—241no—
1257C22—21no—
1258C22—21no—
1259C22—21no—
1260C22—92no—
1261C22—92no—
1262C22—92no—
1263C22—181no—
1264C22—181no—
1265C22—181no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—181no—
1275C22—364no—
1276C22—1084no—
1277C22C22×#111311yescharacteristic
1278C4—21no—
1279C4—21no—
1280C4—92no—
1281C4—181no—
1282C4—181no—
1283C4—181no—
1284C4—181no—
1285C4—181no—
1286C4—181no—
1287C3—21no—
1288C3—21no—
1289C3—21no—
1290C3—41no—
1291C3#1059427211yescharacteristic, complemented
1292C3#1059427811yescharacteristic, complemented
1293C3#1059427911yescharacteristic, complemented
1294C2—41no—
1295C2—182no—
1296C2—182no—
1297C2—182no—
1298C2—361no—
1299C2—361no—
1300C2#1172461811yescharacteristic
1301C2D4×#111311yescharacteristic
1302C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#546
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×#89042C2semidirect
3. C3×#64093C2semidirect
4. C3×#64092C2semidirect
5. C3×C22⋊C4×C3⋊D3C2semidirect
6. #11723727C2semidirect
7. #11723725C2semidirect
8. #11723718C2semidirect
9. #11723701C2semidirect
10. #11723700C2semidirect
11. #11723696C2semidirect
12. #11723694C2semidirect
13. #11723692C2semidirect
14. #11723684C2semidirect
15. #11723684C2semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
30. C2×#6296C22semidirect
34. C2×#6295C22semidirect
35. C2×#6295C22semidirect
37. C2×#6294C22semidirect
39. C33×C22⋊C4C22semidirect
40. C3×#3757C22semidirect
41. C3×#3757C22semidirect
44. C3×#3752C22semidirect
45. C3×#3752C22semidirect
46. C3×C4⋊(C3⋊Dic3)C22semidirect
47. C3×#3750C22semidirect
48. C3×#3750C22semidirect
49. #88815C22semidirect
51. #88814C22semidirect
52. #88814C22semidirect
53. #88814C22semidirect
54. #88814C22semidirect
55. #88813C22semidirect
62. #64093D3semidirect
63. #64092D3semidirect
64. C22⋊C4×C3⋊D3D3semidirect
138. #6295D4semidirect
153. C2×#638C2×D3semidirect
154. C2×C4⋊(C3⋊D3)C2×D3semidirect
155. C2×C4×C3⋊D3C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
157. C2×C4×C3⋊D3C2×D3semidirect
158. C2×C4×C3⋊D3C2×D3semidirect
217. C32×C22⋊C4C2×D3semidirect
218. C32×C22⋊C4C2×D3semidirect
219. C32×C22⋊C4C2×D3semidirect
220. #3757C2×D3semidirect
221. #3757C2×D3semidirect
224. #3752C2×D3semidirect
225. #3752C2×D3semidirect
226. C4⋊(C3⋊Dic3)C2×D3semidirect
227. #3750C2×D3semidirect
228. #3750C2×D3semidirect
296. C2×C3×C3⋊D3#41semidirect
593. C3×C22⋊C4D32semidirect
594. C3×C22⋊C4D32semidirect
595. C3×C22⋊C4D32semidirect
685. C2×C3⋊D3#235semidirect
796. C33#546semidirect
1026. C22⋊C4#1113semidirect
1169. C32#5490semidirect
1170. C32#5612semidirect
1171. C32#5654semidirect
1291. C3#10594272semidirect
1292. C3#10594278semidirect
1293. C3#10594279semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#890422
C3×#640932
C3×#640922
C3×C22⋊C4×C3⋊D32
#117237272
#117237252
#117237182
#117237012
#117237002
#117236962
#117236942
#117236922
#117236842
#105942793
#105942783
#105942723