Finite Group Databasebeta

← #13178234

Subgroups — #13178234

Order 1728.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64091C211yesmaximal, characteristic, complemented
4C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5C3×#64087C211yesmaximal, characteristic, complemented
6#11723727C211yesmaximal, characteristic, complemented
7#11723726C211yesmaximal, characteristic, complemented
8#11723723C211yesmaximal, characteristic, complemented
9#11723696C211yesmaximal, characteristic, complemented
10#11723694C211yesmaximal, characteristic, complemented
11#11723690C211yesmaximal, characteristic, complemented
12#11723687C211yesmaximal, characteristic, complemented
13#11723687C211yesmaximal, characteristic, complemented
14#11723684C211yesmaximal, characteristic, complemented
15#11723670C211yesmaximal, characteristic, complemented
16#10594187—31nomaximal
17#10594184—31nomaximal
18#10594063—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C23×C3×C3⋊D3C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×#634C2211yescharacteristic, complemented
28C2×#6295—24no—
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6295C2211yescharacteristic
32C2×#6295C2211yescharacteristic
33C2×#6295C2211yescharacteristic, complemented
34C2×#6295C2211yescharacteristic, complemented
35C2×#6294C2211yescharacteristic, complemented
36C2×#6294C2211yescharacteristic, complemented
37C2×#6294C2211yescharacteristic, complemented
38#89041—24no—
39C33×C22⋊C4C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3757C2211yescharacteristic
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#88813C2211yescharacteristic, complemented
56C22×#626—31no—
57C22×#626—31no—
58C22×#625—31no—
59C2×#3799—31no—
60C2×#3796—31no—
61C2×#3795—31no—
62#64091D311yescharacteristic, complemented
63C22⋊C4×C3⋊D3D311yescharacteristic, complemented
64#64087D311yescharacteristic, complemented
65C3×#882—31no—
66C3×#882—31no—
67C3×#882—61no—
68C3×D3×C22⋊C4—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—61no—
71C3×#878—31no—
72C3×#878—31no—
73C3×#878—61no—
74#63981—31no—
75#63977—31no—
76#63976—31no—
77#63974—31no—
78#67⋊Dic3—31no—
79Dic3×#67—31no—
80D3×#217—31no—
81D3×#217—31no—
82#63952—31no—
83#63916—31no—
84#63913—31no—
85#63910—31no—
86#63910—31no—
87#63909—31no—
88#63908—31no—
89#63907—31no—
90#63907—31no—
91#63905—31no—
92#63904—31no—
93#63891—31no—
94#63890—31no—
95#63886—31no—
96#63886—31no—
97#63885—31no—
98#63885—31no—
99#63881—31no—
100#63879—31no—
101#63854—31no—
102#63853—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—22no—
109C22×C3×C3⋊D3—41no—
110C22×C3×C3⋊D3—41no—
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C22×C3×C3⋊D3C2311yescharacteristic
114C22×C3×C3⋊D3C2311yescharacteristic
115C22×C3×C3⋊D3C2311yescharacteristic
116C2×C33×C4C2311yescharacteristic
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C2×C3×C3⋊Dic3—22no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C3×C4⋊(C3⋊D3)—22no—
128C3×C4⋊(C3⋊D3)—41no—
129C3×C4×C3⋊D3—22no—
130C3×C4×C3⋊D3—41no—
131C3×#634—22no—
132#6295—22no—
133#6295—22no—
134#6295—22no—
135#6295—22no—
136#6295—41no—
137#6295D414yescomplemented
138#6294—22no—
139#6294—22no—
140#6294—41no—
141#5630—91no—
142#5591—91no—
143#5490—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C23×C3×D3—61no—
151C23×C3×D3—61no—
152C2×#638C2×D311yescharacteristic
153C22×C3⋊Dic3C2×D311yescharacteristic
154C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
155C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
158C2×#634C2×D311yescharacteristic, complemented
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—61no—
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—61no—
165C2×C3×D12—31no—
166C2×C3×D12—31no—
167C2×C3×D12—31no—
168C2×C3×D12—31no—
169C2×C3×D12—61no—
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—61no—
176C2×C3×C4×D3—61no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—31no—
179C2×C3×Dic6—61no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—31no—
192C2×#626—64no—
193C2×#626—64no—
194C2×#625—31no—
195C2×#625—31no—
196C2×#625—31no—
197C2×#625—31no—
198C2×#625—31no—
199C2×#625—31no—
200C2×#625—64no—
201C2×#624—31no—
202C2×#624—31no—
203C2×#624—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209C2×D3×Dic3—31no—
210#3799—64no—
211#3796—64no—
212#3795—64no—
213C32×C22⋊C4—21no—
214C32×C22⋊C4—21no—
215C32×C22⋊C4—21no—
216C32×C22⋊C4—41no—
217C32×C22⋊C4C2×D311yescharacteristic
218C32×C22⋊C4C2×D311yescharacteristic
219C32×C22⋊C4C2×D311yescharacteristic
220#3757C2×D311yescharacteristic
221#3757C2×D311yescharacteristic
222#3752C2×D311yescharacteristic, complemented
223#3752C2×D311yescharacteristic, complemented
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#4112yescomplemented
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—21no—
294C2×C3×C3⋊D3—44no—
295C2×C3×C3⋊D3—44no—
296C2×C3×C3⋊D3C2×D412yes—
297C2×C3×C3⋊D3C2×D412yes—
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—
308C22×#67—91no—
309C2×#239—91no—
310C2×#237—91no—
311C2×#235—91no—
312C22×D12—91no—
313C3×C22⋊Q8—91no—
314C3×#120—91no—
315C2×C3×C22⋊C4—91no—
316#953—91no—
317C2×#217—91no—
318#947—91no—
319#939—91no—
320#939—91no—
321#938—91no—
322#937—91no—
323D4×Dic3—91no—
324#930—91no—
325#929—91no—
326C4×#67—91no—
327C4×#67—91no—
328#895—91no—
329#895—91no—
330#895—91no—
331#894—91no—
332#894—91no—
333#893—91no—
334#886—91no—
335#885—91no—
336#885—91no—
337#884—91no—
338#884—91no—
339#883—91no—
340#883—91no—
341#882—31no—
342#882—31no—
343#882—61no—
344#882—91no—
345#67⋊C4—91no—
346#67⋊C4—91no—
347D3×C22⋊C4—31no—
348D3×C22⋊C4—31no—
349D3×C22⋊C4—61no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352#878—31no—
353#878—31no—
354#878—61no—
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—22no—
365C22×C3⋊D3—22no—
366C22×C3⋊D3—41no—
367C22×C3⋊D3—41no—
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3⋊D3C22×D311yescharacteristic
371C22×C3⋊D3C22×D311yescharacteristic
372C22×C3⋊D3C22×D311yescharacteristic
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—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3—61no—
388C22×C3×D3—62no—
389C22×C3×D3—62no—
390C22×C3×D3—62no—
391C22×C3×D3—62no—
392C22×C3×D3—64no—
393C22×C3×D3—62no—
394C22×C3×D3—62no—
395C22×C3×D3—62no—
396C22×C3×D3—62no—
397C22×C3×D3—122no—
398C22×C3×D3—122no—
399C22×C3×D3—122no—
400C22×C3×D3—121no—
401C22×C3×D3—121no—
402C22×C3×D3—121no—
403C22×C3×D3—121no—
404C22×C3×D3—122no—
405C22×C3×D3—122no—
406C2×C32×C4—21no—
407C2×C32×C4—21no—
408C2×C32×C4—21no—
409C2×C32×C4—21no—
410C2×C32×C4—21no—
411C2×C32×C4—21no—
412C2×C32×C4—41no—
413C2×C32×C4—41no—
414C2×C32×C4C22×D311yescharacteristic
415C2×C32×C4C22×D311yescharacteristic
416C2×C32×C4C22×D311yescharacteristic
417C2×C32×C4C22×D311yescharacteristic
418C2×C32×C4C22×D311yescharacteristic
419C2×C32×C4C22×D311yescharacteristic
420#638—22no—
421C2×C3⋊Dic3—22no—
422C2×C3⋊Dic3C22×D311yescharacteristic
423C2×C3⋊Dic3C22×D311yescharacteristic
424C2×C3⋊Dic3C22×D311yescharacteristic
425C2×C3⋊Dic3C22×D311yescharacteristic
426C2×C3⋊Dic3C22×D311yescharacteristic
427C2×C3⋊Dic3C22×D311yescharacteristic
428C2×C3⋊Dic3C22×D311yescharacteristic
429C4⋊(C3⋊D3)—22no—
430C4⋊(C3⋊D3)—41no—
431C4×C3⋊D3—22no—
432C4×C3⋊D3—41no—
433#634—22no—
434C3×#67—62no—
435C3×#67—62no—
436C3×#67—122no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
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—61no—
452C2×C3×Dic3—61no—
453C2×C3×Dic3—61no—
454C2×C3×Dic3—61no—
455C2×C3×Dic3—61no—
456C2×C3×Dic3—61no—
457C2×C3×Dic3—61no—
458C2×C3×Dic3—62no—
459C2×C3×Dic3—62no—
460C2×C3×Dic3—122no—
461C3×D12—62no—
462C3×D12—62no—
463C3×D12—122no—
464C3×D12—121no—
465C3×D12—121no—
466C3×D12—122no—
467C3×C4×D3—62no—
468C3×C4×D3—62no—
469C3×C4×D3—122no—
470C3×C4×D3—121no—
471C3×C4×D3—121no—
472C3×C4×D3—122no—
473C3×Dic6—62no—
474C3×Dic6—62no—
475C3×Dic6—122no—
476#626—34no—
477#626—34no—
478#626—62no—
479#626—62no—
480#626—62no—
481#626—62no—
482#626—62no—
483#626—62no—
484#626—62no—
485#626—62no—
486#626—121no—
487#626—121no—
488#625—34no—
489#625—62no—
490#625—62no—
491#625—62no—
492#625—62no—
493#625—121no—
494#624—62no—
495#624—62no—
496#624—121no—
497D3×Dic3—62no—
498D3×Dic3—62no—
499D3×Dic3—62no—
500D3×Dic3—62no—
501D3×Dic3—121no—
502D3×Dic3—121no—
503#546—271noSylow
504C2×C33—22no—
505C2×C33C22×D411yescharacteristic
506C2×C33C2×#4111yescharacteristic
507C2×C33H(5,𝔽2)11yescharacteristic
508C3×C3⋊D3—22no—
509C3×C3⋊D3—22no—
510C3×C3⋊D3—41no—
511C3×C3⋊D3—41no—
512C3×C3⋊D3—41no—
513C24×C3—91no—
514C24×C3—91no—
515C23×D3—31no—
516C23×D3—31no—
517C23×D3—31no—
518C23×D3—31no—
519C23×D3—61no—
520C23×D3—61no—
521C2×C3×Q8—91no—
522C2×C3×D4—91no—
523C2×C3×D4—91no—
524C2×C3×D4—91no—
525C22×C3×C4—91no—
526C22×C3×C4—91no—
527C22×C3×C4—91no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—61no—
531C2×#67—91no—
532C2×#67—91no—
533C2×#67—91no—
534C2×#67—91no—
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—184no—
544C2×#67—184no—
545C22×Dic3—31no—
546C22×Dic3—31no—
547C22×Dic3—61no—
548C22×Dic3—91no—
549C22×Dic3—91no—
550C22×Dic3—91no—
551#239—184no—
552#237—184no—
553#235—184no—
554C2×D12—31no—
555C2×D12—31no—
556C2×D12—31no—
557C2×D12—31no—
558C2×D12—61no—
559C2×D12—61no—
560C2×D12—91no—
561C2×D12—91no—
562C2×D12—91no—
563C2×D12—91no—
564C2×D12—91no—
565C2×D12—91no—
566C2×D12—184no—
567C2×C4×D3—31no—
568C2×C4×D3—31no—
569C2×C4×D3—31no—
570C2×C4×D3—31no—
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×C4×D3—91no—
578C2×C4×D3—91no—
579C2×Dic6—31no—
580C2×Dic6—31no—
581C2×Dic6—61no—
582C3×C4⋊C4—91no—
583C3×C4⋊C4—91no—
584C3×C4⋊C4—91no—
585C3×C22⋊C4—21no—
586C3×C22⋊C4—21no—
587C3×C22⋊C4—21no—
588C3×C22⋊C4—41no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4—91no—
592C3×C22⋊C4—91no—
593C3×C22⋊C4—91no—
594C3×C22⋊C4—91no—
595C3×C22⋊C4D3211yescharacteristic
596C3×C22⋊C4D3211yescharacteristic
597C3×C22⋊C4D3211yescharacteristic
598#217—31no—
599#217—31no—
600#217—31no—
601#217—31no—
602#217—61no—
603#217—61no—
604#217—91no—
605#217—91no—
606#217—91no—
607#217—91no—
608#217—91no—
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—31no—
616(C2×D3)⋊C4—31no—
617(C2×D3)⋊C4—61no—
618(C2×D3)⋊C4—61no—
619(C2×D3)⋊C4—61no—
620(C2×D3)⋊C4—61no—
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—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631C4⋊Dic3—31no—
632C4⋊Dic3—31no—
633C4⋊Dic3—61no—
634C4⋊Dic3—91no—
635Dic3⋊C4—31no—
636Dic3⋊C4—31no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—61no—
640Dic3⋊C4—61no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643C4×Dic3—91no—
644C4×Dic3—91no—
645C4×Dic3—91no—
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—22no—
656C22×C32—22no—
657C22×C32—22no—
658C22×C32—41no—
659C22×C32—42no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—81no—
667C22×C32—81no—
668C22×C32#23512yescomplemented
669C22×C32#23712yescomplemented
670C22×C32#23912yescomplemented
671C22×C32C23×D311yescharacteristic
672C22×C32C23×D311yescharacteristic
673C22×C32C23×D311yescharacteristic
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—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—21no—
687C2×C3⋊D3—44no—
688C2×C3⋊D3—44no—
689C2×C3⋊D3D3×D412yes—
690C2×C3⋊D3D3×D412yes—
691C2×C3×D3—32no—
692C2×C3×D3—32no—
693C2×C3×D3—32no—
694C2×C3×D3—32no—
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—62no—
708C2×C3×D3—62no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
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—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
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—121no—
734C2×C3×D3—121no—
735C2×C3×D3—121no—
736C2×C3×D3—124no—
737C2×C3×D3—124no—
738C2×C3×D3—124no—
739C2×C3×D3—124no—
740C2×C3×D3—128no—
741C2×C3×D3—128no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—21no—
745C32×C4—21no—
746C32×C4—21no—
747C32×C4—21no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—41no—
751C32×C4—41no—
752C32×C4—41no—
753C32×C4—41no—
754C32×C4—81no—
755C32×C4—81no—
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3—21no—
760C3⋊Dic3—21no—
761C3⋊Dic3—21no—
762C3⋊Dic3D3×D412yes—
763C3×Dic3—32no—
764C3×Dic3—32no—
765C3×Dic3—62no—
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—61no—
776C3×Dic3—61no—
777C3×Dic3—61no—
778C3×Dic3—121no—
779C3×Dic3—121no—
780C3×Dic3—121no—
781C3×Dic3—121no—
782C3×Dic3—121no—
783C3×Dic3—121no—
784C2×#41—271no—
785C22×D4—271no—
786#124—271no—
787#123—271no—
788#123—271no—
789C22⋊Q8—91no—
790#121—271no—
791#121—271no—
792#121—271no—
793#120—91no—
794#120—271no—
795C4×D4—271no—
796C4×D4—271no—
797C2×C22⋊C4—91no—
798C2×C22⋊C4—271no—
799C33#54611yescharacteristic, complemented, Sylow
800C23×C3—21no—
801C23×C3—21no—
802C23×C3—21no—
803C23×C3—41no—
804C23×C3—91no—
805C23×C3—91no—
806C23×C3—91no—
807C23×C3—91no—
808C23×C3—91no—
809C23×C3—182no—
810C23×C3—182no—
811C23×C3—182no—
812C23×C3—182no—
813C23×C3—361no—
814C23×C3—361no—
815C23×C3C2×D3211yescharacteristic
816C23×C3C2×D3211yescharacteristic
817C23×C3C2×D3211yescharacteristic
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—31no—
827C22×D3—31no—
828C22×D3—61no—
829C22×D3—61no—
830C22×D3—61no—
831C22×D3—61no—
832C22×D3—61no—
833C22×D3—62no—
834C22×D3—62no—
835C22×D3—62no—
836C22×D3—62no—
837C22×D3—64no—
838C22×D3—62no—
839C22×D3—62no—
840C22×D3—62no—
841C22×D3—62no—
842C22×D3—122no—
843C22×D3—122no—
844C22×D3—122no—
845C22×D3—121no—
846C22×D3—121no—
847C22×D3—121no—
848C22×D3—121no—
849C22×D3—122no—
850C22×D3—122no—
851C3×Q8—182no—
852C3×D4—182no—
853C3×D4—182no—
854C3×D4—361no—
855C2×C3×C4—21no—
856C2×C3×C4—21no—
857C2×C3×C4—21no—
858C2×C3×C4—21no—
859C2×C3×C4—21no—
860C2×C3×C4—21no—
861C2×C3×C4—41no—
862C2×C3×C4—41no—
863C2×C3×C4—91no—
864C2×C3×C4—91no—
865C2×C3×C4—91no—
866C2×C3×C4—91no—
867C2×C3×C4—91no—
868C2×C3×C4—91no—
869C2×C3×C4—91no—
870C2×C3×C4—182no—
871C2×C3×C4—182no—
872C2×C3×C4—361no—
873C2×C3×C4C2×D3211yescharacteristic
874C2×C3×C4C2×D3211yescharacteristic
875C2×C3×C4C2×D3211yescharacteristic
876C2×C3×C4C2×D3211yescharacteristic
877C2×C3×C4C2×D3211yescharacteristic
878C2×C3×C4C2×D3211yescharacteristic
879#67—62no—
880#67—62no—
881#67—94no—
882#67—94no—
883#67—122no—
884#67—182no—
885#67—182no—
886#67—182no—
887#67—182no—
888#67—182no—
889#67—182no—
890#67—182no—
891#67—182no—
892#67—361no—
893#67—361no—
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—31no—
908C2×Dic3—61no—
909C2×Dic3—61no—
910C2×Dic3—61no—
911C2×Dic3—61no—
912C2×Dic3—61no—
913C2×Dic3—61no—
914C2×Dic3—61no—
915C2×Dic3—62no—
916C2×Dic3—62no—
917C2×Dic3—122no—
918C2×Dic3—182no—
919C2×Dic3—182no—
920C2×Dic3—361no—
921D12—62no—
922D12—62no—
923D12—94no—
924D12—122no—
925D12—121no—
926D12—121no—
927D12—122no—
928D12—182no—
929D12—182no—
930D12—182no—
931D12—182no—
932D12—361no—
933C4×D3—62no—
934C4×D3—62no—
935C4×D3—122no—
936C4×D3—121no—
937C4×D3—121no—
938C4×D3—122no—
939C4×D3—182no—
940C4×D3—182no—
941C4×D3—182no—
942C4×D3—182no—
943C4×D3—361no—
944C4×D3—361no—
945Dic6—62no—
946Dic6—62no—
947Dic6—122no—
948C2×C32—22no—
949C2×C32—22no—
950C2×C32—22no—
951C2×C32—21no—
952C2×C32—21no—
953C2×C32—21no—
954C2×C32—21no—
955C2×C32—21no—
956C2×C32—21no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—41no—
961C2×C32—41no—
962C2×C32—41no—
963C2×C32—42no—
964C2×C32—42no—
965C2×C32—42no—
966C2×C32—82no—
967C2×C32C2×#23511yescharacteristic
968C2×C32C2×D3×D411yescharacteristic
969C2×C32C2×D3×D411yescharacteristic
970C2×C32C2×D3×D411yescharacteristic
971C2×C32C2×#23711yescharacteristic
972C2×C32#100411yescharacteristic
973C2×C32#100411yescharacteristic
974C2×C32C2×#23911yescharacteristic
975C2×C32#100911yescharacteristic
976C3⋊D3—22no—
977C3⋊D3—22no—
978C3⋊D3—41no—
979C3⋊D3—41no—
980C3⋊D3—41no—
981C3×D3—64no—
982C3×D3—62no—
983C3×D3—62no—
984C3×D3—62no—
985C3×D3—62no—
986C3×D3—122no—
987C3×D3—122no—
988C3×D3—122no—
989C3×D3—121no—
990C3×D3—121no—
991C3×D3—121no—
992C3×D3—121no—
993C3×D3—121no—
994C3×D3—121no—
995C3×D3—241no—
996C24—91no—
997C24—91no—
998#41—544no—
999C2×Q8—91no—
1000C2×D4—91no—
1001C2×D4—91no—
1002C2×D4—91no—
1003C2×D4—271no—
1004C2×D4—271no—
1005C2×D4—271no—
1006C2×D4—271no—
1007C2×D4—271no—
1008C2×D4—271no—
1009C2×D4—544no—
1010C22×C4—91no—
1011C22×C4—91no—
1012C22×C4—91no—
1013C22×C4—271no—
1014C22×C4—271no—
1015C22×C4—271no—
1016C4⋊C4—91no—
1017C4⋊C4—91no—
1018C4⋊C4—91no—
1019C4⋊C4—271no—
1020C22⋊C4—91no—
1021C22⋊C4—91no—
1022C22⋊C4—91no—
1023C22⋊C4—91no—
1024C22⋊C4—91no—
1025C22⋊C4—91no—
1026C22⋊C4—271no—
1027C22⋊C4—271no—
1028C22⋊C4—271no—
1029C22⋊C4—271no—
1030C22⋊C4—271no—
1031C22⋊C4#111311yescharacteristic
1032C42—271no—
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—21no—
1042C22×C3—22no—
1043C22×C3—22no—
1044C22×C3—22no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—41no—
1050C22×C3—41no—
1051C22×C3—41no—
1052C22×C3—42no—
1053C22×C3—81no—
1054C22×C3—81no—
1055C22×C3—92no—
1056C22×C3—92no—
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—181no—
1069C22×C3—181no—
1070C22×C3—364no—
1071C22×C3—364no—
1072C22×C3#379512yescomplemented
1073C22×C3#379612yescomplemented
1074C22×C3#379912yescomplemented
1075C22×C3C22×D3211yescharacteristic
1076C22×C3C22×D3211yescharacteristic
1077C22×C3C22×D3211yescharacteristic
1078C2×D3—32no—
1079C2×D3—32no—
1080C2×D3—32no—
1081C2×D3—32no—
1082C2×D3—62no—
1083C2×D3—62no—
1084C2×D3—62no—
1085C2×D3—62no—
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—62no—
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—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—61no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—121no—
1121C2×D3—121no—
1122C2×D3—121no—
1123C2×D3—124no—
1124C2×D3—124no—
1125C2×D3—124no—
1126C2×D3—124no—
1127C2×D3—128no—
1128C2×D3—128no—
1129C3×C4—21no—
1130C3×C4—21no—
1131C3×C4—21no—
1132C3×C4—21no—
1133C3×C4—21no—
1134C3×C4—21no—
1135C3×C4—41no—
1136C3×C4—41no—
1137C3×C4—41no—
1138C3×C4—41no—
1139C3×C4—41no—
1140C3×C4—41no—
1141C3×C4—81no—
1142C3×C4—81no—
1143C3×C4—92no—
1144C3×C4—181no—
1145C3×C4—181no—
1146C3×C4—181no—
1147C3×C4—181no—
1148C3×C4—181no—
1149C3×C4—181no—
1150Dic3—32no—
1151Dic3—32no—
1152Dic3—62no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—61no—
1157Dic3—61no—
1158Dic3—61no—
1159Dic3—61no—
1160Dic3—61no—
1161Dic3—61no—
1162Dic3—61no—
1163Dic3—61no—
1164Dic3—61no—
1165Dic3—121no—
1166Dic3—121no—
1167Dic3—121no—
1168Dic3—121no—
1169Dic3—121no—
1170Dic3—121no—
1171C32—21no—
1172C32—21no—
1173C32—21no—
1174C32—41no—
1175C32#549011yescharacteristic, complemented
1176C32#559111yescharacteristic, complemented
1177C32#563011yescharacteristic, complemented
1178C23—91no—
1179C23—91no—
1180C23—91no—
1181C23—91no—
1182C23—91no—
1183C23—182no—
1184C23—182no—
1185C23—182no—
1186C23—182no—
1187C23—361no—
1188C23—361no—
1189C23C2×#111311yescharacteristic
1190Q8—182no—
1191D4—182no—
1192D4—182no—
1193D4—274no—
1194D4—361no—
1195D4—542no—
1196D4—542no—
1197D4—542no—
1198D4—542no—
1199D4—1081no—
1200C2×C4—91no—
1201C2×C4—91no—
1202C2×C4—91no—
1203C2×C4—91no—
1204C2×C4—91no—
1205C2×C4—91no—
1206C2×C4—91no—
1207C2×C4—182no—
1208C2×C4—182no—
1209C2×C4—361no—
1210C2×C4—542no—
1211C2×C4—542no—
1212C2×C4—1081no—
1213C2×C4C2×#111311yescharacteristic
1214C2×C4C2×#111311yescharacteristic
1215C2×C3—22no—
1216C2×C3—22no—
1217C2×C3—22no—
1218C2×C3—21no—
1219C2×C3—21no—
1220C2×C3—21no—
1221C2×C3—21no—
1222C2×C3—21no—
1223C2×C3—21no—
1224C2×C3—21no—
1225C2×C3—21no—
1226C2×C3—21no—
1227C2×C3—42no—
1228C2×C3—42no—
1229C2×C3—42no—
1230C2×C3—41no—
1231C2×C3—41no—
1232C2×C3—41no—
1233C2×C3—82no—
1234C2×C3—182no—
1235C2×C3—182no—
1236C2×C3—361no—
1237C2×C3—361no—
1238C2×C3—361no—
1239C2×C3C2×#379511yescharacteristic
1240C2×C3C2×#379611yescharacteristic
1241C2×C3C2×#379911yescharacteristic
1242C2×C3D32×D411yescharacteristic
1243C2×C3D32×D411yescharacteristic
1244C2×C3D32×D411yescharacteristic
1245C2×C3#6431311yescharacteristic
1246C2×C3#6431411yescharacteristic
1247C2×C3#6431411yescharacteristic
1248D3—64no—
1249D3—62no—
1250D3—62no—
1251D3—62no—
1252D3—62no—
1253D3—122no—
1254D3—122no—
1255D3—122no—
1256D3—121no—
1257D3—121no—
1258D3—121no—
1259D3—121no—
1260D3—121no—
1261D3—121no—
1262D3—241no—
1263C22—21no—
1264C22—21no—
1265C22—92no—
1266C22—92no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—181no—
1274C22—181no—
1275C22—181no—
1276C22—181no—
1277C22—181no—
1278C22—181no—
1279C22—181no—
1280C22—364no—
1281C22—364no—
1282C22#8904112yescomplemented
1283C22C22×#111311yescharacteristic
1284C4—21no—
1285C4—21no—
1286C4—92no—
1287C4—181no—
1288C4—181no—
1289C4—181no—
1290C4—181no—
1291C4—181no—
1292C4—181no—
1293C3—21no—
1294C3—21no—
1295C3—21no—
1296C3—41no—
1297C3#1059406311yescharacteristic, complemented
1298C3#1059418411yescharacteristic, complemented
1299C3#1059418711yescharacteristic, complemented
1300C2—22no—
1301C2—182no—
1302C2—182no—
1303C2—361no—
1304C2—361no—
1305C2—361no—
1306C2C2×#8904111yescharacteristic
1307C2D4×#111311yescharacteristic
1308C2#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. C22×#6295C2semidirect
2. C2×#89041C2semidirect
3. C3×#64091C2semidirect
4. C3×C22⋊C4×C3⋊D3C2semidirect
5. C3×#64087C2semidirect
6. #11723727C2semidirect
7. #11723726C2semidirect
8. #11723723C2semidirect
9. #11723696C2semidirect
10. #11723694C2semidirect
11. #11723690C2semidirect
12. #11723687C2semidirect
13. #11723687C2semidirect
14. #11723684C2semidirect
15. #11723670C2semidirect
23. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×#634C22semidirect
33. C2×#6295C22semidirect
34. C2×#6295C22semidirect
35. C2×#6294C22semidirect
36. C2×#6294C22semidirect
37. C2×#6294C22semidirect
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. #88813C22semidirect
62. #64091D3semidirect
63. C22⋊C4×C3⋊D3D3semidirect
64. #64087D3semidirect
137. #6295D4semidirect
154. C2×C4⋊(C3⋊D3)C2×D3semidirect
155. C2×C4⋊(C3⋊D3)C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
157. C2×C4×C3⋊D3C2×D3semidirect
158. C2×#634C2×D3semidirect
222. #3752C2×D3semidirect
223. #3752C2×D3semidirect
224. #3752C2×D3semidirect
225. #3752C2×D3semidirect
226. C4⋊(C3⋊Dic3)C2×D3semidirect
227. #3750C2×D3semidirect
228. #3750C2×D3semidirect
279. C22×C33#41semidirect
668. C22×C32#235semidirect
669. C22×C32#237semidirect
670. C22×C32#239semidirect
799. C33#546semidirect
1072. C22×C3#3795semidirect
1073. C22×C3#3796semidirect
1074. C22×C3#3799semidirect
1175. C32#5490semidirect
1176. C32#5591semidirect
1177. C32#5630semidirect
1282. C22#89041semidirect
1297. C3#10594063semidirect
1298. C3#10594184semidirect
1299. C3#10594187semidirect

Maximal subgroups

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

subgroupindex
C22×#62952
C2×#890412
C3×#640912
C3×C22⋊C4×C3⋊D32
C3×#640872
#117237272
#117237262
#117237232
#117236962
#117236942
#117236902
#117236872
#117236842
#117236702
#105941873
#105941843
#105940633