Finite Group Databasebeta

← #13169455

Subgroups — #13169455

Order 1728.

1092 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723670C211yesmaximal, characteristic
2#11723502C211yesmaximal, characteristic, complemented
3#11723464C211yesmaximal, characteristic, complemented
4#11723394C211yesmaximal, characteristic, complemented
5C3×#63868C211yesmaximal, characteristic, complemented
6C3×#63848C211yesmaximal, characteristic, complemented
7C3×#63844C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11723010C211yesmaximal, characteristic
11#11722983C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722943C211yesmaximal, characteristic, complemented
14#11722938C211yesmaximal, characteristic
15#11722919C211yesmaximal, characteristic, complemented
16#10594480—31nomaximal
17#10594424—31nomaximal
18#10593940—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×Dic3×C3⋊D3C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25#88857C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C32×C4⋊Dic3C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×C4×Dic3C2211yescharacteristic
31#88814C2211yescharacteristic
32#88814C2211yescharacteristic
33#88813C2211yescharacteristic
34#88806C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38#88803C2211yescharacteristic
39#88803C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64097—31no—
56#64081—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#887—31no—
61C3×#876—31no—
62C3×C4×Dic6—31no—
63#63913—31no—
64#63913—31no—
65#63907—31no—
66#63907—31no—
67#63902—31no—
68#63899—31no—
69#63899—31no—
70#63899—31no—
71#63899—61no—
72#63896—31no—
73#63881—31no—
74#63881—31no—
75#63877—31no—
76#63877—31no—
77#63877—31no—
78#63877—31no—
79#63877—61no—
80#63874—31no—
81#63868—31no—
82#63868D311yescharacteristic, complemented
83#63865—31no—
84#63862—31no—
85#63861—31no—
86#63861—31no—
87#63859—31no—
88#63852—31no—
89#63852—31no—
90#63848—31no—
91#63848D311yescharacteristic, complemented
92#63844—31no—
93#63844—31no—
94#63844D311yescharacteristic, complemented
95#63839—31no—
96#63839—31no—
97#63839—61no—
98#63838—31no—
99#63838—31no—
100#63837—31no—
101#63837—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×#634—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6295—22no—
119#6293—22no—
120#6293—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—22no—
123#5702—91no—
124#5702—91no—
125#5568—91no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×#634—31no—
129C2×#634—31no—
130C2×#634C2×D311yescharacteristic
131C2×C3×Dic6—31no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—61no—
134C2×#627—31no—
135C2×#627—31no—
136C2×#627—31no—
137C2×#627—31no—
138C2×#627—61no—
139C2×#627—61no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#625—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—61no—
148C2×D3×Dic3—61no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C42—31no—
152#3752—31no—
153#3752—31no—
154#3752C2×D311yescharacteristic
155#3752C2×D311yescharacteristic
156C4⋊(C3⋊Dic3)—31no—
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—61no—
164#3750—61no—
165#3750—61no—
166#3750—121no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—61no—
182C3×(C2×D3)⋊C4—61no—
183C3×C4⋊Dic3—21no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3C2×D311yescharacteristic
187C3×C4⋊Dic3C2×D311yescharacteristic
188C3×Dic3⋊C4—21no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4C2×D311yescharacteristic
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×C4×Dic3—21no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3C2×D311yescharacteristic
207C3×C4×Dic3C2×D311yescharacteristic
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—61no—
215#3724—61no—
216#3724—61no—
217#3724C2×D311yescharacteristic
218#3724C2×D311yescharacteristic
219#3724C2×D311yescharacteristic
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225#3722—31no—
226#3722—31no—
227#3722C2×D311yescharacteristic
228#3722C2×D311yescharacteristic
229#3722C2×D311yescharacteristic
230#3722C2×D311yescharacteristic
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—61no—
240(C2×D3)⋊Dic3—61no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—61no—
249Dic32—61no—
250Dic32C2×D311yescharacteristic
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3×C3⋊D3—21no—
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3⋊(C3⋊Dic3)#4112yes—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3#4112yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#126—91no—
274C3×#126—91no—
275C3×C4×Q8—91no—
276#947—91no—
277#944—91no—
278#898—31no—
279#898—31no—
280#898—31no—
281#898—91no—
282#898—91no—
283#898—91no—
284#896—91no—
285#896—91no—
286#896—91no—
287#896—91no—
288#896—181no—
289#893—91no—
290#888—91no—
291#888—91no—
292#888—181no—
293#887—31no—
294#887—91no—
295#887—91no—
296#887—91no—
297#887—91no—
298#885—91no—
299#885—91no—
300#885—91no—
301#885—91no—
302#67⋊C4—91no—
303#67⋊C4—91no—
304#879—91no—
305#879—91no—
306#878—91no—
307#878—91no—
308#877—91no—
309#877—91no—
310#876—31no—
311#876—91no—
312#875—91no—
313#872—91no—
314#872—91no—
315#872—91no—
316#872—91no—
317#872—181no—
318C4×Dic6—31no—
319C4×Dic6—91no—
320C4×Dic6—91no—
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—31no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—31no—
327C22×C3×D3—61no—
328C22×C3×D3—61no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—41no—
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—61no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—121no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C4×C3⋊D3—62no—
361C4×C3⋊D3—62no—
362#634—22no—
363#634—62no—
364#634—62no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C3×Dic6—62no—
396C3×Dic6—62no—
397C3×Dic6—122no—
398#627—62no—
399#627—62no—
400#627—62no—
401#627—62no—
402#627—122no—
403#627—122no—
404#626—62no—
405#626—62no—
406#625—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—64no—
412D3×Dic3—122no—
413#556—271noSylow
414C2×C33C2×#4111yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C332−1+411yescharacteristic
417C3×C3⋊D3—41no—
418C3×C3⋊D3—41no—
419C2×C3×Q8—91no—
420C2×#67—91no—
421C2×#67—91no—
422C22×Dic3—91no—
423C22×Dic3—91no—
424C2×D12—91no—
425C2×C4×D3—91no—
426C2×C4×D3—91no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×C4×D3—181no—
430C2×C4×D3—181no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—61no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—181no—
441C2×Dic6—181no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—61no—
447C3×C4⋊C4—61no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C42—31no—
460C3×C42—31no—
461C3×C42—61no—
462C3×C42—91no—
463C3×C42—91no—
464C3×C42—91no—
465#217—91no—
466#217—91no—
467#217—91no—
468#217—91no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—31no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—31no—
480(C2×D3)⋊C4—31no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
488(C2×D3)⋊C4—91no—
489(C2×D3)⋊C4—91no—
490(C2×D3)⋊C4—91no—
491(C2×D3)⋊C4—181no—
492(C2×D3)⋊C4—181no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—181no—
498C4⋊Dic3D3211yescharacteristic
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—181no—
521Dic3⋊C4—181no—
522Dic3⋊C4—181no—
523Dic3⋊C4—181no—
524Dic3⋊C4—181no—
525Dic3⋊C4—181no—
526Dic3⋊C4—361no—
527Dic3⋊C4D3211yescharacteristic
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—181no—
544C4×Dic3—181no—
545C4×Dic3D3211yescharacteristic
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—41no—
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C22×C32C23×D311yescharacteristic
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3⋊D3—21no—
557C2×C3⋊D3—21no—
558C2×C3⋊D3—21no—
559C2×C3×D3—62no—
560C2×C3×D3—62no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—61no—
564C2×C3×D3—61no—
565C2×C3×D3—61no—
566C2×C3×D3—61no—
567C2×C3×D3—61no—
568C2×C3×D3—61no—
569C2×C3×D3—61no—
570C2×C3×D3—61no—
571C2×C3×D3—61no—
572C2×C3×D3—61no—
573C2×C3×D3—121no—
574C2×C3×D3—121no—
575C2×C3×D3—121no—
576C2×C3×D3—121no—
577C32×C4—21no—
578C32×C4—21no—
579C32×C4—21no—
580C32×C4—41no—
581C32×C4—41no—
582C32×C4—41no—
583C32×C4—61no—
584C32×C4—61no—
585C32×C4—61no—
586C32×C4—61no—
587C32×C4—61no—
588C32×C4—61no—
589C32×C4—81no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3—21no—
593C3⋊Dic3—32no—
594C3⋊Dic3—32no—
595C3⋊Dic3—32no—
596C3⋊Dic3—62no—
597C3⋊Dic3—62no—
598C3⋊Dic3—62no—
599C3⋊Dic3—61no—
600C3⋊Dic3—61no—
601C3⋊Dic3—61no—
602C3⋊Dic3—122no—
603C3⋊Dic3—121no—
604C3⋊Dic3—121no—
605C3⋊Dic3—121no—
606C3⋊Dic3—241no—
607C3⋊Dic3#23512yes—
608C3×Dic3—22no—
609C3×Dic3—22no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—21no—
622C3×Dic3—32no—
623C3×Dic3—32no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—41no—
627C3×Dic3—41no—
628C3×Dic3—62no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—121no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C4⋊Q8—271no—
639#126—91no—
640#126—91no—
641#126—271no—
642#126—271no—
643#124—271no—
644#124—271no—
645C22⋊Q8—271no—
646C22⋊Q8—271no—
647C4×Q8—91no—
648C4×Q8—271no—
649C4×Q8—271no—
650C4×D4—271no—
651#117—271no—
652#117—271no—
653C33#55611yescharacteristic, complemented, Sylow
654C23×C3—91no—
655C23×C3—91no—
656C22×D3—31no—
657C22×D3—31no—
658C22×D3—31no—
659C22×D3—31no—
660C22×D3—61no—
661C22×D3—61no—
662C3×Q8—182no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—41no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—91no—
688C2×C3×C4—91no—
689C2×C3×C4C2×D3211yescharacteristic
690C2×C3×C4C2×D3211yescharacteristic
691C2×C3×C4C2×D3211yescharacteristic
692#67—182no—
693#67—182no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—182no—
719C2×Dic3—182no—
720C2×Dic3—361no—
721C2×Dic3—361no—
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728D12—182no—
729C4×D3—182no—
730C4×D3—182no—
731C4×D3—182no—
732C4×D3—182no—
733C4×D3—184no—
734C4×D3—362no—
735Dic6—62no—
736Dic6—62no—
737Dic6—122no—
738Dic6—182no—
739Dic6—182no—
740Dic6—182no—
741Dic6—182no—
742Dic6—182no—
743Dic6—182no—
744Dic6—362no—
745Dic6—362no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—41no—
756C2×C32—41no—
757C2×C32—41no—
758C2×C32C2×#23511yescharacteristic
759C2×C32#100711yescharacteristic
760C2×C32D3×#4111yescharacteristic
761C2×C32D3×#4111yescharacteristic
762C2×C32D3×#4111yescharacteristic
763C2×C32D3×#4111yescharacteristic
764C2×C32D3×#4111yescharacteristic
765C2×C32#101011yescharacteristic
766C2×C32#101011yescharacteristic
767C3⋊D3—41no—
768C3⋊D3—41no—
769C3×D3—122no—
770C3×D3—122no—
771C3×D3—121no—
772C3×D3—121no—
773C3×D3—121no—
774C3×D3—121no—
775C2×Q8—91no—
776C2×Q8—271no—
777C2×Q8—271no—
778C2×D4—271no—
779C22×C4—271no—
780C22×C4—271no—
781C4⋊C4—31no—
782C4⋊C4—31no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C22⋊C4—91no—
794C22⋊C4—91no—
795C22⋊C4—91no—
796C22⋊C4—91no—
797C22⋊C4—91no—
798C22⋊C4—91no—
799C22⋊C4—271no—
800C22⋊C4—271no—
801C22⋊C4—271no—
802C22⋊C4—271no—
803C42—31no—
804C42—91no—
805C42—91no—
806C42—91no—
807C42—271no—
808C42—271no—
809C42—271no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—41no—
814C22×C3—181no—
815C22×C3—181no—
816C22×C3—181no—
817C22×C3—181no—
818C22×C3—181no—
819C22×C3—181no—
820C22×C3C22×D3211yescharacteristic
821C22×C3C22×D3211yescharacteristic
822C22×C3C22×D3211yescharacteristic
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—41no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—62no—
848C3×C4—62no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—61no—
860C3×C4—61no—
861C3×C4—81no—
862C3×C4—92no—
863C3×C4—121no—
864C3×C4—121no—
865C3×C4—121no—
866C3×C4—121no—
867C3×C4—181no—
868C3×C4—181no—
869C3×C4—181no—
870Dic3—21no—
871Dic3—21no—
872Dic3—21no—
873Dic3—21no—
874Dic3—21no—
875Dic3—21no—
876Dic3—32no—
877Dic3—32no—
878Dic3—62no—
879Dic3—61no—
880Dic3—61no—
881Dic3—61no—
882Dic3—61no—
883Dic3—61no—
884Dic3—61no—
885Dic3—92no—
886Dic3—92no—
887Dic3—92no—
888Dic3—121no—
889Dic3—121no—
890Dic3—121no—
891Dic3—182no—
892Dic3—182no—
893Dic3—182no—
894Dic3—181no—
895Dic3—181no—
896Dic3—181no—
897Dic3—362no—
898Dic3—361no—
899Dic3—361no—
900Dic3—361no—
901Dic3—721no—
902C32—21no—
903C32—21no—
904C32—21no—
905C32—41no—
906C32#556811yescharacteristic, complemented
907C32#570211yescharacteristic, complemented
908C32#570211yescharacteristic, complemented
909C23—91no—
910C23—91no—
911Q8—182no—
912Q8—542no—
913Q8—542no—
914D4—542no—
915C2×C4—31no—
916C2×C4—31no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—91no—
922C2×C4—91no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—271no—
926C2×C4—271no—
927C2×C4—542no—
928C2×C4—542no—
929C2×C4D3311yescharacteristic
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—41no—
940C2×C3—41no—
941C2×C3—41no—
942C2×C3—361no—
943C2×C3—361no—
944C2×C3#6429711yescharacteristic
945C2×C3#6429811yescharacteristic
946C2×C3D3×#23511yescharacteristic
947C2×C3D3×#23511yescharacteristic
948C2×C3#6430611yescharacteristic
949C2×C3#6431211yescharacteristic
950C2×C3#6431211yescharacteristic
951C2×C3#6431511yescharacteristic
952C2×C3#6431911yescharacteristic
953D3—122no—
954D3—122no—
955D3—121no—
956D3—121no—
957D3—121no—
958D3—121no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22C2×D3311yescharacteristic
966C4—21no—
967C4—61no—
968C4—61no—
969C4—61no—
970C4—61no—
971C4—61no—
972C4—61no—
973C4—92no—
974C4—181no—
975C4—181no—
976C4—181no—
977C4—272no—
978C4—541no—
979C3—21no—
980C3—21no—
981C3—21no—
982C3—41no—
983C3#1059394011yescharacteristic, complemented
984C3#1059442411yescharacteristic, complemented
985C3#1059448011yescharacteristic, complemented
986C2—361no—
987C2—361no—
988C2#1172437611yescharacteristic
989C2#1172439611yescharacteristic
990C2#1172441011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6295C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723502C2semidirect
3. #11723464C2semidirect
4. #11723394C2semidirect
5. C3×#63868C2semidirect
6. C3×#63848C2semidirect
7. C3×#63844C2semidirect
8. #11723027C2semidirect
9. #11723023C2semidirect
11. #11722983C2semidirect
12. #11722943C2semidirect
13. #11722943C2semidirect
15. #11722919C2semidirect
82. #63868D3semidirect
91. #63848D3semidirect
94. #63844D3semidirect
653. C33#556semidirect
906. C32#5568semidirect
907. C32#5702semidirect
908. C32#5702semidirect
983. C3#10593940semidirect
984. C3#10594424semidirect
985. C3#10594480semidirect

Maximal subgroups

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

subgroupindex
#117236702
#117235022
#117234642
#117233942
C3×#638682
C3×#638482
C3×#638442
#117230272
#117230232
#117230102
#117229832
#117229432
#117229382
#117229192
#105944803
#105944243
#105939403