Finite Group Databasebeta

← #13178139

Subgroups — #13178139

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64085C211yesmaximal, characteristic, complemented
2C3×#64081C211yesmaximal, characteristic, complemented
3C3×C4×#634C211yesmaximal, characteristic, complemented
4#11723692C211yesmaximal, characteristic, complemented
5#11723684C211yesmaximal, characteristic
6#11723683C211yesmaximal, characteristic, complemented
7#11723676C211yesmaximal, characteristic, complemented
8#11723676C211yesmaximal, characteristic, complemented
9#11723675C211yesmaximal, characteristic, complemented
10#11723672C211yesmaximal, characteristic
11#11723671C211yesmaximal, characteristic, complemented
12#11723670C211yesmaximal, characteristic
13#11723666C211yesmaximal, characteristic, complemented
14#11723665C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10593940—31nomaximal
17#10593931—31nomaximal
18#10593871—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6296C2211yescharacteristic
22C2×#6296C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C33×C42C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64085D311yescharacteristic, complemented
55#64081D311yescharacteristic, complemented
56C4×#634D311yescharacteristic, complemented
57C3×#876—31no—
58C3×#876—31no—
59C3×#876—61no—
60C3×#872—31no—
61C3×#872—31no—
62C3×#872—61no—
63C3×C4×Dic6—31no—
64C3×C4×Dic6—31no—
65C3×C4×Dic6—61no—
66#63915—31no—
67#63913—31no—
68#63907—31no—
69#63907—31no—
70#63904—31no—
71#63899—31no—
72#63895—31no—
73#63893—31no—
74#63881—31no—
75#63879—31no—
76#63878—31no—
77#63877—31no—
78#63868—31no—
79#63868—31no—
80#63865—31no—
81#63862—31no—
82#63862—31no—
83#63861—31no—
84#63859—31no—
85#63859—31no—
86#63858—31no—
87#63852—31no—
88#63852—31no—
89#63851—31no—
90#63851—31no—
91#63848—31no—
92#63840—31no—
93#63839—31no—
94#63839—31no—
95#63838—31no—
96#63838—31no—
97#63837—31no—
98#63837—31no—
99#63837—31no—
100#63837—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4×C3⋊D3—22no—
118C3×#634—22no—
119#6296—22no—
120#6296—22no—
121#6295—22no—
122#6294—22no—
123#5702—91no—
124#5568—91no—
125#5533—91no—
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×#634C2×D311yescharacteristic
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—61no—
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—31no—
139C2×#627—31no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C32×C42—21no—
147C32×C42—21no—
148C32×C42—21no—
149C32×C42—41no—
150C32×C42C2×D311yescharacteristic
151C32×C42C2×D311yescharacteristic
152C32×C42C2×D311yescharacteristic
153#3752C2×D311yescharacteristic
154#3752C2×D311yescharacteristic
155#3752C2×D311yescharacteristic
156#3752C2×D311yescharacteristic
157#3752C2×D311yescharacteristic
158C4⋊(C3⋊Dic3)C2×D311yescharacteristic
159#3750C2×D311yescharacteristic
160#3750C2×D311yescharacteristic
161#3750C2×D311yescharacteristic
162#3750C2×D311yescharacteristic
163#3750C2×D311yescharacteristic
164#3750C2×D311yescharacteristic
165#3750C2×D311yescharacteristic
166C4×C3⋊Dic3C2×D311yescharacteristic
167C4×C3⋊Dic3C2×D311yescharacteristic
168C4×C3⋊Dic3C2×D311yescharacteristic
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—61no—
180C3×(C2×D3)⋊C4—61no—
181C3×(C2×D3)⋊C4—61no—
182C3×(C2×D3)⋊C4—61no—
183C3×(C2×D3)⋊C4—61no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—61no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
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⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—61no—
202C3×Dic3⋊C4—61no—
203C3×Dic3⋊C4—61no—
204C3×Dic3⋊C4—61no—
205C3×Dic3⋊C4—61no—
206C3×Dic3⋊C4—61no—
207C3×Dic3⋊C4—61no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—61no—
215C3×C4×Dic3—61no—
216C3×C4×Dic3—61no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—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—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
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—
261C33×C4—21no—
262C33×C4—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3#4112yes—
272C3×C3⋊Dic3#4112yes—
273C3×#126—91no—
274C3×C4×Q8—91no—
275C3×#117—91no—
276#947—91no—
277#944—91no—
278C4×#67—91no—
279#924—91no—
280#898—91no—
281#898—91no—
282#898—91no—
283#898—91no—
284#897—91no—
285#896—91no—
286#896—91no—
287#896—91no—
288#893—91no—
289#892—91no—
290#888—91no—
291#888—91no—
292#887—91no—
293#887—91no—
294#887—91no—
295#887—91no—
296#885—91no—
297#885—91no—
298#885—91no—
299#885—91no—
300#67⋊C4—91no—
301#879—91no—
302#879—91no—
303#879—91no—
304#878—91no—
305#877—91no—
306#876—31no—
307#876—31no—
308#876—61no—
309#876—91no—
310#876—91no—
311#875—91no—
312#872—31no—
313#872—31no—
314#872—61no—
315#872—91no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—61no—
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—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—21no—
336C2×C32×C4—21no—
337C2×C32×C4—21no—
338C2×C32×C4—41no—
339C2×C32×C4—41no—
340C2×C32×C4—41no—
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C4×C3⋊D3—22no—
361#634—22no—
362C2×C3×Dic3—31no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
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—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C3×C4×D3—62no—
393C3×C4×D3—62no—
394C3×C4×D3—64no—
395C3×Dic6—62no—
396C3×Dic6—62no—
397C3×Dic6—64no—
398#627—62no—
399#627—62no—
400#627—62no—
401#627—62no—
402#627—62no—
403#627—62no—
404#626—62no—
405#626—62no—
406#625—62no—
407#624—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410#556—271noSylow
411C2×C33C2×#4111yescharacteristic
412C2×C33C2×#4111yescharacteristic
413C2×C332−1+411yescharacteristic
414C3×C3⋊D3—41no—
415C3×C3⋊D3—41no—
416C2×C3×Q8—91no—
417C22×C3×C4—91no—
418C2×#67—91no—
419C2×#67—91no—
420C22×Dic3—91no—
421C2×D12—91no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—61no—
425C2×C4×D3—91no—
426C2×C4×D3—91no—
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—61no—
430C2×Dic6—91no—
431C2×Dic6—91no—
432C2×Dic6—91no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C3×C4⋊C4—91no—
437C3×C4⋊C4—91no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C22⋊C4—91no—
445C3×C22⋊C4—91no—
446C3×C22⋊C4—91no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C42—21no—
450C3×C42—21no—
451C3×C42—21no—
452C3×C42—41no—
453C3×C42—91no—
454C3×C42—91no—
455C3×C42—91no—
456C3×C42D3211yescharacteristic
457C3×C42D3211yescharacteristic
458C3×C42D3211yescharacteristic
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—91no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
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—61no—
475(C2×D3)⋊C4—61no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
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—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—61no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
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—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513Dic3⋊C4—61no—
514Dic3⋊C4—61no—
515Dic3⋊C4—61no—
516Dic3⋊C4—61no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—61no—
532C4×Dic3—61no—
533C4×Dic3—61no—
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—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—41no—
547C22×C32C23×D311yescharacteristic
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C2×C3⋊D3—21no—
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3×D3—62no—
557C2×C3×D3—61no—
558C2×C3×D3—61no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
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—121no—
570C2×C3×D3—121no—
571C2×C3×D3—121no—
572C2×C3×D3—121no—
573C2×C3×D3—121no—
574C32×C4—21no—
575C32×C4—21no—
576C32×C4—21no—
577C32×C4—22no—
578C32×C4—22no—
579C32×C4—22no—
580C32×C4—21no—
581C32×C4—21no—
582C32×C4—21no—
583C32×C4—21no—
584C32×C4—21no—
585C32×C4—21no—
586C32×C4—41no—
587C32×C4—41no—
588C32×C4—41no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—42no—
593C32×C4—42no—
594C32×C4—42no—
595C3⋊Dic3—21no—
596C3⋊Dic3—21no—
597C3⋊Dic3—21no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3#23512yes—
604C3⋊Dic3#23512yes—
605C3×Dic3—32no—
606C3×Dic3—32no—
607C3×Dic3—32no—
608C3×Dic3—32no—
609C3×Dic3—62no—
610C3×Dic3—62no—
611C3×Dic3—62no—
612C3×Dic3—61no—
613C3×Dic3—61no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—121no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3—121no—
634C3×Dic3—121no—
635C4⋊Q8—271no—
636#126—91no—
637#126—271no—
638#126—271no—
639#126—271no—
640#124—271no—
641#124—271no—
642C22⋊Q8—271no—
643C22⋊Q8—271no—
644C4×Q8—91no—
645C4×Q8—271no—
646C4×Q8—271no—
647C4×D4—271no—
648#117—91no—
649#117—271no—
650C33#55611yescharacteristic, complemented, Sylow
651C23×C3—91no—
652C23×C3—91no—
653C22×D3—31no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—31no—
657C22×D3—61no—
658C22×D3—61no—
659C3×Q8—182no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—91no—
678C2×C3×C4—91no—
679C2×C3×C4—91no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—182no—
683C2×C3×C4C2×D3211yescharacteristic
684C2×C3×C4C2×D3211yescharacteristic
685C2×C3×C4C2×D3211yescharacteristic
686C2×C3×C4C2×D3211yescharacteristic
687C2×C3×C4C2×D3211yescharacteristic
688C2×C3×C4C2×D3211yescharacteristic
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—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—182no—
725D12—182no—
726C4×D3—62no—
727C4×D3—62no—
728C4×D3—64no—
729C4×D3—182no—
730C4×D3—182no—
731Dic6—62no—
732Dic6—62no—
733Dic6—64no—
734Dic6—182no—
735Dic6—182no—
736Dic6—182no—
737Dic6—182no—
738Dic6—182no—
739Dic6—182no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32—41no—
752C2×C32C2×#23511yescharacteristic
753C2×C32C2×#23511yescharacteristic
754C2×C32#100711yescharacteristic
755C2×C32D3×#4111yescharacteristic
756C2×C32D3×#4111yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32#101011yescharacteristic
760C2×C32#101011yescharacteristic
761C3⋊D3—41no—
762C3⋊D3—41no—
763C3×D3—122no—
764C3×D3—121no—
765C3×D3—121no—
766C3×D3—121no—
767C3×D3—121no—
768C3×D3—241no—
769C2×Q8—91no—
770C2×Q8—271no—
771C2×Q8—271no—
772C2×D4—271no—
773C22×C4—91no—
774C22×C4—271no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C22⋊C4—91no—
788C22⋊C4—91no—
789C22⋊C4—91no—
790C22⋊C4—91no—
791C22⋊C4—91no—
792C22⋊C4—271no—
793C22⋊C4—271no—
794C22⋊C4—271no—
795C22⋊C4—271no—
796C22⋊C4—271no—
797C42—91no—
798C42—91no—
799C42—91no—
800C42—271no—
801C42—271no—
802C42—271no—
803C42#111311yescharacteristic
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—41no—
808C22×C3—181no—
809C22×C3—181no—
810C22×C3—181no—
811C22×C3—181no—
812C22×C3—181no—
813C22×C3—181no—
814C22×C3C22×D3211yescharacteristic
815C22×C3C22×D3211yescharacteristic
816C22×C3C22×D3211yescharacteristic
817C2×D3—62no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—22no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—41no—
853C3×C4—42no—
854C3×C4—42no—
855C3×C4—42no—
856C3×C4—92no—
857C3×C4—92no—
858C3×C4—181no—
859C3×C4—181no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863C3×C4—181no—
864C3×C4—181no—
865C3×C4—181no—
866Dic3—32no—
867Dic3—32no—
868Dic3—32no—
869Dic3—32no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—61no—
880Dic3—61no—
881Dic3—61no—
882Dic3—61no—
883Dic3—61no—
884Dic3—61no—
885Dic3—61no—
886Dic3—61no—
887Dic3—61no—
888Dic3—61no—
889Dic3—121no—
890Dic3—121no—
891Dic3—121no—
892Dic3—121no—
893Dic3—121no—
894Dic3—121no—
895Dic3—121no—
896C32—21no—
897C32—21no—
898C32—21no—
899C32—41no—
900C32#553311yescharacteristic, complemented
901C32#556811yescharacteristic, complemented
902C32#570211yescharacteristic, complemented
903C23—91no—
904C23—91no—
905Q8—182no—
906Q8—542no—
907Q8—542no—
908D4—542no—
909C2×C4—91no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—91no—
918C2×C4—91no—
919C2×C4—182no—
920C2×C4—542no—
921C2×C4C2×#111311yescharacteristic
922C2×C4C2×#111311yescharacteristic
923C2×C4C2×#111311yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—41no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—361no—
937C2×C3—361no—
938C2×C3#6429711yescharacteristic
939C2×C3#6429711yescharacteristic
940C2×C3#6429811yescharacteristic
941C2×C3D3×#23511yescharacteristic
942C2×C3D3×#23511yescharacteristic
943C2×C3D3×#23511yescharacteristic
944C2×C3D3×#23511yescharacteristic
945C2×C3#6430611yescharacteristic
946C2×C3#6430611yescharacteristic
947D3—122no—
948D3—121no—
949D3—121no—
950D3—121no—
951D3—121no—
952D3—241no—
953C22—181no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22C22×#111311yescharacteristic
960C4—21no—
961C4—21no—
962C4—21no—
963C4—92no—
964C4—92no—
965C4—181no—
966C4—181no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4—181no—
971C4—181no—
972C4—181no—
973C3—21no—
974C3—21no—
975C3—21no—
976C3—41no—
977C3#1059387111yescharacteristic, complemented
978C3#1059393111yescharacteristic, complemented
979C3#1059394011yescharacteristic, complemented
980C2—361no—
981C2—361no—
982C2#1172461411yescharacteristic
983C2#1172461811yescharacteristic
984C2#1172461811yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radicalC2×#6295C22
hypercenterC42#1113
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C3×#64085C2semidirect
2. C3×#64081C2semidirect
3. C3×C4×#634C2semidirect
4. #11723692C2semidirect
6. #11723683C2semidirect
7. #11723676C2semidirect
8. #11723676C2semidirect
9. #11723675C2semidirect
11. #11723671C2semidirect
13. #11723666C2semidirect
14. #11723665C2semidirect
15. #11723665C2semidirect
54. #64085D3semidirect
55. #64081D3semidirect
56. C4×#634D3semidirect
650. C33#556semidirect
900. C32#5533semidirect
901. C32#5568semidirect
902. C32#5702semidirect
977. C3#10593871semidirect
978. C3#10593931semidirect
979. C3#10593940semidirect

Maximal subgroups

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

subgroupindex
C3×#640852
C3×#640812
C3×C4×#6342
#117236922
#117236842
#117236832
#117236762
#117236752
#117236722
#117236712
#117236702
#117236662
#117236652
#105939403
#105939313
#105938713