Finite Group Databasebeta

← #13178320

Subgroups — #13178320

Order 1728.

1088 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64105C211yesmaximal, characteristic, complemented
2C3×#64101C211yesmaximal, characteristic, complemented
3C3×#64098C211yesmaximal, characteristic, complemented
4#11723694C211yesmaximal, characteristic
5#11723690C211yesmaximal, characteristic
6#11723688C211yesmaximal, characteristic, complemented
7#11723684C211yesmaximal, characteristic
8#11723683C211yesmaximal, characteristic, complemented
9#11723682C211yesmaximal, characteristic, complemented
10#11723679C211yesmaximal, characteristic, complemented
11#11723676C211yesmaximal, characteristic, complemented
12#11723675C211yesmaximal, characteristic, complemented
13#11723673C211yesmaximal, characteristic, complemented
14#11723669C211yesmaximal, characteristic, complemented
15#11723668C211yesmaximal, characteristic, complemented
16#10594411—31nomaximal
17#10594408—31nomaximal
18#10594334—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×C4×C3⋊Dic3C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64105D311yescharacteristic, complemented
55#64101D311yescharacteristic, complemented
56#64098D311yescharacteristic, complemented
57C3×#896—31no—
58C3×#896—31no—
59C3×#896—61no—
60C3×#892—31no—
61C3×#892—31no—
62C3×#892—61no—
63C3×#889—31no—
64C3×#889—31no—
65C3×#889—61no—
66#63905—31no—
67#63904—31no—
68#63896—31no—
69#63891—31no—
70#63890—31no—
71#63888—31no—
72#63887—31no—
73#63883—31no—
74#63881—31no—
75#63879—31no—
76#63878—31no—
77#63877—31no—
78D3×Dic3⋊C4—31no—
79D3×Dic3⋊C4—31no—
80#63874—31no—
81#63870—31no—
82#63868—31no—
83#63867—31no—
84#63867—31no—
85#63862—31no—
86#63861—31no—
87#63859—31no—
88#63858—31no—
89#63855—31no—
90#63855—31no—
91#63854—31no—
92#63853—31no—
93#63850—31no—
94#63848—31no—
95#63847—31no—
96#63846—31no—
97#63845—31no—
98#63844—31no—
99#63843—31no—
100Dic3×Dic6—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×C4×C3⋊D3—22no—
119C3×#634—22no—
120#6295—22no—
121#6294—22no—
122#6294—22no—
123#5693—91no—
124#5639—91no—
125#5531—91no—
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×C4×C3⋊D3C2×D311yescharacteristic
128C2×#634C2×D311yescharacteristic
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—61no—
134C2×C3×C4×D3—61no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—61no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—21no—
149C32×C4⋊C4—21no—
150C32×C4⋊C4—41no—
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C2×D311yescharacteristic
154#3752C2×D311yescharacteristic
155#3752C2×D311yescharacteristic
156#3752C2×D311yescharacteristic
157#3752C2×D311yescharacteristic
158C4⋊(C3⋊Dic3)C2×D311yescharacteristic
159C4⋊(C3⋊Dic3)C2×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—61no—
178C3×(C2×D3)⋊C4—61no—
179C3×(C2×D3)⋊C4—61no—
180C3×(C2×D3)⋊C4—61no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—61no—
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—61no—
200C3×Dic3⋊C4—61no—
201C3×Dic3⋊C4—61no—
202C3×Dic3⋊C4—61no—
203C3×Dic3⋊C4—61no—
204C3×Dic3⋊C4—61no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—61no—
212C3×C4×Dic3—61no—
213C3×C4×Dic3—61no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
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—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—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—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—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#4112yes—
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—21no—
272C3×C3⋊Dic3#4112yes—
273C3×#125—91no—
274C3×C22⋊Q8—91no—
275C3×#117—91no—
276#946—91no—
277Q8×Dic3—91no—
278#929—91no—
279C4×#67—91no—
280#926—91no—
281C2×Dic3⋊C4—91no—
282#898—91no—
283#898—91no—
284#898—91no—
285#896—31no—
286#896—31no—
287#896—61no—
288#896—91no—
289#894—91no—
290#894—91no—
291#893—91no—
292#892—31no—
293#892—31no—
294#892—61no—
295#892—91no—
296D3×C4⋊C4—91no—
297D3×C4⋊C4—91no—
298#890—91no—
299#889—31no—
300#889—31no—
301#889—61no—
302#889—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#887—91no—
307#886—91no—
308#883—91no—
309#883—91no—
310#67⋊C4—91no—
311#879—91no—
312#879—91no—
313#878—91no—
314#877—91no—
315#876—91no—
316#872—91no—
317#872—91no—
318#872—91no—
319#870—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—
361C4×C3⋊D3—22no—
362#634—22no—
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—31no—
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—
392C2×C3×Dic3—61no—
393C3×C4×D3—62no—
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×C4×D3—64no—
398C3×C4×D3—122no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401C3×Dic6—122no—
402#626—62no—
403#626—62no—
404#625—62no—
405#624—62no—
406#624—62no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411#552—271noSylow
412C2×C33C2×#4111yescharacteristic
413C2×C33C2×#4111yescharacteristic
414C2×C332−1+411yescharacteristic
415C3×C3⋊D3—22no—
416C3×C3⋊D3—41no—
417C2×C3×Q8—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C2×#67—91no—
421C2×#67—91no—
422C22×Dic3—91no—
423C22×Dic3—91no—
424C2×D12—91no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—61no—
430C2×C4×D3—61no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—61no—
438C3×C4⋊C4—21no—
439C3×C4⋊C4—21no—
440C3×C4⋊C4—21no—
441C3×C4⋊C4—41no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4D3211yescharacteristic
451C3×C4⋊C4D3211yescharacteristic
452C3×C4⋊C4D3211yescharacteristic
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C42—91no—
458C3×C42—91no—
459C3×C42—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—61no—
473(C2×D3)⋊C4—61no—
474(C2×D3)⋊C4—61no—
475(C2×D3)⋊C4—61no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
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—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
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—61no—
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513Dic3⋊C4—61no—
514Dic3⋊C4—61no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—61no—
536C4×Dic3—61no—
537C4×Dic3—61no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3⋊D3#23512yes—
557C2×C3×D3—32no—
558C2×C3×D3—32no—
559C2×C3×D3—62no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—61no—
564C2×C3×D3—62no—
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—121no—
572C2×C3×D3—121no—
573C2×C3×D3—121no—
574C2×C3×D3—121no—
575C32×C4—21no—
576C32×C4—22no—
577C32×C4—21no—
578C32×C4—21no—
579C32×C4—21no—
580C32×C4—21no—
581C32×C4—21no—
582C32×C4—21no—
583C32×C4—21no—
584C32×C4—21no—
585C32×C4—41no—
586C32×C4—41no—
587C32×C4—42no—
588C32×C4—41no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—41no—
593C32×C4—41no—
594C32×C4—81no—
595C32×C4—81no—
596C3⋊Dic3—21no—
597C3⋊Dic3—21no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—21no—
605C3⋊Dic3#23712yes—
606C3×Dic3—32no—
607C3×Dic3—32no—
608C3×Dic3—62no—
609C3×Dic3—62no—
610C3×Dic3—62no—
611C3×Dic3—61no—
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—61no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3—121no—
632C3×Dic3—121no—
633C3×Dic3—121no—
634C3×Dic3—121no—
635C3×Dic3—121no—
636#126—271no—
637#126—271no—
638#125—91no—
639#125—271no—
640#125—271no—
641#123—271no—
642#123—271no—
643C22⋊Q8—91no—
644C22⋊Q8—271no—
645C4×Q8—271no—
646C4×D4—271no—
647#117—91no—
648#117—271no—
649#117—271no—
650C2×C4⋊C4—271no—
651C33#55211yescharacteristic, complemented, Sylow
652C23×C3—91no—
653C23×C3—91no—
654C22×D3—31no—
655C22×D3—31no—
656C22×D3—31no—
657C22×D3—31no—
658C22×D3—61no—
659C22×D3—61no—
660C3×Q8—182no—
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—21no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
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—91no—
683C2×C3×C4—182no—
684C2×C3×C4—182no—
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
692C2×C3×C4C2×D3211yescharacteristic
693C2×C3×C4C2×D3211yescharacteristic
694#67—182no—
695#67—182no—
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—31no—
715C2×Dic3—31no—
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—61no—
725C2×Dic3—61no—
726C2×Dic3—182no—
727C2×Dic3—182no—
728D12—182no—
729C4×D3—62no—
730C4×D3—62no—
731C4×D3—62no—
732C4×D3—62no—
733C4×D3—64no—
734C4×D3—122no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—182no—
738C4×D3—182no—
739Dic6—62no—
740Dic6—62no—
741Dic6—122no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—41no—
752C2×C32—41no—
753C2×C32—41no—
754C2×C32C2×#23511yescharacteristic
755C2×C32C2×#23711yescharacteristic
756C2×C32#100711yescharacteristic
757C2×C32#100711yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C2×C32D3×#4111yescharacteristic
761C2×C32D3×#4111yescharacteristic
762C2×C32#101011yescharacteristic
763C3⋊D3—22no—
764C3⋊D3—41no—
765C3×D3—62no—
766C3×D3—62no—
767C3×D3—122no—
768C3×D3—122no—
769C3×D3—121no—
770C3×D3—121no—
771C2×Q8—91no—
772C2×D4—271no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—271no—
776C22×C4—271no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4#111311yescharacteristic
793C22⋊C4—91no—
794C22⋊C4—91no—
795C22⋊C4—91no—
796C22⋊C4—91no—
797C22⋊C4—271no—
798C22⋊C4—271no—
799C22⋊C4—271no—
800C22⋊C4—271no—
801C42—91no—
802C42—91no—
803C42—91no—
804C42—271no—
805C42—271no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—41no—
810C22×C3—92no—
811C22×C3—181no—
812C22×C3—181no—
813C22×C3—181no—
814C22×C3—181no—
815C22×C3—181no—
816C22×C3C22×D3211yescharacteristic
817C22×C3C22×D3211yescharacteristic
818C22×C3C22×D3211yescharacteristic
819C2×D3—32no—
820C2×D3—32no—
821C2×D3—62no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—62no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
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—41no—
854C3×C4—41no—
855C3×C4—42no—
856C3×C4—81no—
857C3×C4—81no—
858C3×C4—92no—
859C3×C4—181no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863C3×C4—181no—
864C3×C4—181no—
865C3×C4—181no—
866C3×C4—181no—
867C3×C4—181no—
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—61no—
890Dic3—61no—
891Dic3—121no—
892Dic3—121no—
893Dic3—121no—
894Dic3—121no—
895Dic3—121no—
896Dic3—121no—
897Dic3—121no—
898C32—21no—
899C32—21no—
900C32—21no—
901C32—41no—
902C32#553111yescharacteristic, complemented
903C32#563911yescharacteristic, complemented
904C32#569311yescharacteristic, complemented
905C23—91no—
906C23—91no—
907Q8—182no—
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—182no—
921C2×C4—542no—
922C2×C4—542no—
923C2×C4C2×#111311yescharacteristic
924C2×C4C2×#111311yescharacteristic
925C2×C4C2×#111311yescharacteristic
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—182no—
939C2×C3—361no—
940C2×C3D3×#23511yescharacteristic
941C2×C3D3×#23511yescharacteristic
942C2×C3#6430611yescharacteristic
943C2×C3D3×#23711yescharacteristic
944C2×C3D3×#23711yescharacteristic
945C2×C3#6431211yescharacteristic
946C2×C3#6431511yescharacteristic
947C2×C3#6431511yescharacteristic
948C2×C3#6431611yescharacteristic
949D3—62no—
950D3—62no—
951D3—122no—
952D3—122no—
953D3—121no—
954D3—121no—
955C22—92no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22C22×#111311yescharacteristic
962C4—21no—
963C4—21no—
964C4—21no—
965C4—92no—
966C4—181no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4—181no—
971C4—181no—
972C4—181no—
973C4—181no—
974C4—181no—
975C3—21no—
976C3—21no—
977C3—21no—
978C3—41no—
979C3#1059433411yescharacteristic, complemented
980C3#1059440811yescharacteristic, complemented
981C3#1059441111yescharacteristic, complemented
982C2—182no—
983C2—361no—
984C2#1172461811yescharacteristic
985C2#1172462211yescharacteristic
986C2#1172462411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×#6295C22
hypercenterC4⋊C4#1113
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64105C2semidirect
2. C3×#64101C2semidirect
3. C3×#64098C2semidirect
6. #11723688C2semidirect
8. #11723683C2semidirect
9. #11723682C2semidirect
10. #11723679C2semidirect
11. #11723676C2semidirect
12. #11723675C2semidirect
13. #11723673C2semidirect
14. #11723669C2semidirect
15. #11723668C2semidirect
54. #64105D3semidirect
55. #64101D3semidirect
56. #64098D3semidirect
651. C33#552semidirect
902. C32#5531semidirect
903. C32#5639semidirect
904. C32#5693semidirect
979. C3#10594334semidirect
980. C3#10594408semidirect
981. C3#10594411semidirect

Maximal subgroups

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

subgroupindex
C3×#641052
C3×#641012
C3×#640982
#117236942
#117236902
#117236882
#117236842
#117236832
#117236822
#117236792
#117236762
#117236752
#117236732
#117236692
#117236682
#105944113
#105944083
#105943343