Finite Group Databasebeta

← #13178314

Subgroups — #13178314

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64105C211yesmaximal, characteristic
2C3×#64098C211yesmaximal, characteristic, complemented
3C3×#64096C211yesmaximal, characteristic, complemented
4#11723692C211yesmaximal, characteristic
5#11723688C211yesmaximal, characteristic
6#11723683C211yesmaximal, characteristic
7#11723683C211yesmaximal, characteristic
8C4×#6294C211yesmaximal, characteristic
9#11723679C211yesmaximal, characteristic, complemented
10#11723671C211yesmaximal, characteristic
11#11723668C211yesmaximal, characteristic, complemented
12#11723666C211yesmaximal, characteristic, complemented
13#11723666C211yesmaximal, characteristic, complemented
14#11723665C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10594398—31nomaximal
17#10594388—31nomaximal
18#10594386—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×#6296C2211yescharacteristic
23C2×#6296C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×C4×C3⋊Dic3C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88813C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64105D311yescharacteristic
55#64098D311yescharacteristic, complemented
56#64096D311yescharacteristic, complemented
57C3×#896—31no—
58C3×#896—31no—
59C3×#896—61no—
60C3×#889—31no—
61C3×#889—31no—
62C3×#889—61no—
63C3×#887—31no—
64C3×#887—31no—
65C3×#887—61no—
66#63899—31no—
67#63896—31no—
68#63895—31no—
69#63893—31no—
70#63888—31no—
71#63887—31no—
72C4×#624—31no—
73#63878—31no—
74#63878—31no—
75#63877—31no—
76#63877—31no—
77C4×D3×Dic3—31no—
78C4×D3×Dic3—31no—
79#63870—31no—
80#63867—31no—
81#63867—31no—
82#63865—31no—
83#63851—31no—
84#63851—31no—
85#63844—31no—
86#63843—31no—
87Dic3×Dic6—31no—
88#63840—31no—
89#63840—31no—
90#63839—31no—
91#63839—31no—
92#63839—31no—
93#63839—31no—
94#63838—31no—
95#63838—31no—
96#63837—31no—
97#63837—31no—
98#63837—31no—
99#63837—31no—
100#63836—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
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—
119C3×#634—22no—
120#6296—22no—
121#6296—22no—
122#6294—22no—
123#6294Q814yescomplemented
124#5688—91no—
125#5622—91no—
126#5578—91no—
127C2×C4×C3⋊D3C2×D311yescharacteristic
128C2×#634C2×D311yescharacteristic
129C2×#634C2×D311yescharacteristic
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—61no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—61no—
138C2×C3×Dic6—61no—
139C2×#627—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—31no—
144C2×#627—31no—
145C2×#624—31no—
146C2×#624—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150C2×D3×Dic3—31no—
151C32×C4⋊C4—21no—
152C32×C4⋊C4—21no—
153C32×C4⋊C4—21no—
154C32×C4⋊C4—41no—
155C32×C4⋊C4C2×D311yescharacteristic
156C32×C4⋊C4C2×D311yescharacteristic
157C32×C4⋊C4C2×D311yescharacteristic
158#3752C2×D311yescharacteristic
159#3752C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic
161#3750C2×D311yescharacteristic
162#3750C2×D311yescharacteristic
163#3750C2×D311yescharacteristic
164#3750C2×D311yescharacteristic
165#3750C2×D311yescharacteristic
166#3750C2×D311yescharacteristic
167#3750C2×D311yescharacteristic
168#3750C2×D311yescharacteristic
169C4×C3⋊Dic3C2×D311yescharacteristic
170C4×C3⋊Dic3C2×D311yescharacteristic
171C4×C3⋊Dic3C2×D311yescharacteristic
172C4×C3⋊Dic3C2×D311yescharacteristic
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×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—61no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
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—61no—
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×Dic3⋊C4—61no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
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—
217C3×C4×Dic3—61no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—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—
235Dic3⋊Dic3—31no—
236#3722—31no—
237#3722—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254C22×C33C2411yescharacteristic
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3C2×Q812yes—
258C33×C4—21no—
259C33×C4—21no—
260C33×C4—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3C2×Q812yes—
269C3×C3⋊Dic3C2×Q812yes—
270C3×C3⋊Dic3#4112yes—
271C3×C3⋊Dic3#4112yes—
272C3×#125—91no—
273C3×C22⋊Q8—91no—
274C3×C4×Q8—91no—
275#946—91no—
276Q8×Dic3—91no—
277#944—91no—
278#944—91no—
279#924—91no—
280C2×C4×Dic3—91no—
281#897—91no—
282#896—31no—
283#896—31no—
284#896—61no—
285#896—91no—
286#896—91no—
287#896—91no—
288#896—91no—
289#892—91no—
290#892—91no—
291#889—31no—
292#889—31no—
293#889—61no—
294#889—91no—
295#889—91no—
296#888—91no—
297#888—91no—
298#888—91no—
299#888—91no—
300#887—31no—
301#887—31no—
302#887—61no—
303#887—91no—
304#887—91no—
305#887—91no—
306#887—91no—
307#887—91no—
308#878—91no—
309#878—91no—
310#877—91no—
311#877—91no—
312#872—91no—
313#872—91no—
314C42×D3—91no—
315C42×D3—91no—
316#870—91no—
317C4×Dic6—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C22×C3⋊D3C22×D311yescharacteristic
321C22×C3×D3—31no—
322C22×C3×D3—31no—
323C22×C3×D3—61no—
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—21no—
333C2×C32×C4—41no—
334C2×C32×C4—41no—
335C2×C32×C4—41no—
336C2×C32×C4C22×D311yescharacteristic
337C2×C32×C4C22×D311yescharacteristic
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C3⋊Dic3C22×D311yescharacteristic
346C2×C3⋊Dic3C22×D311yescharacteristic
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×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
356C4×C3⋊D3—22no—
357#634—22no—
358#634—22no—
359C2×C3×Dic3—31no—
360C2×C3×Dic3—31no—
361C2×C3×Dic3—31no—
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—61no—
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—122no—
395C3×Dic6—62no—
396C3×Dic6—62no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399C3×Dic6—64no—
400C3×Dic6—122no—
401#627—62no—
402#627—62no—
403#627—62no—
404#627—62no—
405#627—62no—
406#627—62no—
407#624—34no—
408#624—62no—
409D3×Dic3—34no—
410D3×Dic3—34no—
411D3×Dic3—62no—
412D3×Dic3—62no—
413#533—271noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C3×C3⋊D3—22no—
418C2×C3×Q8—91no—
419C2×C3×Q8—91no—
420C22×C3×C4—91no—
421C22×Dic3—91no—
422C22×Dic3—91no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—61no—
426C2×C4×D3—91no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—61no—
435C2×Dic6—61no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—91no—
442C3×C4⋊C4—21no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—41no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4D3211yescharacteristic
456C3×C4⋊C4D3211yescharacteristic
457C3×C4⋊C4D3211yescharacteristic
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C42—91no—
461C3×C42—91no—
462C3×C42—91no—
463C3×C42—91no—
464#217—91no—
465#217—91no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—61no—
471(C2×D3)⋊C4—61no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—61no—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481C4⋊Dic3—91no—
482C4⋊Dic3—91no—
483C4⋊Dic3—91no—
484C4⋊Dic3—91no—
485Dic3⋊C4—31no—
486Dic3⋊C4—31no—
487Dic3⋊C4—31no—
488Dic3⋊C4—31no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—31no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—61no—
502Dic3⋊C4—61no—
503Dic3⋊C4—61no—
504Dic3⋊C4—61no—
505Dic3⋊C4—61no—
506Dic3⋊C4—61no—
507Dic3⋊C4—61no—
508Dic3⋊C4—61no—
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—91no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—61no—
530C4×Dic3—61no—
531C4×Dic3—61no—
532C4×Dic3—61no—
533C4×Dic3—91no—
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—91no—
544C4×Dic3—91no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—41no—
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3D3×Q812yes—
555C2×C3×D3—32no—
556C2×C3×D3—32no—
557C2×C3×D3—62no—
558C2×C3×D3—61no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—121no—
563C2×C3×D3—121no—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—41no—
575C32×C4—41no—
576C32×C4—42no—
577C32×C4—41no—
578C32×C4—41no—
579C32×C4—41no—
580C32×C4—41no—
581C32×C4—41no—
582C32×C4—41no—
583C32×C4—81no—
584C32×C4—81no—
585C3⋊Dic3—21no—
586C3⋊Dic3—21no—
587C3⋊Dic3—21no—
588C3⋊Dic3—21no—
589C3⋊Dic3—21no—
590C3⋊Dic3—21no—
591C3⋊Dic3—21no—
592C3⋊Dic3#23512yes—
593C3⋊Dic3#23712yes—
594C3⋊Dic3D3×Q812yes—
595C3⋊Dic3D3×Q812yes—
596C3×Dic3—32no—
597C3×Dic3—32no—
598C3×Dic3—32no—
599C3×Dic3—32no—
600C3×Dic3—32no—
601C3×Dic3—32no—
602C3×Dic3—32no—
603C3×Dic3—32no—
604C3×Dic3—62no—
605C3×Dic3—62no—
606C3×Dic3—62no—
607C3×Dic3—62no—
608C3×Dic3—62no—
609C3×Dic3—61no—
610C3×Dic3—61no—
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—121no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3—121no—
627C3×Dic3—121no—
628C3×Dic3—121no—
629C4⋊Q8—271no—
630C4⋊Q8—271no—
631#125—91no—
632#125—271no—
633C22⋊Q8—91no—
634C22⋊Q8—271no—
635C22⋊Q8—271no—
636C22⋊Q8—271no—
637C4×Q8—91no—
638C4×Q8—271no—
639C4×Q8—271no—
640C4×Q8—271no—
641#117—271no—
642#117—271no—
643C2×C42—271no—
644C33#53311yescharacteristic, complemented, Sylow
645C23×C3—91no—
646C22×D3—31no—
647C22×D3—31no—
648C22×D3—61no—
649C3×Q8—182no—
650C3×Q8—182no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—91no—
664C2×C3×C4—91no—
665C2×C3×C4—91no—
666C2×C3×C4—91no—
667C2×C3×C4—91no—
668C2×C3×C4—91no—
669C2×C3×C4—91no—
670C2×C3×C4—91no—
671C2×C3×C4—91no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—182no—
675C2×C3×C4C2×D3211yescharacteristic
676C2×C3×C4C2×D3211yescharacteristic
677C2×C3×C4C2×D3211yescharacteristic
678C2×C3×C4C2×D3211yescharacteristic
679C2×C3×C4C2×D3211yescharacteristic
680C2×C3×C4C2×D3211yescharacteristic
681C2×C3×C4C2×D3211yescharacteristic
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C2×D3211yescharacteristic
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
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—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—94no—
718C2×Dic3—182no—
719C4×D3—62no—
720C4×D3—62no—
721C4×D3—94no—
722C4×D3—94no—
723C4×D3—122no—
724C4×D3—182no—
725C4×D3—182no—
726Dic6—62no—
727Dic6—62no—
728Dic6—62no—
729Dic6—62no—
730Dic6—64no—
731Dic6—122no—
732Dic6—182no—
733Dic6—182no—
734Dic6—182no—
735Dic6—182no—
736Dic6—182no—
737Dic6—182no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32C2×#23511yescharacteristic
751C2×C32C2×#23711yescharacteristic
752C2×C32C2×D3×Q811yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32D3×#4111yescharacteristic
756C2×C32D3×#4111yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C3⋊D3—22no—
760C3×D3—62no—
761C3×D3—62no—
762C3×D3—122no—
763C2×Q8—91no—
764C2×Q8—91no—
765C2×Q8—271no—
766C2×Q8—271no—
767C22×C4—91no—
768C22×C4—271no—
769C22×C4—271no—
770C4⋊C4—91no—
771C4⋊C4—91no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—271no—
780C4⋊C4—271no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4#111311yescharacteristic
786C22⋊C4—91no—
787C22⋊C4—91no—
788C22⋊C4—271no—
789C22⋊C4—271no—
790C42—91no—
791C42—91no—
792C42—91no—
793C42—91no—
794C42—271no—
795C42—271no—
796C42—271no—
797C42—271no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—41no—
802C22×C3—92no—
803C22×C3—181no—
804C22×C3—181no—
805C22×C3C22×D3211yescharacteristic
806C22×C3C22×D3211yescharacteristic
807C22×C3C22×D3211yescharacteristic
808C2×D3—32no—
809C2×D3—32no—
810C2×D3—62no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—121no—
816C2×D3—121no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—41no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—42no—
836C3×C4—81no—
837C3×C4—81no—
838C3×C4—92no—
839C3×C4—92no—
840C3×C4—92no—
841C3×C4—92no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845C3×C4—181no—
846C3×C4—181no—
847C3×C4—181no—
848C3×C4—181no—
849Dic3—32no—
850Dic3—32no—
851Dic3—32no—
852Dic3—32no—
853Dic3—32no—
854Dic3—32no—
855Dic3—32no—
856Dic3—32no—
857Dic3—62no—
858Dic3—62no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—61no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—121no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—121no—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32#557811yescharacteristic, complemented
887C32#562211yescharacteristic, complemented
888C32#568811yescharacteristic, complemented
889C23—91no—
890Q8—182no—
891Q8—182no—
892Q8—542no—
893Q8—542no—
894C2×C4—91no—
895C2×C4—91no—
896C2×C4—91no—
897C2×C4—91no—
898C2×C4—91no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—182no—
906C2×C4—274no—
907C2×C4—542no—
908C2×C4C2×#111311yescharacteristic
909C2×C4C2×#111311yescharacteristic
910C2×C4C2×#111311yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—41no—
923C2×C3—182no—
924C2×C3D3×#23511yescharacteristic
925C2×C3D3×#23511yescharacteristic
926C2×C3#6430611yescharacteristic
927C2×C3D3×#23711yescharacteristic
928C2×C3D3×#23711yescharacteristic
929C2×C3#6431211yescharacteristic
930C2×C3D32×Q811yescharacteristic
931C2×C3D32×Q811yescharacteristic
932C2×C3D32×Q811yescharacteristic
933D3—62no—
934D3—62no—
935D3—122no—
936C22—92no—
937C22—181no—
938C22—181no—
939C22C22×#111311yescharacteristic
940C4—21no—
941C4—21no—
942C4—21no—
943C4—92no—
944C4—92no—
945C4—92no—
946C4—92no—
947C4—181no—
948C4—181no—
949C4—181no—
950C4—181no—
951C4—181no—
952C4—181no—
953C4—181no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3#1059438611yescharacteristic, complemented
959C3#1059438811yescharacteristic, complemented
960C3#1059439811yescharacteristic, complemented
961C2—182no—
962C2#1172461811yescharacteristic
963C2#1172462211yescharacteristic
964C2Q8×#111311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC4⋊C4#1113
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64098C2semidirect
3. C3×#64096C2semidirect
9. #11723679C2semidirect
11. #11723668C2semidirect
12. #11723666C2semidirect
13. #11723666C2semidirect
14. #11723665C2semidirect
15. #11723665C2semidirect
55. #64098D3semidirect
56. #64096D3semidirect
123. #6294Q8semidirect
644. C33#533semidirect
886. C32#5578semidirect
887. C32#5622semidirect
888. C32#5688semidirect
958. C3#10594386semidirect
959. C3#10594388semidirect
960. C3#10594398semidirect

Maximal subgroups

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

subgroupindex
C3×#641052
C3×#640982
C3×#640962
#117236922
#117236882
#117236832
C4×#62942
#117236792
#117236712
#117236682
#117236662
#117236652
#105943983
#105943883
#105943863