Finite Group Databasebeta

← #13168350

Subgroups — #13168350

Order 1728.

1048 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic
2#11723418C211yesmaximal, characteristic
3#11723401C211yesmaximal, characteristic, complemented
4#11723394C211yesmaximal, characteristic, complemented
5C3×#63883C211yesmaximal, characteristic
6C3×#63845C211yesmaximal, characteristic, complemented
7C3×#63840C211yesmaximal, characteristic, complemented
8#11723037C211yesmaximal, characteristic, complemented
9#11723033C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11723012C211yesmaximal, characteristic, complemented
12#11722972C211yesmaximal, characteristic
13#11722970C211yesmaximal, characteristic
14#11722915C211yesmaximal, characteristic
15#11722915C211yesmaximal, characteristic
16#10594400—31nomaximal
17#10594344—31nomaximal
18#10594342—31nomaximal
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26#88857C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64099—31no—
56#64097—31no—
57C3×D3×C4⋊C4—31no—
58C3×D3×C4⋊C4—31no—
59C3×#890—31no—
60C3×#889—31no—
61C3×#888—31no—
62C3×#888—31no—
63#63919—31no—
64#63918—31no—
65#63895—31no—
66#63888—31no—
67#63883D311yescharacteristic
68#63872—31no—
69#63871—31no—
70#63869—31no—
71#63867—31no—
72#63866—31no—
73#63857—31no—
74#63857—31no—
75#63856—31no—
76#63856—31no—
77#63855—31no—
78#63855—31no—
79#63851—31no—
80#63851—31no—
81#63851—31no—
82#63851—31no—
83#63851—61no—
84#63846—31no—
85#63846—31no—
86#63846—31no—
87#63846—31no—
88#63846—61no—
89#63845—31no—
90#63845D311yescharacteristic, complemented
91#63841—31no—
92#63841—31no—
93#63840—31no—
94#63840—31no—
95#63840D311yescharacteristic, complemented
96#63839—31no—
97#63839—31no—
98#63839—31no—
99#63839—61no—
100#63836—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4×C3⋊D3—41no—
112C3×#634—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6293—41no—
120#6293—41no—
121C3×#627—41no—
122C3×#624—41no—
123C3×#624Q814yescomplemented
124#5729—91no—
125#5689—91no—
126#5500—91no—
127C2×C4×C3⋊D3C2×D311yescharacteristic
128C2×#634—31no—
129C2×#634—31no—
130C2×#634C2×D311yescharacteristic
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—61no—
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—61no—
143C2×#627—31no—
144C2×#627—31no—
145C2×#627—31no—
146C2×#627—31no—
147C2×#627—61no—
148C2×#627—61no—
149C2×#627C2×D311yescharacteristic
150C2×#624C2×D311yescharacteristic
151C2×#624C2×D311yescharacteristic
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4—31no—
155#3752—31no—
156#3752—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—61no—
168#3750—61no—
169#3750—61no—
170#3750—121no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—61no—
182C3×Dic3⋊C4—21no—
183C3×Dic3⋊C4—21no—
184C3×Dic3⋊C4—21no—
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⋊C4C2×D311yescharacteristic
194C3×Dic3⋊C4C2×D311yescharacteristic
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×Dic3⋊C4C2×D311yescharacteristic
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—61no—
208#3724C2×D311yescharacteristic
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234#3722—31no—
235#3722—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—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3C2×Q812yes—
258C33×C4—21no—
259C3⋊(C3⋊Dic3)—21no—
260C3⋊(C3⋊Dic3)—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3C2×Q812yes—
271C32×Dic3C2×Q812yes—
272C3×C4⋊Q8—91no—
273C3×#125—91no—
274C2×C3×C4⋊C4—91no—
275#946—91no—
276#946—91no—
277#944—91no—
278#944—91no—
279#926—91no—
280#926—91no—
281#924—91no—
282#924—91no—
283#924—91no—
284#924—91no—
285#897—91no—
286#897—91no—
287#896—91no—
288#896—91no—
289#896—91no—
290#896—91no—
291#896—181no—
292#892—91no—
293#892—91no—
294D3×C4⋊C4—31no—
295D3×C4⋊C4—31no—
296#890—31no—
297#890—91no—
298#890—91no—
299#890—91no—
300#890—91no—
301#890—91no—
302#890—181no—
303#889—31no—
304#889—91no—
305#889—91no—
306#889—91no—
307#888—31no—
308#888—31no—
309#888—91no—
310#888—91no—
311#888—91no—
312#888—91no—
313#888—91no—
314#888—91no—
315#888—181no—
316#872—91no—
317#872—91no—
318#870—91no—
319#869—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—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—41no—
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—121no—
350C2×C3⋊Dic3—121no—
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C4×C3⋊D3—41no—
357#634—41no—
358#634—121no—
359#634—121no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
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—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
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
393C3×C4×D3—34no—
394C3×C4×D3—34no—
395C3×C4×D3—121no—
396C3×C4×D3—121no—
397C3×C4×D3—121no—
398C3×C4×D3—121no—
399C3×C4×D3—122no—
400C3×Dic6—121no—
401C3×Dic6—121no—
402C3×Dic6—121no—
403C3×Dic6—121no—
404C3×Dic6—122no—
405#627—41no—
406#627—121no—
407#627—121no—
408#627—121no—
409#627—121no—
410#627—122no—
411#627—122no—
412#624—41no—
413#624Dic614yescomplemented
414#544—271noSylow
415C2×C33C22×Q811yescharacteristic
416C2×C33H(5,𝔽2)11yescharacteristic
417C2×C332−1+411yescharacteristic
418C3×C3⋊D3—22no—
419C2×C3×Q8—91no—
420C2×C3×Q8—91no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
423C22×C3×C4—91no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—61no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—61no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—91no—
442C2×Dic6—181no—
443C2×Dic6—181no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—61no—
451C3×C4⋊C4—61no—
452C3×C4⋊C4—61no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C4⋊C4—91no—
458C3×C4⋊C4—91no—
459C3×C4⋊C4—91no—
460C3×C4⋊C4—91no—
461C3×C42—91no—
462C3×C42—91no—
463#217—91no—
464#217—91no—
465#217—91no—
466#217—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—181no—
476(C2×D3)⋊C4—181no—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—181no—
497C4⋊Dic3—181no—
498C4⋊Dic3—181no—
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—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—181no—
525Dic3⋊C4—181no—
526Dic3⋊C4—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—361no—
531Dic3⋊C4D3211yescharacteristic
532Dic3⋊C4D3211yescharacteristic
533Dic3⋊C4D3211yescharacteristic
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—181no—
545C4×Dic3—181no—
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⋊D3C2×Dic612yes—
556C2×C3×D3—32no—
557C2×C3×D3—32no—
558C2×C3×D3—62no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—121no—
564C2×C3×D3—121no—
565C32×C4—21no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—32no—
569C32×C4—32no—
570C32×C4—41no—
571C32×C4—41no—
572C32×C4—41no—
573C32×C4—61no—
574C32×C4—61no—
575C32×C4—61no—
576C32×C4—61no—
577C32×C4—81no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—21no—
581C3⋊Dic3—21no—
582C3⋊Dic3—21no—
583C3⋊Dic3—61no—
584C3⋊Dic3—62no—
585C3⋊Dic3—61no—
586C3⋊Dic3—61no—
587C3⋊Dic3—61no—
588C3⋊Dic3—61no—
589C3⋊Dic3—61no—
590C3⋊Dic3—121no—
591C3⋊Dic3—121no—
592C3⋊Dic3—122no—
593C3⋊Dic3—121no—
594C3⋊Dic3—121no—
595C3⋊Dic3—121no—
596C3⋊Dic3—241no—
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—22no—
606C3×Dic3—22no—
607C3×Dic3—41no—
608C3×Dic3—41no—
609C3×Dic3—41no—
610C3×Dic3—41no—
611C3×Dic3—62no—
612C3×Dic3—62no—
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×Dic3C2×Dic612yes—
627C3×Dic3C2×Dic612yes—
628C3×Dic3D3×Q812yes—
629C3×Dic3D3×Q812yes—
630C4⋊Q8—91no—
631C4⋊Q8—271no—
632C4⋊Q8—271no—
633C4⋊Q8—271no—
634#125—91no—
635#125—271no—
636#125—271no—
637#125—271no—
638C22⋊Q8—271no—
639C22⋊Q8—271no—
640C22⋊Q8—271no—
641C22⋊Q8—271no—
642#117—271no—
643#117—271no—
644C2×C4⋊C4—91no—
645C33#54411yescharacteristic, complemented, Sylow
646C23×C3—91no—
647C22×D3—31no—
648C22×D3—31no—
649C22×D3—61no—
650C3×Q8—361no—
651C3×Q8—361no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—41no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—94no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—91no—
678C2×C3×C4—91no—
679C2×C3×C4—91no—
680C2×C3×C4—361no—
681C2×C3×C4—361no—
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C2×D3211yescharacteristic
684C2×C3×C4C2×D3211yescharacteristic
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—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—91no—
701C2×Dic3—91no—
702C2×Dic3—91no—
703C2×Dic3—91no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—181no—
707C2×Dic3—181no—
708C2×Dic3—181no—
709C2×Dic3—181no—
710C2×Dic3—181no—
711C2×Dic3—181no—
712C2×Dic3—361no—
713C2×Dic3—361no—
714C2×Dic3C2×D3211yescharacteristic
715C2×Dic3C2×D3211yescharacteristic
716C2×Dic3C2×D3211yescharacteristic
717C2×Dic3C2×D3211yescharacteristic
718C2×Dic3C2×D3211yescharacteristic
719C2×Dic3C2×D3211yescharacteristic
720C4×D3—34no—
721C4×D3—34no—
722C4×D3—121no—
723C4×D3—121no—
724C4×D3—121no—
725C4×D3—121no—
726C4×D3—122no—
727Dic6—121no—
728Dic6—121no—
729Dic6—121no—
730Dic6—121no—
731Dic6—122no—
732Dic6—361no—
733Dic6—361no—
734Dic6—361no—
735Dic6—361no—
736Dic6—361no—
737Dic6—361no—
738Dic6—362no—
739Dic6—362no—
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×C32C22×Dic611yescharacteristic
753C2×C32#100411yescharacteristic
754C2×C32#100411yescharacteristic
755C2×C32C2×D3×Q811yescharacteristic
756C2×C32C2×D3×Q811yescharacteristic
757C2×C32#100711yescharacteristic
758C2×C32#100711yescharacteristic
759C2×C32#100911yescharacteristic
760C2×C32#101011yescharacteristic
761C3⋊D3—22no—
762C3×D3—62no—
763C3×D3—62no—
764C3×D3—122no—
765C2×Q8—91no—
766C2×Q8—91no—
767C2×Q8—271no—
768C2×Q8—271no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C4⋊C4—31no—
773C4⋊C4—31no—
774C4⋊C4—31no—
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—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C22⋊C4—271no—
793C22⋊C4—271no—
794C22⋊C4—271no—
795C22⋊C4—271no—
796C42—91no—
797C42—91no—
798C42—271no—
799C42—271no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—41no—
804C22×C3—92no—
805C22×C3—181no—
806C22×C3—181no—
807C22×C3C22×D3211yescharacteristic
808C22×C3C22×D3211yescharacteristic
809C22×C3C22×D3211yescharacteristic
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—62no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—121no—
818C2×D3—121no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—32no—
823C3×C4—32no—
824C3×C4—32no—
825C3×C4—32no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—61no—
838C3×C4—61no—
839C3×C4—81no—
840C3×C4—121no—
841C3×C4—121no—
842C3×C4—121no—
843C3×C4—121no—
844C3×C4—181no—
845C3×C4—181no—
846C3×C4—181no—
847C3×C4—181no—
848C3×C4—181no—
849Dic3—21no—
850Dic3—21no—
851Dic3—21no—
852Dic3—21no—
853Dic3—62no—
854Dic3—62no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—121no—
866Dic3—121no—
867Dic3—121no—
868Dic3—182no—
869Dic3—181no—
870Dic3—181no—
871Dic3—181no—
872Dic3—181no—
873Dic3—181no—
874Dic3—181no—
875Dic3—361no—
876Dic3—361no—
877Dic3—361no—
878Dic3—361no—
879Dic3—361no—
880Dic3—362no—
881Dic3—721no—
882Dic3D3×Dic612yes—
883Dic3D3×Dic612yes—
884C32—21no—
885C32—21no—
886C32—21no—
887C32—41no—
888C32#550011yescharacteristic, complemented
889C32#568911yescharacteristic, complemented
890C32#572911yescharacteristic, complemented
891C23—91no—
892Q8—361no—
893Q8—361no—
894Q8—1081no—
895Q8—1081no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—31no—
900C2×C4—31no—
901C2×C4—31no—
902C2×C4—94no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—91no—
907C2×C4—91no—
908C2×C4—271no—
909C2×C4—271no—
910C2×C4—361no—
911C2×C4—361no—
912C2×C4D3311yescharacteristic
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—182no—
926C2×C3C2×D3×Dic611yescharacteristic
927C2×C3C2×D3×Dic611yescharacteristic
928C2×C3#6429711yescharacteristic
929C2×C3#6431311yescharacteristic
930C2×C3#6431411yescharacteristic
931C2×C3#6431411yescharacteristic
932C2×C3#6431511yescharacteristic
933C2×C3#6431611yescharacteristic
934C2×C3D32×Q811yescharacteristic
935D3—62no—
936D3—62no—
937D3—122no—
938C22—92no—
939C22—181no—
940C22—181no—
941C22C2×D3311yescharacteristic
942C4—21no—
943C4—32no—
944C4—32no—
945C4—61no—
946C4—61no—
947C4—61no—
948C4—61no—
949C4—181no—
950C4—181no—
951C4—181no—
952C4—181no—
953C4—181no—
954C4—541no—
955C4—541no—
956C3—21no—
957C3—21no—
958C3—21no—
959C3—41no—
960C3#1059434211yescharacteristic, complemented
961C3#1059434411yescharacteristic, complemented
962C3#1059440011yescharacteristic, complemented
963C2—182no—
964C2D32×Dic611yescharacteristic
965C2#1172439711yescharacteristic
966C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#544
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723401C2semidirect
4. #11723394C2semidirect
6. C3×#63845C2semidirect
7. C3×#63840C2semidirect
8. #11723037C2semidirect
9. #11723033C2semidirect
10. #11723013C2semidirect
11. #11723012C2semidirect
90. #63845D3semidirect
95. #63840D3semidirect
123. C3×#624Q8semidirect
413. #624Dic6semidirect
645. C33#544semidirect
888. C32#5500semidirect
889. C32#5689semidirect
890. C32#5729semidirect
960. C3#10594342semidirect
961. C3#10594344semidirect
962. C3#10594400semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117234182
#117234012
#117233942
C3×#638832
C3×#638452
C3×#638402
#117230372
#117230332
#117230132
#117230122
#117229722
#117229702
#117229152
#105944003
#105943443
#105943423