Finite Group Databasebeta

← #13178191

Subgroups — #13178191

Order 1728.

1342 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic
2C2×#89040C211yesmaximal, characteristic, complemented
3C3×#64094C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C3×#64087C211yesmaximal, characteristic, complemented
6#11723724C211yesmaximal, characteristic, complemented
7#11723721C211yesmaximal, characteristic, complemented
8#11723718C211yesmaximal, characteristic, complemented
9C4⋊#6296C211yesmaximal, characteristic, complemented
10#11723694C211yesmaximal, characteristic, complemented
11#11723692C211yesmaximal, characteristic, complemented
12#11723690C211yesmaximal, characteristic, complemented
13#11723688C211yesmaximal, characteristic, complemented
14#11723683C211yesmaximal, characteristic, complemented
15#11723666C211yesmaximal, characteristic, complemented
16#10594070—31nomaximal
17#10594057—31nomaximal
18#10594056—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×#634C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic
25C2×#6296C2211yescharacteristic
26C2×#6296C2211yescharacteristic
27C2×#6296C2211yescharacteristic
28C2×#6295C2211yescharacteristic
29#89046—24no—
30C2×#6294C2211yescharacteristic
31C2×#6294C2211yescharacteristic
32C2×#6294C2211yescharacteristic
33#89040—24no—
34C33×C22⋊C4C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45C3×#3750C2211yescharacteristic
46C3×C4×C3⋊Dic3C2211yescharacteristic
47#88815C2211yescharacteristic
48#88815C2211yescharacteristic
49#88815C2211yescharacteristic
50#88815C2211yescharacteristic
51#88815C2211yescharacteristic
52#88814C2211yescharacteristic
53#88814C2211yescharacteristic
54#88814C2211yescharacteristic
55#88813C2211yescharacteristic
56C2×#3805—31no—
57C2×#3804—31no—
58C2×#3804—31no—
59C2×#3797—31no—
60C2×D3×Dic6—31no—
61C2×D3×Dic6—31no—
62#64094D311yescharacteristic, complemented
63#64092D311yescharacteristic, complemented
64#64087D311yescharacteristic, complemented
65C3×#885—31no—
66C3×#885—31no—
67C3×#885—61no—
68C3×#883—31no—
69C3×#883—31no—
70C3×#883—61no—
71C3×#878—31no—
72C3×#878—31no—
73C3×#878—61no—
74#63982—31no—
75#63975—31no—
76#63969—31no—
77#63969—31no—
78#63964—31no—
79#63964—31no—
80#63959—31no—
81#63959—31no—
82#63953—31no—
83#63919—31no—
84#63918—31no—
85#63918—31no—
86#63905—31no—
87#63899—31no—
88#63896—31no—
89#63895—31no—
90#63893—31no—
91#63891—31no—
92#63890—31no—
93#63888—31no—
94#63887—31no—
95#63878—31no—
96#63877—31no—
97#63854—31no—
98#63853—31no—
99#63850—31no—
100#63840—31no—
101#63839—31no—
102#63839—31no—
103#63836—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C3×#638—22no—
110C3×#638—22no—
111C2×C3×C3⋊Dic3—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C3×C4×C3⋊D3—22no—
123C3×#634—22no—
124C3×#634—22no—
125#6296—22no—
126#6296—22no—
127#6296—22no—
128#6295—22no—
129#6294—22no—
130#6294—22no—
131#6294D414yes—
132#5675—91no—
133#5648—91no—
134#5628—91no—
135C2×#638C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3C2×D311yescharacteristic
138C2×C4×C3⋊D3C2×D311yescharacteristic
139C2×#634C2×D311yescharacteristic
140C2×#634C2×D311yescharacteristic
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C2×C3×#67—61no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—61no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—61no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—61no—
158C2×C3×Dic6—61no—
159C2×#627—31no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#627—31no—
164C2×#627—31no—
165C2×#627—31no—
166C2×#627—31no—
167C2×#627—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#625—31no—
171C2×#624—31no—
172C2×#624—31no—
173C2×#624—31no—
174#3805—64no—
175#3804—64no—
176#3804—64no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183#3797—64no—
184D3×Dic6—64no—
185D3×Dic6—64no—
186C32×C22⋊C4—21no—
187C32×C22⋊C4—21no—
188C32×C22⋊C4—21no—
189C32×C22⋊C4—41no—
190C32×C22⋊C4C2×D311yescharacteristic
191C32×C22⋊C4C2×D311yescharacteristic
192C32×C22⋊C4C2×D311yescharacteristic
193#3757C2×D311yescharacteristic
194#3757C2×D311yescharacteristic
195#3757C2×D311yescharacteristic
196#3752C2×D311yescharacteristic
197#3752C2×D311yescharacteristic
198#3752C2×D311yescharacteristic
199C4⋊(C3⋊Dic3)C2×D311yescharacteristic
200C4⋊(C3⋊Dic3)C2×D311yescharacteristic
201#3750C2×D311yescharacteristic
202#3750C2×D311yescharacteristic
203#3750C2×D311yescharacteristic
204C4×C3⋊Dic3C2×D311yescharacteristic
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—61no—
212C3×#217—61no—
213C3×#217—61no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—61no—
221C3×(C2×D3)⋊C4—61no—
222C3×(C2×D3)⋊C4—61no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×C4⋊Dic3—61no—
228C3×C4⋊Dic3—61no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—61no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4—61no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—61no—
241#3724—31no—
242#3724—31no—
243#3724—31no—
244#3724—31no—
245#3724—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265Dic32—31no—
266Dic32—31no—
267Dic32—31no—
268C22×C33—21no—
269C22×C33—21no—
270C22×C33—21no—
271C22×C33C2411yescharacteristic
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3C2×D412yes—
278C33×C4—21no—
279C33×C4—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3C2×D412yes—
289C3×C3⋊Dic3C2×D412yes—
290C2×D3×Q8—91no—
291C2×D3×Q8—91no—
292C2×#237—91no—
293C2×#237—91no—
294C2×#235—91no—
295C22×Dic6—91no—
296C3×#124—91no—
297C3×#123—91no—
298C3×C22⋊Q8—91no—
299#946—91no—
300#944—91no—
301#936—91no—
302#935—91no—
303#929—91no—
304#924—91no—
305#897—91no—
306#896—91no—
307#896—91no—
308#894—91no—
309#894—91no—
310#892—91no—
311#888—91no—
312#888—91no—
313#888—91no—
314#888—91no—
315#886—91no—
316#885—31no—
317#885—31no—
318#885—61no—
319#885—91no—
320#885—91no—
321#883—31no—
322#883—31no—
323#883—61no—
324#883—91no—
325#883—91no—
326#883—91no—
327#883—91no—
328#878—31no—
329#878—31no—
330#878—61no—
331#878—91no—
332#878—91no—
333#878—91no—
334#878—91no—
335#877—91no—
336#872—91no—
337#869—91no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—21no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—41no—
360C2×C32×C4—41no—
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363C2×C32×C4C22×D311yescharacteristic
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367#638—22no—
368#638—22no—
369C2×C3⋊Dic3—22no—
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C4×C3⋊D3—22no—
381#634—22no—
382#634—22no—
383C3×#67—62no—
384C3×#67—62no—
385C3×#67—62no—
386C3×#67—62no—
387C3×#67—122no—
388C3×#67—122no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—62no—
420C2×C3×Dic3—62no—
421C2×C3×Dic3—122no—
422C3×C4×D3—62no—
423C3×C4×D3—62no—
424C3×C4×D3—122no—
425C3×Dic6—62no—
426C3×Dic6—62no—
427C3×Dic6—62no—
428C3×Dic6—62no—
429C3×Dic6—122no—
430C3×Dic6—122no—
431#627—62no—
432#627—62no—
433#627—62no—
434#627—62no—
435#627—62no—
436#627—62no—
437#627—62no—
438#627—62no—
439#627—62no—
440#626—62no—
441#626—62no—
442#625—62no—
443#624—34no—
444#624—62no—
445#624—62no—
446D3×Dic3—34no—
447D3×Dic3—34no—
448D3×Dic3—62no—
449D3×Dic3—62no—
450D3×Dic3—62no—
451D3×Dic3—62no—
452#536—271noSylow
453C2×C33—41no—
454C2×C33C22×D411yescharacteristic
455C2×C332−1+411yescharacteristic
456C2×C332−1+411yescharacteristic
457C3×C3⋊D3—22no—
458C3×C3⋊D3—41no—
459C2×C3×Q8—91no—
460C2×C3×Q8—91no—
461C2×C3×D4—91no—
462C2×C3×D4—91no—
463C22×C3×C4—91no—
464C22×C3×C4—91no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—61no—
470C2×#67—61no—
471C2×#67—91no—
472C2×#67—91no—
473C22×Dic3—31no—
474C22×Dic3—31no—
475C22×Dic3—61no—
476C22×Dic3—91no—
477C22×Dic3—91no—
478C22×Dic3—91no—
479D3×Q8—184no—
480D3×Q8—184no—
481#237—184no—
482#237—184no—
483#235—184no—
484C2×D12—91no—
485C2×C4×D3—31no—
486C2×C4×D3—31no—
487C2×C4×D3—61no—
488C2×C4×D3—91no—
489C2×C4×D3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—91no—
493C2×C4×D3—91no—
494C2×Dic6—31no—
495C2×Dic6—31no—
496C2×Dic6—31no—
497C2×Dic6—31no—
498C2×Dic6—61no—
499C2×Dic6—61no—
500C2×Dic6—91no—
501C2×Dic6—91no—
502C2×Dic6—91no—
503C2×Dic6—91no—
504C2×Dic6—91no—
505C2×Dic6—91no—
506C2×Dic6—91no—
507C2×Dic6—91no—
508C2×Dic6—91no—
509C2×Dic6—184no—
510C3×C4⋊C4—91no—
511C3×C4⋊C4—91no—
512C3×C4⋊C4—91no—
513C3×C4⋊C4—91no—
514C3×C4⋊C4—91no—
515C3×C22⋊C4—21no—
516C3×C22⋊C4—21no—
517C3×C22⋊C4—21no—
518C3×C22⋊C4—41no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4D3211yescharacteristic
526C3×C22⋊C4D3211yescharacteristic
527C3×C22⋊C4D3211yescharacteristic
528C3×C42—91no—
529#217—31no—
530#217—31no—
531#217—31no—
532#217—31no—
533#217—31no—
534#217—31no—
535#217—61no—
536#217—61no—
537#217—61no—
538#217—91no—
539#217—91no—
540#217—91no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—61no—
548(C2×D3)⋊C4—61no—
549(C2×D3)⋊C4—61no—
550(C2×D3)⋊C4—91no—
551(C2×D3)⋊C4—91no—
552(C2×D3)⋊C4—91no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556C4⋊Dic3—31no—
557C4⋊Dic3—31no—
558C4⋊Dic3—31no—
559C4⋊Dic3—31no—
560C4⋊Dic3—61no—
561C4⋊Dic3—61no—
562C4⋊Dic3—91no—
563C4⋊Dic3—91no—
564C4⋊Dic3—91no—
565C4⋊Dic3—91no—
566C4⋊Dic3—91no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—61no—
574Dic3⋊C4—61no—
575Dic3⋊C4—61no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586C4×Dic3—31no—
587C4×Dic3—31no—
588C4×Dic3—61no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C22×C32—21no—
593C22×C32—22no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—41no—
606C22×C32—41no—
607C22×C32—41no—
608C22×C32—42no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—81no—
616C22×C32—81no—
617C22×C32C23×D311yescharacteristic
618C22×C32C23×D311yescharacteristic
619C22×C32C23×D311yescharacteristic
620C2×C3⋊D3—21no—
621C2×C3⋊D3—21no—
622C2×C3⋊D3—21no—
623C2×C3⋊D3—21no—
624C2×C3⋊D3—21no—
625C2×C3⋊D3D3×D412yes—
626C2×C3×D3—32no—
627C2×C3×D3—32no—
628C2×C3×D3—62no—
629C2×C3×D3—61no—
630C2×C3×D3—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C32×C4—21no—
645C32×C4—21no—
646C32×C4—21no—
647C32×C4—21no—
648C32×C4—21no—
649C32×C4—21no—
650C32×C4—41no—
651C32×C4—41no—
652C32×C4—41no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—41no—
656C32×C4—81no—
657C32×C4—81no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3⋊Dic3—21no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3D3×D412yes—
667C3⋊Dic3D3×D412yes—
668C3×Dic3—32no—
669C3×Dic3—32no—
670C3×Dic3—32no—
671C3×Dic3—32no—
672C3×Dic3—62no—
673C3×Dic3—62no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3—121no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C2×#41—271no—
699C22×Q8—271no—
700C4⋊Q8—271no—
701C4⋊Q8—271no—
702#124—91no—
703#124—271no—
704#123—91no—
705#123—271no—
706#123—271no—
707#123—271no—
708C22⋊Q8—91no—
709C22⋊Q8—271no—
710C22⋊Q8—271no—
711C22⋊Q8—271no—
712#117—271no—
713C33#53611yescharacteristic, complemented, Sylow
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—41no—
718C23×C3—91no—
719C23×C3—91no—
720C23×C3C2×D3211yescharacteristic
721C23×C3C2×D3211yescharacteristic
722C23×C3C2×D3211yescharacteristic
723C22×D3—31no—
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—31no—
727C22×D3—61no—
728C22×D3—61no—
729C3×Q8—182no—
730C3×Q8—182no—
731C3×D4—182no—
732C3×D4—182no—
733C2×C3×C4—21no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—41no—
740C2×C3×C4—41no—
741C2×C3×C4—91no—
742C2×C3×C4—91no—
743C2×C3×C4—91no—
744C2×C3×C4—91no—
745C2×C3×C4—91no—
746C2×C3×C4—91no—
747C2×C3×C4—91no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—182no—
752C2×C3×C4—182no—
753C2×C3×C4C2×D3211yescharacteristic
754C2×C3×C4C2×D3211yescharacteristic
755C2×C3×C4C2×D3211yescharacteristic
756C2×C3×C4C2×D3211yescharacteristic
757C2×C3×C4C2×D3211yescharacteristic
758C2×C3×C4C2×D3211yescharacteristic
759#67—62no—
760#67—62no—
761#67—62no—
762#67—62no—
763#67—122no—
764#67—122no—
765#67—182no—
766#67—182no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—31no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—61no—
788C2×Dic3—61no—
789C2×Dic3—61no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—61no—
795C2×Dic3—61no—
796C2×Dic3—61no—
797C2×Dic3—62no—
798C2×Dic3—62no—
799C2×Dic3—94no—
800C2×Dic3—122no—
801C2×Dic3—182no—
802C2×Dic3—182no—
803D12—182no—
804C4×D3—62no—
805C4×D3—62no—
806C4×D3—94no—
807C4×D3—94no—
808C4×D3—122no—
809C4×D3—182no—
810C4×D3—182no—
811C4×D3—182no—
812C4×D3—182no—
813Dic6—62no—
814Dic6—62no—
815Dic6—62no—
816Dic6—62no—
817Dic6—122no—
818Dic6—122no—
819Dic6—182no—
820Dic6—182no—
821Dic6—182no—
822Dic6—182no—
823Dic6—182no—
824Dic6—182no—
825Dic6—182no—
826Dic6—182no—
827Dic6—182no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—41no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—42no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—81no—
845C2×C32—81no—
846C2×C32—82no—
847C2×C32C2×D3×D411yescharacteristic
848C2×C32C2×D3×D411yescharacteristic
849C2×C32C2×D3×D411yescharacteristic
850C2×C32#100711yescharacteristic
851C2×C32#101011yescharacteristic
852C2×C32#101011yescharacteristic
853C2×C32#101011yescharacteristic
854C2×C32#101011yescharacteristic
855C2×C32#101011yescharacteristic
856C3⋊D3—22no—
857C3⋊D3—41no—
858C3×D3—62no—
859C3×D3—62no—
860C3×D3—122no—
861C3×D3—121no—
862C3×D3—121no—
863C3×D3—241no—
864#41—544no—
865C2×Q8—91no—
866C2×Q8—91no—
867C2×Q8—271no—
868C2×Q8—271no—
869C2×Q8—271no—
870C2×Q8—544no—
871C2×D4—91no—
872C2×D4—91no—
873C2×D4—271no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—271no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—271no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C4⋊C4—271no—
888C4⋊C4—271no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4#111311yescharacteristic
899C42—91no—
900C42—271no—
901C22×C3—22no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—42no—
923C22×C3—41no—
924C22×C3—81no—
925C22×C3—81no—
926C22×C3—92no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3C22×D3211yescharacteristic
933C22×C3C22×D3211yescharacteristic
934C22×C3C22×D3211yescharacteristic
935C2×D3—32no—
936C2×D3—32no—
937C2×D3—62no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—121no—
949C2×D3—121no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3—121no—
953C3×C4—21no—
954C3×C4—21no—
955C3×C4—21no—
956C3×C4—21no—
957C3×C4—21no—
958C3×C4—21no—
959C3×C4—41no—
960C3×C4—41no—
961C3×C4—41no—
962C3×C4—41no—
963C3×C4—41no—
964C3×C4—41no—
965C3×C4—81no—
966C3×C4—81no—
967C3×C4—92no—
968C3×C4—92no—
969C3×C4—181no—
970C3×C4—181no—
971C3×C4—181no—
972C3×C4—181no—
973C3×C4—181no—
974C3×C4—181no—
975C3×C4—181no—
976C3×C4—181no—
977Dic3—32no—
978Dic3—32no—
979Dic3—32no—
980Dic3—32no—
981Dic3—62no—
982Dic3—62no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—61no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—61no—
996Dic3—61no—
997Dic3—61no—
998Dic3—61no—
999Dic3—121no—
1000Dic3—121no—
1001Dic3—121no—
1002Dic3—121no—
1003Dic3—121no—
1004Dic3—121no—
1005Dic3—121no—
1006Dic3—121no—
1007C32—21no—
1008C32—21no—
1009C32—21no—
1010C32—41no—
1011C32#562811yescharacteristic, complemented
1012C32#564811yescharacteristic, complemented
1013C32#567511yescharacteristic, complemented
1014C23—91no—
1015C23—91no—
1016C23C2×#111311yescharacteristic
1017Q8—182no—
1018Q8—182no—
1019Q8—542no—
1020Q8—542no—
1021Q8—542no—
1022D4—182no—
1023D4—182no—
1024D4—542no—
1025C2×C4—91no—
1026C2×C4—91no—
1027C2×C4—91no—
1028C2×C4—91no—
1029C2×C4—91no—
1030C2×C4—91no—
1031C2×C4—91no—
1032C2×C4—91no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—182no—
1036C2×C4—182no—
1037C2×C4—274no—
1038C2×C4—542no—
1039C2×C4—542no—
1040C2×C4C2×#111311yescharacteristic
1041C2×C4C2×#111311yescharacteristic
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—42no—
1052C2×C3—41no—
1053C2×C3—41no—
1054C2×C3—41no—
1055C2×C3—41no—
1056C2×C3—41no—
1057C2×C3—41no—
1058C2×C3—81no—
1059C2×C3—81no—
1060C2×C3—82no—
1061C2×C3—182no—
1062C2×C3—361no—
1063C2×C3#6429711yescharacteristic
1064C2×C3#6429711yescharacteristic
1065C2×C3#6429811yescharacteristic
1066C2×C3#6430911yescharacteristic
1067C2×C3#6430911yescharacteristic
1068C2×C3#6430911yescharacteristic
1069C2×C3D32×D411yescharacteristic
1070C2×C3D32×D411yescharacteristic
1071C2×C3D32×D411yescharacteristic
1072D3—62no—
1073D3—62no—
1074D3—122no—
1075D3—121no—
1076D3—121no—
1077D3—241no—
1078C22—21no—
1079C22—21no—
1080C22—21no—
1081C22—92no—
1082C22—181no—
1083C22—181no—
1084C22—181no—
1085C22—181no—
1086C22—181no—
1087C22C22×#111311yescharacteristic
1088C4—21no—
1089C4—21no—
1090C4—92no—
1091C4—92no—
1092C4—181no—
1093C4—181no—
1094C4—181no—
1095C4—181no—
1096C4—181no—
1097C4—181no—
1098C4—181no—
1099C4—181no—
1100C3—21no—
1101C3—21no—
1102C3—21no—
1103C3—41no—
1104C3#1059405611yescharacteristic, complemented
1105C3#1059405711yescharacteristic, complemented
1106C3#1059407011yescharacteristic, complemented
1107C2—41no—
1108C2—182no—
1109C2—361no—
1110C2#1172461411yescharacteristic
1111C2#1172462011yescharacteristic
1112C2D4×#111311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×#89046C2
hypercenterC22⋊C4#1113
hypocenterC33#536
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#89040C2semidirect
3. C3×#64094C2semidirect
4. C3×#64092C2semidirect
5. C3×#64087C2semidirect
6. #11723724C2semidirect
7. #11723721C2semidirect
8. #11723718C2semidirect
9. C4⋊#6296C2semidirect
10. #11723694C2semidirect
11. #11723692C2semidirect
12. #11723690C2semidirect
13. #11723688C2semidirect
14. #11723683C2semidirect
15. #11723666C2semidirect
62. #64094D3semidirect
63. #64092D3semidirect
64. #64087D3semidirect
713. C33#536semidirect
1011. C32#5628semidirect
1012. C32#5648semidirect
1013. C32#5675semidirect
1104. C3#10594056semidirect
1105. C3#10594057semidirect
1106. C3#10594070semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#890402
C3×#640942
C3×#640922
C3×#640872
#117237242
#117237212
#117237182
C4⋊#62962
#117236942
#117236922
#117236902
#117236882
#117236832
#117236662
#105940703
#105940573
#105940563