Finite Group Databasebeta

← #13169165

Subgroups — #13169165

Order 1728.

1100 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723687C211yesmaximal, characteristic
2#11723436C211yesmaximal, characteristic, complemented
3#11723433C211yesmaximal, characteristic, complemented
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63897C211yesmaximal, characteristic, complemented
6C3×#63888C211yesmaximal, characteristic, complemented
7C3×#63839C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723010C211yesmaximal, characteristic, complemented
10#11723007C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic, complemented
12#11722984C211yesmaximal, characteristic, complemented
13#11722970C211yesmaximal, characteristic, complemented
14#11722931C211yesmaximal, characteristic, complemented
15#11722922C211yesmaximal, characteristic, complemented
16#10595343—31nomaximal
17#10594567—31nomaximal
18#10594458—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37#88803C2211yescharacteristic
38#88803C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64156—31no—
55#64107—31no—
56#64096—31no—
57C3×#946—31no—
58C3×#944—31no—
59C3×#896—31no—
60C3×#894—31no—
61C3×#894—31no—
62C3×#888—31no—
63#63915—31no—
64#63913—31no—
65#63910—31no—
66#63907—31no—
67#63907—31no—
68#63905—31no—
69#63904—31no—
70#63904—31no—
71C4×#625—31no—
72#63897D311yescharacteristic, complemented
73#63896—31no—
74#63895—31no—
75#63893—31no—
76#63888—31no—
77#63888D311yescharacteristic, complemented
78#63886—31no—
79#63885—31no—
80#63878—31no—
81#63877—31no—
82#63863—31no—
83#63863—31no—
84#63863—61no—
85#63862—31no—
86#63862—31no—
87#63862—31no—
88#63862—61no—
89#63858—31no—
90#63856—31no—
91#63854—31no—
92#63852—31no—
93#63852—31no—
94#63851—31no—
95#63850—31no—
96#63848—31no—
97#63839D311yescharacteristic, complemented
98#63838—31no—
99#63838—31no—
100#63838—61no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4⋊(C3⋊D3)—41no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×Dic6—41no—
119#6295—22no—
120#6295—41no—
121#6294—22no—
122#6293—22no—
123C3×#627—41no—
124C3×#624—41no—
125C3×#624—41no—
126#5733—91no—
127#5662—91no—
128#5640—91no—
129C2×C32×Q8—31no—
130C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
131C2×#634—31no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×D12—61no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6C2×D311yescharacteristic
143C2×C3×Dic6C2×D311yescharacteristic
144C2×#627—31no—
145C2×#627—31no—
146C2×#627—61no—
147C2×#627C2×D311yescharacteristic
148C2×#626—31no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#626—31no—
152C2×#625—31no—
153C2×#625—31no—
154C2×#624—31no—
155C2×#624C2×D311yescharacteristic
156C2×#624C2×D311yescharacteristic
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752C2×D311yescharacteristic
168C4⋊(C3⋊Dic3)—31no—
169#3750—31no—
170#3750—31no—
171#3750C2×D311yescharacteristic
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—61no—
178C4×C3⋊Dic3—61no—
179C4×C3⋊Dic3—61no—
180C4×C3⋊Dic3—121no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—61no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×Dic3⋊C4—21no—
195C3×Dic3⋊C4—21no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—61no—
205C3×Dic3⋊C4C2×D311yescharacteristic
206C3×Dic3⋊C4C2×D311yescharacteristic
207C3×Dic3⋊C4C2×D311yescharacteristic
208C3×Dic3⋊C4C2×D311yescharacteristic
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211#3724—31no—
212#3724—31no—
213#3724—61no—
214#3724C2×D311yescharacteristic
215#3724C2×D311yescharacteristic
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3C2×D311yescharacteristic
223Dic3⋊Dic3C2×D311yescharacteristic
224#3722—31no—
225#3722C2×D311yescharacteristic
226#3722C2×D311yescharacteristic
227#3722C2×D311yescharacteristic
228#3722C2×D311yescharacteristic
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—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—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—61no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3⋊(C3⋊Dic3)—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3#4112yes—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×C4⋊Q8—91no—
279C3×#123—91no—
280C3×C22⋊Q8—91no—
281#947—91no—
282#947—91no—
283#947—91no—
284#947—181no—
285#946—31no—
286#946—91no—
287#944—31no—
288#939—91no—
289#936—91no—
290#929—91no—
291C4×#67—91no—
292C4×#67—91no—
293#924—91no—
294#898—91no—
295#898—91no—
296#898—91no—
297#898—91no—
298#898—181no—
299#897—91no—
300#896—31no—
301#896—91no—
302#896—91no—
303#895—91no—
304#894—31no—
305#894—31no—
306#894—91no—
307#893—91no—
308#892—91no—
309#888—31no—
310#887—91no—
311#887—91no—
312#887—91no—
313#887—181no—
314#885—91no—
315#885—91no—
316#885—91no—
317#885—91no—
318#884—91no—
319#883—91no—
320#879—91no—
321#879—91no—
322#878—91no—
323#877—91no—
324#875—91no—
325#872—91no—
326C22×C3⋊D3C22×D311yescharacteristic
327C22×C3⋊D3C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—31no—
335C22×C3×D3—61no—
336C22×C3×D3—61no—
337C22×C3×D3—61no—
338C32×Q8—121no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—31no—
348C2×C32×C4—41no—
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—61no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3—121no—
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C4⋊(C3⋊D3)—41no—
370#634—62no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
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×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
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C3×D12—121no—
399C3×D12—121no—
400C3×D12—122no—
401C3×C4×D3—121no—
402C3×C4×D3—121no—
403C3×C4×D3—121no—
404C3×C4×D3—121no—
405C3×Dic6—41no—
406C3×Dic6—41no—
407C3×Dic6—42no—
408C3×Dic6—121no—
409C3×Dic6—121no—
410#627—41no—
411#627—62no—
412#627—62no—
413#627—64no—
414#626—62no—
415#626—62no—
416#626—121no—
417#626—121no—
418#625—62no—
419#625—121no—
420#624—41no—
421#624—41no—
422#624—62no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425#542—271noSylow
426C2×C33C2×#4111yescharacteristic
427C2×C33H(5,𝔽2)11yescharacteristic
428C2×C332−1+411yescharacteristic
429C3×C3⋊D3—41no—
430C3×C3⋊D3—41no—
431C3×C3⋊D3—41no—
432C2×C3×Q8—31no—
433C2×C3×Q8—31no—
434C2×C3×Q8—61no—
435C2×C3×Q8—91no—
436C2×C3×D4—91no—
437C22×C3×C4—91no—
438C22×C3×C4—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C22×Dic3—91no—
444C2×D12—31no—
445C2×D12—31no—
446C2×D12—61no—
447C2×D12—91no—
448C2×D12—91no—
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—91no—
458C2×Dic6—91no—
459C2×Dic6—91no—
460C2×Dic6—181no—
461C2×Dic6D3211yescharacteristic
462C3×C4⋊C4—31no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—61no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C22⋊C4—91no—
477C3×C22⋊C4—91no—
478C3×C42—91no—
479#217—91no—
480#217—91no—
481#217—91no—
482#217—91no—
483#217—91no—
484#217—91no—
485#217—91no—
486(C2×D3)⋊C4—31no—
487(C2×D3)⋊C4—31no—
488(C2×D3)⋊C4—31no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—31no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—31no—
495(C2×D3)⋊C4—31no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515(C2×D3)⋊C4—181no—
516(C2×D3)⋊C4—181no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—181no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—61no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—181no—
539Dic3⋊C4—181no—
540Dic3⋊C4D3211yescharacteristic
541Dic3⋊C4D3211yescharacteristic
542C4×Dic3—31no—
543C4×Dic3—31no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—91no—
547C4×Dic3—91no—
548C4×Dic3—91no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—181no—
554C4×Dic3—181no—
555C4×Dic3—181no—
556C4×Dic3—181no—
557C4×Dic3—181no—
558C4×Dic3—361no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—41no—
563C22×C32C23×D311yescharacteristic
564C22×C32C23×D311yescharacteristic
565C22×C32C23×D311yescharacteristic
566C2×C3⋊D3—21no—
567C2×C3⋊D3—21no—
568C2×C3⋊D3—21no—
569C2×C3⋊D3—21no—
570C2×C3⋊D3—21no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3×D3—61no—
576C2×C3×D3—61no—
577C2×C3×D3—61no—
578C2×C3×D3—61no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—61no—
584C2×C3×D3—61no—
585C2×C3×D3—61no—
586C2×C3×D3—61no—
587C2×C3×D3—61no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—121no—
594C2×C3×D3—121no—
595C2×C3×D3—121no—
596C2×C3×D3—121no—
597C2×C3×D3—121no—
598C2×C3×D3—121no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C32×C4—21no—
603C32×C4—22no—
604C32×C4—21no—
605C32×C4—21no—
606C32×C4—41no—
607C32×C4—41no—
608C32×C4—42no—
609C32×C4—61no—
610C32×C4—61no—
611C32×C4—61no—
612C32×C4—61no—
613C32×C4—61no—
614C32×C4—61no—
615C3⋊Dic3—21no—
616C3⋊Dic3—21no—
617C3⋊Dic3—61no—
618C3⋊Dic3—61no—
619C3⋊Dic3—62no—
620C3⋊Dic3—62no—
621C3⋊Dic3—61no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—61no—
625C3⋊Dic3—121no—
626C3⋊Dic3—121no—
627C3⋊Dic3—121no—
628C3⋊Dic3—121no—
629C3⋊Dic3—122no—
630C3⋊Dic3—122no—
631C3⋊Dic3#23912yes—
632C3×Dic3—22no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—32no—
646C3×Dic3—32no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—41no—
650C3×Dic3—41no—
651C3×Dic3—41no—
652C3×Dic3—62no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—121no—
658C3×Dic3—121no—
659C4⋊Q8—91no—
660#126—271no—
661#126—271no—
662#124—271no—
663#124—271no—
664#124—271no—
665#123—91no—
666#123—271no—
667C22⋊Q8—91no—
668C22⋊Q8—271no—
669C22⋊Q8—271no—
670#121—271no—
671C4×Q8—271no—
672C4×D4—271no—
673#117—271no—
674C33#54211yescharacteristic, complemented, Sylow
675C23×C3—91no—
676C23×C3—91no—
677C23×C3—91no—
678C22×D3—31no—
679C22×D3—31no—
680C22×D3—31no—
681C22×D3—31no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—61no—
685C22×D3—61no—
686C22×D3—61no—
687C3×Q8—121no—
688C3×Q8—121no—
689C3×Q8—122no—
690C3×Q8—361no—
691C3×D4—361no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—41no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—91no—
717C2×C3×C4—361no—
718C2×C3×C4—361no—
719C2×C3×C4C2×D3211yescharacteristic
720C2×C3×C4C2×D3211yescharacteristic
721C2×C3×C4C2×D3211yescharacteristic
722#67—182no—
723#67—182no—
724#67—361no—
725#67—361no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—91no—
736C2×Dic3—91no—
737C2×Dic3—91no—
738C2×Dic3—91no—
739C2×Dic3—91no—
740C2×Dic3—91no—
741C2×Dic3—181no—
742C2×Dic3—181no—
743C2×Dic3—181no—
744C2×Dic3—181no—
745C2×Dic3—181no—
746C2×Dic3—181no—
747C2×Dic3—182no—
748C2×Dic3—361no—
749C2×Dic3—361no—
750C2×Dic3C2×D3211yescharacteristic
751C2×Dic3C2×D3211yescharacteristic
752C2×Dic3C2×D3211yescharacteristic
753C2×Dic3C2×D3211yescharacteristic
754C2×Dic3C2×D3211yescharacteristic
755C2×Dic3C2×D3211yescharacteristic
756D12—121no—
757D12—121no—
758D12—122no—
759D12—182no—
760D12—361no—
761C4×D3—121no—
762C4×D3—121no—
763C4×D3—121no—
764C4×D3—121no—
765C4×D3—182no—
766C4×D3—182no—
767Dic6—41no—
768Dic6—121no—
769Dic6—121no—
770Dic6—182no—
771Dic6—182no—
772Dic6—182no—
773Dic6—184no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—41no—
784C2×C32—41no—
785C2×C32—41no—
786C2×C32#100411yescharacteristic
787C2×C32#100411yescharacteristic
788C2×C32#100411yescharacteristic
789C2×C32C2×#23911yescharacteristic
790C2×C32#100711yescharacteristic
791C2×C32#100711yescharacteristic
792C2×C32D3×#4111yescharacteristic
793C2×C32D3×#4111yescharacteristic
794C2×C32#101011yescharacteristic
795C3⋊D3—41no—
796C3⋊D3—41no—
797C3⋊D3—41no—
798C3×D3—121no—
799C3×D3—121no—
800C3×D3—121no—
801C3×D3—121no—
802C3×D3—121no—
803C3×D3—121no—
804C3×D3—241no—
805C3×D3—241no—
806C3×D3—241no—
807C2×Q8—31no—
808C2×Q8—91no—
809C2×Q8—271no—
810C2×D4—91no—
811C2×D4—271no—
812C2×D4—271no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—271no—
816C4⋊C4—31no—
817C4⋊C4—31no—
818C4⋊C4—91no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—91no—
822C4⋊C4—91no—
823C4⋊C4—271no—
824C4⋊C4—271no—
825C4⋊C4—271no—
826C22⋊C4—91no—
827C22⋊C4—91no—
828C22⋊C4—91no—
829C22⋊C4—91no—
830C22⋊C4—91no—
831C22⋊C4—271no—
832C22⋊C4—271no—
833C22⋊C4—271no—
834C22⋊C4—271no—
835C22⋊C4—271no—
836C22⋊C4—271no—
837C22⋊C4—271no—
838C42—91no—
839C42—271no—
840C42—271no—
841C42—271no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—41no—
846C22×C3—181no—
847C22×C3—181no—
848C22×C3—181no—
849C22×C3—181no—
850C22×C3—181no—
851C22×C3—181no—
852C22×C3—181no—
853C22×C3—181no—
854C22×C3—181no—
855C22×C3C22×D3211yescharacteristic
856C22×C3C22×D3211yescharacteristic
857C22×C3C22×D3211yescharacteristic
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—61no—
861C2×D3—61no—
862C2×D3—61no—
863C2×D3—61no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—61no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C3×C4—22no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—42no—
892C3×C4—62no—
893C3×C4—61no—
894C3×C4—61no—
895C3×C4—61no—
896C3×C4—61no—
897C3×C4—61no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—92no—
906C3×C4—121no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910C3×C4—121no—
911C3×C4—181no—
912C3×C4—181no—
913Dic3—21no—
914Dic3—21no—
915Dic3—21no—
916Dic3—21no—
917Dic3—21no—
918Dic3—21no—
919Dic3—32no—
920Dic3—32no—
921Dic3—62no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—121no—
927Dic3—121no—
928Dic3—182no—
929Dic3—182no—
930Dic3—181no—
931Dic3—181no—
932Dic3—181no—
933Dic3—181no—
934Dic3—181no—
935Dic3—181no—
936Dic3—361no—
937Dic3—361no—
938Dic3—361no—
939Dic3—361no—
940Dic3—362no—
941Dic3—362no—
942C32—21no—
943C32—21no—
944C32—21no—
945C32—41no—
946C32#564011yescharacteristic, complemented
947C32#566211yescharacteristic, complemented
948C32#573311yescharacteristic, complemented
949C23—91no—
950C23—91no—
951C23—91no—
952Q8—121no—
953Q8—361no—
954Q8—542no—
955D4—361no—
956D4—542no—
957D4—1081no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—31no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—91no—
967C2×C4—271no—
968C2×C4—271no—
969C2×C4—361no—
970C2×C4—361no—
971C2×C4—542no—
972C2×C4D3311yescharacteristic
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—41no—
983C2×C3—41no—
984C2×C3—41no—
985C2×C3—361no—
986C2×C3—361no—
987C2×C3—361no—
988C2×C3#6429711yescharacteristic
989C2×C3#6430611yescharacteristic
990C2×C3#6431311yescharacteristic
991C2×C3#6431311yescharacteristic
992C2×C3#6431511yescharacteristic
993C2×C3#6431611yescharacteristic
994C2×C3D3×#23911yescharacteristic
995C2×C3D3×#23911yescharacteristic
996C2×C3#6433011yescharacteristic
997D3—121no—
998D3—121no—
999D3—121no—
1000D3—121no—
1001D3—121no—
1002D3—121no—
1003D3—241no—
1004D3—241no—
1005D3—241no—
1006C22—181no—
1007C22—181no—
1008C22—181no—
1009C22—181no—
1010C22—181no—
1011C22—181no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22C2×D3311yescharacteristic
1016C4—21no—
1017C4—61no—
1018C4—61no—
1019C4—61no—
1020C4—61no—
1021C4—61no—
1022C4—61no—
1023C4—92no—
1024C4—181no—
1025C4—181no—
1026C4—541no—
1027C4—541no—
1028C3—21no—
1029C3—21no—
1030C3—21no—
1031C3—41no—
1032C3#1059445811yescharacteristic, complemented
1033C3#1059456711yescharacteristic, complemented
1034C3#1059534311yescharacteristic, complemented
1035C2—361no—
1036C2—361no—
1037C2—361no—
1038C2#1172439111yescharacteristic
1039C2#1172439711yescharacteristic
1040C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723687C2
hypercenterC2×C4D33
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723436C2semidirect
3. #11723433C2semidirect
4. #11723391C2semidirect
5. C3×#63897C2semidirect
6. C3×#63888C2semidirect
7. C3×#63839C2semidirect
8. #11723025C2semidirect
9. #11723010C2semidirect
10. #11723007C2semidirect
11. #11722995C2semidirect
12. #11722984C2semidirect
13. #11722970C2semidirect
14. #11722931C2semidirect
15. #11722922C2semidirect
72. #63897D3semidirect
77. #63888D3semidirect
97. #63839D3semidirect
674. C33#542semidirect
946. C32#5640semidirect
947. C32#5662semidirect
948. C32#5733semidirect
1032. C3#10594458semidirect
1033. C3#10594567semidirect
1034. C3#10595343semidirect

Maximal subgroups

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

subgroupindex
#117236872
#117234362
#117234332
#117233912
C3×#638972
C3×#638882
C3×#638392
#117230252
#117230102
#117230072
#117229952
#117229842
#117229702
#117229312
#117229222
#105953433
#105945673
#105944583