Finite Group Databasebeta

← #13150890

Subgroups — #13150890

Order 1728.

1333 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88740C211yesmaximal, characteristic, complemented
2C2×#88676C211yesmaximal, characteristic, complemented
3#64138⋊C3C211yesmaximal, characteristic, complemented
4C2×#3752⋊C3C211yesmaximal, characteristic, complemented
5#11721322C211yesmaximal, characteristic, complemented
6#11721321C211yesmaximal, characteristic, complemented
7#11721293C211yesmaximal, characteristic, complemented
8#11721163C211yesmaximal, characteristic, complemented
9#11721161C211yesmaximal, characteristic, complemented
10#11721157C211yesmaximal, characteristic, complemented
11#11721143C211yesmaximal, characteristic, complemented
12#11721142C211yesmaximal, characteristic, complemented
13#11721135C211yesmaximal, characteristic, complemented
14#11721124C211yesmaximal, characteristic, complemented
15#11721104C211yesmaximal, characteristic, complemented
16#10595068—31nomaximal
17#10595065—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C2×#6235C2211yescharacteristic
22C2×#6235C2211yescharacteristic, complemented
23#88740—24no—
24C2×C4⋊#272C2211yescharacteristic, complemented
25C2×C4×#272C2211yescharacteristic, complemented
26C2×C4×#272C2211yescharacteristic, complemented
27C2×#6229C2211yescharacteristic, complemented
28C2×#638⋊C3C2211yescharacteristic
29C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
30#88676—24no—
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic
33C2×#6200C2211yescharacteristic, complemented
34C2×#6200C2211yescharacteristic, complemented
35C2×#6199C2211yescharacteristic, complemented
36C2×#6198C2211yescharacteristic
37C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
38#3757⋊C3C2211yescharacteristic, complemented
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic, complemented
42#3752⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45#3750⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#88451C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88450C2211yescharacteristic
50#88450C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88449C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C2×C3×#235—31no—
56C2×C3×#235—31no—
57C2×C3×#235—61no—
58C2×#3811—31no—
59C2×D3×#67—31no—
60#64138D311yescharacteristic, complemented
61C2×#3752D311yescharacteristic, complemented
62C3×#929—31no—
63C2×C3×(C2×D3)⋊C4—31no—
64#63981—31no—
65#63980—31no—
66#63978—31no—
67#63976—31no—
68#67⋊Dic3—31no—
69Dic3×#67—31no—
70#63922—31no—
71#63922—31no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4—31no—
74#63907—31no—
75#63907—31no—
76#63906—31no—
77#63906—31no—
78#63905—31no—
79#63904—31no—
80#63888—31no—
81#63887—31no—
82#63886—31no—
83#63885—31no—
84#63879—31no—
85#63850—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272C2311yescharacteristic
88C22×#272C2311yescharacteristic
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—22no—
91C22×(C3⋊D3)⋊C3—41no—
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C2×((C3⋊D3)⋊C3)⋊C2—22no—
96C2×((C3⋊D3)⋊C3)⋊C2—22no—
97C2×((C3⋊D3)⋊C3)⋊C2—41no—
98C2×C4×H(3,𝔽3)—22no—
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100C2×C4×H(3,𝔽3)C2311yescharacteristic
101#6235—22no—
102#6235D414yescomplemented
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105C4⋊#272—22no—
106C4×#272—22no—
107C4×#272—22no—
108#6229—22no—
109#638⋊C3—22no—
110C2×(C3⋊Dic3)⋊C3—41no—
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
115C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
116#6200—22no—
117#6200—22no—
118#6200—41no—
119#6200—41no—
120#6199—41no—
121#6198—22no—
122((C3⋊D3)⋊C3)⋊C4—22no—
123#5829—91no—
124#5654—91no—
125#5490—91no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—31no—
128C22×D32—31no—
129C22×D32—31no—
130C22×C32×C4—21no—
131C22×C32×C4C2×D311yescharacteristic, complemented
132C22×C32×C4C2×D311yescharacteristic, complemented
133C2×#638C2×D311yescharacteristic
134C22×C3⋊Dic3C2×D311yescharacteristic, complemented
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—61no—
141C2×C3×#67—61no—
142C22×C3×Dic3—31no—
143C3×#235—64no—
144C3×#235—64no—
145C3×#235—68no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—61no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—61no—
154C2×C3×C4×D3—61no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—61no—
158#3811—64no—
159D3×#67—64no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#625—31no—
169C2×#625—31no—
170C2×#624—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174#3757C2×D311yescharacteristic, complemented
175#3752C2×D311yescharacteristic
176#3752C2×D311yescharacteristic
177#3752C2×D311yescharacteristic, complemented
178#3752C2×D311yescharacteristic, complemented
179#3752C2×D311yescharacteristic, complemented
180#3752C2×D311yescharacteristic, complemented
181#3750C2×D311yescharacteristic, complemented
182#3750C2×D311yescharacteristic, complemented
183C3×#217—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×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192#3724—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195Dic3⋊Dic3—31no—
196#3722—31no—
197#3722—31no—
198#3722—31no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206Dic32—31no—
207Dic32—31no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)—21no—
210C22×H(3,𝔽3)C2×D412yes—
211C22×H(3,𝔽3)C2411yescharacteristic
212C2×#272—21no—
213C2×#272—21no—
214C2×#272—21no—
215C2×#272—21no—
216C2×#272—21no—
217C2×#272C2×D412yes—
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—21no—
223C2×(C3⋊D3)⋊C3—21no—
224C2×(C3⋊D3)⋊C3—21no—
225C2×(C3⋊D3)⋊C3—21no—
226C2×(C3⋊D3)⋊C3—44no—
227C2×(C3⋊D3)⋊C3#4112yescomplemented
228((C3⋊D3)⋊C3)⋊C2—44no—
229C4×H(3,𝔽3)—21no—
230C4×H(3,𝔽3)—21no—
231#1084—21no—
232#1084C2×D412yes—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3—21no—
237(C3⋊Dic3)⋊C3—21no—
238C2×C3×#41—91no—
239C22×#67—91no—
240C2×D3×D4—91no—
241C2×D3×D4—91no—
242C2×#235—31no—
243C2×#235—31no—
244C2×#235—61no—
245C3×#123—91no—
246C2×C3×C22⋊C4—91no—
247#953—91no—
248#947—91no—
249#946—91no—
250#939—91no—
251#939—91no—
252#939—91no—
253#937—91no—
254#937—91no—
255D4×Dic3—91no—
256#930—91no—
257#930—91no—
258#929—31no—
259#929—91no—
260#929—91no—
261C4×#67—91no—
262C4×#67—91no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—91no—
265C2×(C2×D3)⋊C4—91no—
266#896—91no—
267#895—91no—
268#894—91no—
269#893—91no—
270#885—91no—
271#885—91no—
272#884—91no—
273#884—91no—
274#884—91no—
275#883—91no—
276#882—91no—
277#882—91no—
278#882—91no—
279#67⋊C4—91no—
280#67⋊C4—91no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4—91no—
283#878—91no—
284C23×C32—21no—
285C23×C32C22×D311yescharacteristic
286C23×C32C22×D311yescharacteristic
287C22×C3⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—41no—
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—31no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—31no—
300C22×C3×D3—61no—
301C22×C3×D3—61no—
302C22×C3×D3—62no—
303C22×C3×D3—62no—
304C22×C3×D3—121no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—62no—
308C2×D32—62no—
309C2×D32—121no—
310C2×D32—121no—
311C2×C32×C4—24no—
312C2×C32×C4—22no—
313C2×C32×C4—22no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320#638—22no—
321C2×C3⋊Dic3—41no—
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C3×#67—34no—
328C3×#67—34no—
329C3×#67—64no—
330C3×#67—64no—
331C3×#67—62no—
332C3×#67—62no—
333C3×#67—62no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
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—121no—
346C3×D12—62no—
347C3×D12—62no—
348C3×D12—64no—
349C3×C4×D3—62no—
350C3×C4×D3—62no—
351C3×C4×D3—62no—
352C3×C4×D3—62no—
353C3×C4×D3—64no—
354C3×C4×D3—64no—
355C3×Dic6—62no—
356C3×Dic6—62no—
357C3×Dic6—64no—
358#626—62no—
359#626—62no—
360#626—62no—
361#626—62no—
362#626—121no—
363#626—121no—
364#625—62no—
365#625—62no—
366#625—121no—
367#625—121no—
368#624—62no—
369D3×Dic3—62no—
370D3×Dic3—121no—
371D3×Dic3—121no—
372#546—271noSylow
373C2×H(3,𝔽3)—22no—
374C2×H(3,𝔽3)C22×D411yescharacteristic
375C2×H(3,𝔽3)C2×#4111yescharacteristic
376C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
377#272—22no—
378#272—41no—
379(C3⋊D3)⋊C3—22no—
380(C3⋊D3)⋊C3—41no—
381(C3⋊D3)⋊C3—41no—
382C24×C3—91no—
383C23×D3—31no—
384C23×D3—91no—
385C23×D3—91no—
386C23×D3—91no—
387C23×D3—91no—
388C3×#41—184no—
389C2×C3×Q8—91no—
390C2×C3×D4—91no—
391C2×C3×D4—91no—
392C2×C3×D4—91no—
393C2×C3×D4—91no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—61no—
397C22×C3×C4—91no—
398C22×C3×C4—91no—
399C22×C3×C4—91no—
400C22×C3×C4D3211yescharacteristic
401C2×#67—31no—
402C2×#67—31no—
403C2×#67—31no—
404C2×#67—31no—
405C2×#67—31no—
406C2×#67—61no—
407C2×#67—61no—
408C2×#67—91no—
409C2×#67—91no—
410C2×#67—91no—
411C2×#67—91no—
412C2×#67—91no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—91no—
418C2×#67—91no—
419C2×#67—184no—
420C22×Dic3—31no—
421C22×Dic3—91no—
422C22×Dic3—91no—
423C22×Dic3—91no—
424D3×D4—184no—
425D3×D4—184no—
426#235—64no—
427#235—64no—
428#235—68no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—61no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12—91no—
435C2×D12—91no—
436C2×D12—91no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3—31no—
440C2×C4×D3—31no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×Dic6—31no—
448C2×Dic6—31no—
449C2×Dic6—61no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459#217—31no—
460#217—91no—
461#217—91no—
462#217—91no—
463#217—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—31no—
471(C2×D3)⋊C4—31no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
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—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498C4×Dic3—91no—
499C4×Dic3—91no—
500C4×Dic3—91no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—22no—
507C22×C32—41no—
508C22×C32—41no—
509C22×C32D3×D412yes—
510C22×C32D3×D412yes—
511C22×C32C23×D311yescharacteristic
512C22×C32C23×D311yescharacteristic
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—44no—
522C2×C3⋊D3#23512yescomplemented
523C2×C3×D3—32no—
524C2×C3×D3—32no—
525C2×C3×D3—32no—
526C2×C3×D3—62no—
527C2×C3×D3—61no—
528C2×C3×D3—61no—
529C2×C3×D3—61no—
530C2×C3×D3—61no—
531C2×C3×D3—61no—
532C2×C3×D3—61no—
533C2×C3×D3—62no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—61no—
542C2×C3×D3—61no—
543C2×C3×D3—61no—
544C2×C3×D3—61no—
545C2×C3×D3—61no—
546C2×C3×D3—121no—
547C2×C3×D3—121no—
548C2×C3×D3—121no—
549C2×C3×D3—121no—
550C2×C3×D3—124no—
551D32—124no—
552D32—124no—
553C32×C4—22no—
554C32×C4—22no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—21no—
559C3⋊Dic3—21no—
560C3⋊Dic3—21no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3×Dic3—32no—
565C3×Dic3—32no—
566C3×Dic3—62no—
567C3×Dic3—62no—
568C3×Dic3—61no—
569C3×Dic3—61no—
570C3×Dic3—61no—
571C3×Dic3—61no—
572C3×Dic3—61no—
573C3×Dic3—61no—
574C3×Dic3—61no—
575C2×#41—91no—
576C22×D4—271no—
577#124—271no—
578#123—91no—
579#123—271no—
580C22⋊Q8—271no—
581#121—271no—
582#121—271no—
583#121—271no—
584#120—271no—
585#120—271no—
586C4×D4—271no—
587C4×D4—271no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—271no—
590H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—61no—
594C23×C3—91no—
595C23×C3—91no—
596C23×C3—91no—
597C23×C3—91no—
598C23×C3—91no—
599C23×C3—182no—
600C23×C3—182no—
601C23×C3—361no—
602C23×C3C2×D3211yescharacteristic
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—31no—
608C22×D3—31no—
609C22×D3—31no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—91no—
615C22×D3—91no—
616C22×D3—91no—
617C22×D3—121no—
618C22×D3—182no—
619C22×D3—182no—
620C22×D3—182no—
621C22×D3—182no—
622C22×D3—182no—
623C22×D3—182no—
624C22×D3—182no—
625C22×D3—182no—
626C22×D3—361no—
627C22×D3—361no—
628C22×D3—361no—
629C22×D3—361no—
630C3×Q8—182no—
631C3×D4—94no—
632C3×D4—182no—
633C3×D4—182no—
634C3×D4—182no—
635C2×C3×C4—22no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—62no—
641C2×C3×C4—62no—
642C2×C3×C4—64no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—91no—
648C2×C3×C4—91no—
649C2×C3×C4—91no—
650C2×C3×C4—91no—
651C2×C3×C4—91no—
652C2×C3×C4—182no—
653C2×C3×C4—182no—
654C2×C3×C4—361no—
655C2×C3×C4C2×D3211yescharacteristic
656C2×C3×C4C2×D3211yescharacteristic
657#67—34no—
658#67—34no—
659#67—64no—
660#67—62no—
661#67—62no—
662#67—64no—
663#67—62no—
664#67—182no—
665#67—182no—
666#67—182no—
667#67—182no—
668#67—182no—
669#67—182no—
670#67—182no—
671#67—361no—
672#67—361no—
673#67—361no—
674#67—361no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—91no—
687C2×Dic3—91no—
688C2×Dic3—91no—
689C2×Dic3—91no—
690C2×Dic3—91no—
691C2×Dic3—121no—
692C2×Dic3—182no—
693C2×Dic3—361no—
694C2×Dic3—361no—
695D12—62no—
696D12—62no—
697D12—64no—
698D12—182no—
699D12—182no—
700D12—182no—
701D12—361no—
702D12—361no—
703C4×D3—62no—
704C4×D3—62no—
705C4×D3—62no—
706C4×D3—62no—
707C4×D3—64no—
708C4×D3—64no—
709C4×D3—182no—
710C4×D3—182no—
711C4×D3—361no—
712C4×D3—361no—
713Dic6—62no—
714Dic6—62no—
715Dic6—64no—
716C2×C32—22no—
717C2×C32—22no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—21no—
721C2×C32—42no—
722C2×C32C2×#23511yescharacteristic
723C2×C32C2×D3×D411yescharacteristic
724C2×C32C2×D3×D411yescharacteristic
725C2×C32#100411yescharacteristic
726C2×C32D3×#4111yescharacteristic
727C2×C32#100911yescharacteristic
728C3⋊D3—22no—
729C3⋊D3—41no—
730C3⋊D3—41no—
731C3×D3—62no—
732C3×D3—62no—
733C3×D3—62no—
734C3×D3—122no—
735C3×D3—122no—
736C3×D3—121no—
737C3×D3—121no—
738C3×D3—121no—
739C3×D3—121no—
740C24—91no—
741C24—271no—
742#41—184no—
743C2×Q8—91no—
744C2×D4—91no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—91no—
748C2×D4—271no—
749C2×D4—271no—
750C2×D4—271no—
751C2×D4—271no—
752C2×D4—271no—
753C2×D4—544no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—271no—
758C22×C4—271no—
759C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
760C4⋊C4—91no—
761C4⋊C4—91no—
762C4⋊C4—271no—
763C4⋊C4—271no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—91no—
768C22⋊C4—91no—
769C22⋊C4—91no—
770C22⋊C4—91no—
771C22⋊C4—271no—
772C22⋊C4—271no—
773C22⋊C4—271no—
774C22⋊C4—271no—
775C22⋊C4—271no—
776C42—271no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—31no—
780C22×C3—31no—
781C22×C3—32no—
782C22×C3—32no—
783C22×C3—61no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—62no—
789C22×C3—92no—
790C22×C3—92no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—181no—
799C22×C3—181no—
800C22×C3—181no—
801C22×C3—181no—
802C22×C3—181no—
803C22×C3—181no—
804C22×C3—181no—
805C22×C3—181no—
806C22×C3—364no—
807C22×C3#381112yes—
808C22×C3C22×D3211yescharacteristic
809C2×D3—32no—
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—62no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—62no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—92no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—124no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—181no—
844C2×D3—181no—
845C2×D3—181no—
846C2×D3—364no—
847C2×D3—364no—
848C2×D3—364no—
849C2×D3—364no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—92no—
859C3×C4—181no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863C3×C4—181no—
864C3×C4—181no—
865Dic3—32no—
866Dic3—32no—
867Dic3—62no—
868Dic3—61no—
869Dic3—61no—
870Dic3—62no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—181no—
877Dic3—181no—
878Dic3—181no—
879Dic3—181no—
880Dic3—181no—
881C32—21no—
882C32#549011yescharacteristic, complemented
883C32#565411yescharacteristic, complemented
884C23—91no—
885C23—91no—
886C23—91no—
887C23—91no—
888C23—91no—
889C23—182no—
890C23—182no—
891C23—361no—
892C23—542no—
893C23—542no—
894C23—1081no—
895C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
896Q8—182no—
897D4—94no—
898D4—182no—
899D4—182no—
900D4—182no—
901D4—542no—
902D4—542no—
903D4—542no—
904D4—1081no—
905D4—1081no—
906C2×C4—22no—
907C2×C4—91no—
908C2×C4—91no—
909C2×C4—91no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—182no—
915C2×C4—182no—
916C2×C4—361no—
917C2×C4—542no—
918C2×C4—1081no—
919C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
920C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
921C2×C3—22no—
922C2×C3—31no—
923C2×C3—31no—
924C2×C3—31no—
925C2×C3—31no—
926C2×C3—31no—
927C2×C3—31no—
928C2×C3—62no—
929C2×C3—62no—
930C2×C3—61no—
931C2×C3—61no—
932C2×C3—61no—
933C2×C3—122no—
934C2×C3—182no—
935C2×C3—182no—
936C2×C3—361no—
937C2×C3—361no—
938C2×C3—361no—
939C2×C3D3×#23511yescharacteristic
940C2×C3#6430711yescharacteristic
941C2×C3C2×#381111yescharacteristic
942D3—62no—
943D3—62no—
944D3—62no—
945D3—122no—
946D3—121no—
947D3—121no—
948D3—122no—
949D3—121no—
950D3—121no—
951D3—182no—
952D3—361no—
953D3—361no—
954C22—21no—
955C22—21no—
956C22—92no—
957C22—92no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22—181no—
968C22—181no—
969C22—181no—
970C22—181no—
971C22—364no—
972C22—1084no—
973C22#8867712yes—
974C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
975C4—21no—
976C4—21no—
977C4—92no—
978C4—181no—
979C4—181no—
980C4—181no—
981C4—181no—
982C4—181no—
983C4—181no—
984C3—31no—
985C3—31no—
986C3—61no—
987C3#1059507711yescharacteristic
988C2—22no—
989C2—182no—
990C2—182no—
991C2—361no—
992C2—361no—
993C2—361no—
994C2#1172249011yescharacteristic
995C2#1172249211yescharacteristic
996C2C2×#8867711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88740C2semidirect
2. C2×#88676C2semidirect
3. #64138⋊C3C2semidirect
4. C2×#3752⋊C3C2semidirect
5. #11721322C2semidirect
6. #11721321C2semidirect
7. #11721293C2semidirect
8. #11721163C2semidirect
9. #11721161C2semidirect
10. #11721157C2semidirect
11. #11721143C2semidirect
12. #11721142C2semidirect
13. #11721135C2semidirect
14. #11721124C2semidirect
15. #11721104C2semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
22. C2×#6235C22semidirect
24. C2×C4⋊#272C22semidirect
25. C2×C4×#272C22semidirect
26. C2×C4×#272C22semidirect
27. C2×#6229C22semidirect
29. C22×(C3⋊Dic3)⋊C3C22semidirect
33. C2×#6200C22semidirect
34. C2×#6200C22semidirect
35. C2×#6199C22semidirect
38. #3757⋊C3C22semidirect
41. #3752⋊C3C22semidirect
42. #3752⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. #3750⋊C3C22semidirect
46. #3750⋊C3C22semidirect
47. #88451C22semidirect
48. #88451C22semidirect
50. #88450C22semidirect
51. #88450C22semidirect
52. #88449C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
60. #64138D3semidirect
61. C2×#3752D3semidirect
102. #6235D4semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C2×D3semidirect
134. C22×C3⋊Dic3C2×D3semidirect
174. #3757C2×D3semidirect
177. #3752C2×D3semidirect
178. #3752C2×D3semidirect
179. #3752C2×D3semidirect
180. #3752C2×D3semidirect
181. #3750C2×D3semidirect
182. #3750C2×D3semidirect
227. C2×(C3⋊D3)⋊C3#41semidirect
522. C2×C3⋊D3#235semidirect
590. H(3,𝔽3)#546semidirect
759. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
882. C32#5490semidirect
883. C32#5654semidirect

Maximal subgroups

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

subgroupindex
C2×#887402
C2×#886762
#64138⋊C32
C2×#3752⋊C32
#117213222
#117213212
#117212932
#117211632
#117211612
#117211572
#117211432
#117211422
#117211352
#117211242
#117211042
#105950683
#105950653