Finite Group Databasebeta

← #13151468

Subgroups — #13151468

Order 1728.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#272C211yesmaximal, characteristic, complemented
2C2×#88677C211yesmaximal, characteristic, complemented
3C2×#88676C211yesmaximal, characteristic, complemented
4C22×#6200C211yesmaximal, characteristic, complemented
5#64148⋊C3C211yesmaximal, characteristic, complemented
6#64146⋊C3C211yesmaximal, characteristic, complemented
7#11721323C211yesmaximal, characteristic, complemented
8#11721323C211yesmaximal, characteristic, complemented
9#11721317C211yesmaximal, characteristic, complemented
10#11721312C211yesmaximal, characteristic, complemented
11#11721293C211yesmaximal, characteristic, complemented
12#11721163C211yesmaximal, characteristic, complemented
13#11721157C211yesmaximal, characteristic, complemented
14#11721142C211yesmaximal, characteristic, complemented
15#11721124C211yesmaximal, characteristic, complemented
16#10595291—31nomaximal
17#10595287—31nomaximal
18C23×#272C2211yescharacteristic, complemented
19C23×#272C2211yescharacteristic, complemented
20C23×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
21C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic, complemented
22C2×D4×H(3,𝔽3)C2211yescharacteristic, complemented
23C2×#6235C2211yescharacteristic
24C2×#6235C2211yescharacteristic, complemented
25D4×#272—24no—
26C2×C4⋊#272C2211yescharacteristic, complemented
27C2×C4×#272C2211yescharacteristic, complemented
28C2×#638⋊C3C2211yescharacteristic, complemented
29C2×#638⋊C3C2211yescharacteristic, complemented
30C2×#638⋊C3C2211yescharacteristic, complemented
31C2×#638⋊C3C2211yescharacteristic, complemented
32C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
33#88677—24no—
34#88676—24no—
35C2×#6200—24no—
36C2×#6200C2211yescharacteristic
37C2×#6200C2211yescharacteristic, complemented
38C2×#6200C2211yescharacteristic, complemented
39C2×#6200C2211yescharacteristic, complemented
40C2×#6200C2211yescharacteristic, complemented
41C2×#6200C2211yescharacteristic, complemented
42C2×#6200C2211yescharacteristic, complemented
43C2×#6199C2211yescharacteristic, complemented
44C2×#6198C2211yescharacteristic, complemented
45C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
46#3757⋊C3C2211yescharacteristic, complemented
47#3757⋊C3C2211yescharacteristic, complemented
48#3752⋊C3C2211yescharacteristic, complemented
49#3752⋊C3C2211yescharacteristic, complemented
50#3752⋊C3C2211yescharacteristic, complemented
51#3750⋊C3C2211yescharacteristic, complemented
52#88451C2211yescharacteristic, complemented
53#88451C2211yescharacteristic, complemented
54#88451C2211yescharacteristic, complemented
55#88449C2211yescharacteristic, complemented
56#88447C2211yescharacteristic, complemented
57C2×C3×D3×D4—31no—
58C2×C3×D3×D4—31no—
59C2×C3×D3×D4—61no—
60C2×#3811—31no—
61C2×D3×#67—31no—
62C2×D3×#67—31no—
63C2×D3×#67—31no—
64C22×#626—31no—
65C22×#625—31no—
66#64148D311yescharacteristic, complemented
67#64146D311yescharacteristic, complemented
68C3×#939—31no—
69C3×#937—31no—
70#63979—31no—
71#63979—31no—
72#63977—31no—
73#63977—31no—
74#63976—31no—
75#63976—31no—
76#67⋊Dic3—31no—
77Dic3×#67—31no—
78#63970—31no—
79#63958—31no—
80#63922—31no—
81#63922—31no—
82#63906—31no—
83#63906—31no—
84#63904—31no—
85#63886—31no—
86#63885—31no—
87#63879—31no—
88C23×H(3,𝔽3)C2311yescharacteristic
89C23×H(3,𝔽3)C2311yescharacteristic
90C22×#272—22no—
91C22×#272—22no—
92C22×#272—22no—
93C22×#272—22no—
94C22×#272—41no—
95C22×#272—41no—
96C22×#272C2311yescharacteristic
97C22×#272C2311yescharacteristic
98C22×#272C2311yescharacteristic
99C22×(C3⋊D3)⋊C3—22no—
100C22×(C3⋊D3)⋊C3—22no—
101C22×(C3⋊D3)⋊C3—41no—
102C22×(C3⋊D3)⋊C3C2311yescharacteristic
103C22×(C3⋊D3)⋊C3C2311yescharacteristic
104C22×(C3⋊D3)⋊C3C2311yescharacteristic
105C2×((C3⋊D3)⋊C3)⋊C2—22no—
106C2×((C3⋊D3)⋊C3)⋊C2—22no—
107C2×((C3⋊D3)⋊C3)⋊C2—41no—
108D4×H(3,𝔽3)—22no—
109C2×C4×H(3,𝔽3)C2311yescharacteristic
110#6235—22no—
111#6235D414yescomplemented
112C2×#1084C2311yescharacteristic
113C4⋊#272—22no—
114C4×#272—22no—
115#638⋊C3—22no—
116#638⋊C3—22no—
117#638⋊C3—22no—
118#638⋊C3—41no—
119C2×(C3⋊Dic3)⋊C3—22no—
120C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
121C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
122C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
123C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
124C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
125#6200—22no—
126#6200—22no—
127#6200—22no—
128#6200—22no—
129#6200—22no—
130#6200—41no—
131#6200D414yescomplemented
132#6199—22no—
133#6198—22no—
134((C3⋊D3)⋊C3)⋊C4—22no—
135D4×#67—91no—
136#5609—91no—
137#5590—91no—
138C23×C3⋊D3C2×D311yescharacteristic, complemented
139C23×C3×D3—31no—
140C23×C3×D3—31no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C23×C3×D3—31no—
144C23×C3×D3—61no—
145C23×C3×D3—61no—
146C22×D32—31no—
147C22×D32—31no—
148C2×C32×D4—21no—
149C2×C32×D4C2×D311yescharacteristic, complemented
150C2×C32×D4C2×D311yescharacteristic, complemented
151C2×#638C2×D311yescharacteristic, complemented
152C2×#638C2×D311yescharacteristic, complemented
153C2×#638C2×D311yescharacteristic, complemented
154C2×#638C2×D311yescharacteristic, complemented
155C22×C3⋊Dic3C2×D311yescharacteristic, complemented
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—61no—
165C2×C3×#67—61no—
166C22×C3×Dic3—31no—
167C3×D3×D4—64no—
168C3×D3×D4—64no—
169C3×D3×D4—68no—
170C2×C3×D12—31no—
171C2×C3×D12—31no—
172C2×C3×D12—61no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—61no—
176#3811—64no—
177D3×#67—64no—
178D3×#67—64no—
179D3×#67—64no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—64no—
190C2×#625—31no—
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—31no—
195C2×#625—31no—
196C2×#625—31no—
197C2×#625—64no—
198C2×#624—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202#3757C2×D311yescharacteristic, complemented
203#3757C2×D311yescharacteristic, complemented
204#3752C2×D311yescharacteristic, complemented
205#3752C2×D311yescharacteristic, complemented
206#3752C2×D311yescharacteristic, complemented
207#3750C2×D311yescharacteristic, complemented
208C3×#217—31no—
209C3×#217—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×Dic3⋊C4—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216(C2×D3)⋊Dic3—31no—
217(C2×D3)⋊Dic3—31no—
218(C2×D3)⋊Dic3—31no—
219(C2×D3)⋊Dic3—31no—
220(C2×D3)⋊Dic3—31no—
221(C2×D3)⋊Dic3—31no—
222Dic32—31no—
223Dic32—31no—
224C22×H(3,𝔽3)—21no—
225C22×H(3,𝔽3)—21no—
226C22×H(3,𝔽3)—21no—
227C22×H(3,𝔽3)—21no—
228C22×H(3,𝔽3)—21no—
229C22×H(3,𝔽3)C2×D412yescomplemented
230C22×H(3,𝔽3)C2411yescharacteristic
231C2×#272—21no—
232C2×#272—21no—
233C2×#272—21no—
234C2×#272—21no—
235C2×#272—21no—
236C2×#272—21no—
237C2×#272—21no—
238C2×#272—44no—
239C2×#272—44no—
240C2×#272C2×D412yescomplemented
241C2×#272C2×D412yescomplemented
242C2×(C3⋊D3)⋊C3—21no—
243C2×(C3⋊D3)⋊C3—21no—
244C2×(C3⋊D3)⋊C3—21no—
245C2×(C3⋊D3)⋊C3—21no—
246C2×(C3⋊D3)⋊C3—21no—
247C2×(C3⋊D3)⋊C3—21no—
248C2×(C3⋊D3)⋊C3—21no—
249C2×(C3⋊D3)⋊C3—21no—
250C2×(C3⋊D3)⋊C3—44no—
251C2×(C3⋊D3)⋊C3C2×D412yescomplemented
252((C3⋊D3)⋊C3)⋊C2—44no—
253C4×H(3,𝔽3)—21no—
254#1084C2×D412yescomplemented
255(C3⋊Dic3)⋊C3—21no—
256(C3⋊Dic3)⋊C3—21no—
257(C3⋊Dic3)⋊C3—21no—
258(C3⋊Dic3)⋊C3—21no—
259(C3⋊Dic3)⋊C3C2×D412yescomplemented
260C22×C3×D4—91no—
261C22×#67—91no—
262C22×#67—91no—
263C22×#67—91no—
264C22×#67—91no—
265C2×D3×D4—31no—
266C2×D3×D4—31no—
267C2×D3×D4—61no—
268C2×D3×D4—91no—
269C2×D3×D4—91no—
270C2×D3×D4—91no—
271C2×D3×D4—91no—
272C22×D12—91no—
273C3×#121—91no—
274C3×#120—91no—
275#953—91no—
276#953—91no—
277#940—91no—
278#940—91no—
279#940—91no—
280#939—31no—
281#939—91no—
282#939—91no—
283#939—91no—
284#938—91no—
285#937—31no—
286#937—91no—
287#937—91no—
288#937—91no—
289#937—91no—
290D4×Dic3—91no—
291#930—91no—
292C4×#67—91no—
293C4×#67—91no—
294#895—91no—
295#893—91no—
296#884—91no—
297#884—91no—
298#884—91no—
299#884—91no—
300#882—91no—
301#882—91no—
302#882—91no—
303#882—91no—
304#67⋊C4—91no—
305#67⋊C4—91no—
306C23×C32—21no—
307C23×C32—21no—
308C23×C32C22×D311yescharacteristic
309C23×C32C22×D311yescharacteristic
310C23×C32C22×D311yescharacteristic
311C23×C32C22×D311yescharacteristic
312C22×C3⋊D3—22no—
313C22×C3⋊D3—22no—
314C22×C3⋊D3—41no—
315C22×C3⋊D3C22×D311yescharacteristic
316C22×C3⋊D3C22×D311yescharacteristic
317C22×C3⋊D3C22×D311yescharacteristic
318C22×C3×D3—31no—
319C22×C3×D3—31no—
320C22×C3×D3—31no—
321C22×C3×D3—31no—
322C22×C3×D3—31no—
323C22×C3×D3—31no—
324C22×C3×D3—31no—
325C22×C3×D3—31no—
326C22×C3×D3—31no—
327C22×C3×D3—61no—
328C22×C3×D3—61no—
329C22×C3×D3—61no—
330C22×C3×D3—62no—
331C22×C3×D3—62no—
332C22×C3×D3—62no—
333C22×C3×D3—62no—
334C22×C3×D3—62no—
335C22×C3×D3—62no—
336C22×C3×D3—62no—
337C22×C3×D3—64no—
338C22×C3×D3—64no—
339C22×C3×D3—62no—
340C22×C3×D3—62no—
341C22×C3×D3—62no—
342C22×C3×D3—122no—
343C22×C3×D3—122no—
344C22×C3×D3—121no—
345C22×C3×D3—121no—
346C22×C3×D3—121no—
347C22×C3×D3—121no—
348C22×C3×D3—121no—
349C22×C3×D3—122no—
350C22×C3×D3—122no—
351C2×D32—62no—
352C2×D32—62no—
353C2×D32—62no—
354C2×D32—62no—
355C2×D32—121no—
356C2×D32—121no—
357C32×D4—24no—
358C32×D4—22no—
359C32×D4—22no—
360C2×C32×C4—21no—
361C2×C32×C4C22×D311yescharacteristic
362C2×C32×C4C22×D311yescharacteristic
363#638—22no—
364#638—22no—
365#638—22no—
366#638—41no—
367C2×C3⋊Dic3—22no—
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C3×#67—34no—
374C3×#67—34no—
375C3×#67—64no—
376C3×#67—62no—
377C3×#67—62no—
378C3×#67—62no—
379C3×#67—62no—
380C3×#67—64no—
381C3×#67—62no—
382C3×#67—121no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—62no—
392C3×D12—62no—
393C3×D12—62no—
394C3×D12—64no—
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×C4×D3—64no—
398#626—34no—
399#626—62no—
400#626—62no—
401#626—62no—
402#626—62no—
403#626—62no—
404#626—62no—
405#626—62no—
406#626—121no—
407#625—34no—
408#625—62no—
409#625—62no—
410#625—62no—
411#625—62no—
412#625—62no—
413#625—121no—
414#624—62no—
415D3×Dic3—62no—
416D3×Dic3—62no—
417D3×Dic3—62no—
418D42—271noSylow
419C2×H(3,𝔽3)—22no—
420C2×H(3,𝔽3)—41no—
421C2×H(3,𝔽3)C22×D411yescharacteristic
422C2×H(3,𝔽3)C22×D411yescharacteristic
423C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
424#272—22no—
425#272—22no—
426#272—41no—
427(C3⋊D3)⋊C3—22no—
428(C3⋊D3)⋊C3—41no—
429(C3⋊D3)⋊C3—41no—
430C24×C3—91no—
431C24×C3—91no—
432C24×C3—91no—
433C23×D3—31no—
434C23×D3—31no—
435C23×D3—31no—
436C23×D3—31no—
437C23×D3—31no—
438C23×D3—61no—
439C23×D3—61no—
440C23×D3—91no—
441C23×D3—91no—
442C23×D3—91no—
443C23×D3—91no—
444C2×C3×D4—31no—
445C2×C3×D4—31no—
446C2×C3×D4—61no—
447C2×C3×D4—91no—
448C2×C3×D4—91no—
449C2×C3×D4—91no—
450C2×C3×D4—91no—
451C2×C3×D4—91no—
452C2×C3×D4—91no—
453C2×C3×D4—91no—
454C2×C3×D4—184no—
455C2×C3×D4D3211yescharacteristic
456C22×C3×C4—91no—
457C22×C3×C4—91no—
458C2×#67—31no—
459C2×#67—31no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—61no—
467C2×#67—61no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—91no—
472C2×#67—91no—
473C2×#67—91no—
474C2×#67—91no—
475C2×#67—91no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—91no—
480C2×#67—91no—
481C2×#67—91no—
482C2×#67—91no—
483C2×#67—91no—
484C2×#67—91no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—184no—
489C2×#67—184no—
490C2×#67—184no—
491C2×#67—184no—
492C22×Dic3—31no—
493C22×Dic3—91no—
494C22×Dic3—91no—
495C22×Dic3—91no—
496D3×D4—64no—
497D3×D4—64no—
498D3×D4—68no—
499D3×D4—184no—
500D3×D4—184no—
501D3×D4—184no—
502D3×D4—184no—
503C2×D12—31no—
504C2×D12—31no—
505C2×D12—61no—
506C2×D12—91no—
507C2×D12—91no—
508C2×D12—91no—
509C2×D12—91no—
510C2×D12—91no—
511C2×D12—91no—
512C2×D12—91no—
513C2×D12—91no—
514C2×D12—184no—
515C2×C4×D3—31no—
516C2×C4×D3—31no—
517C2×C4×D3—61no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—91no—
521C2×C4×D3—91no—
522C3×C4⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528#217—31no—
529#217—31no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535(C2×D3)⋊C4—31no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547C4⋊Dic3—91no—
548Dic3⋊C4—31no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—21no—
558C22×C32—21no—
559C22×C32—22no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—22no—
568C22×C32—41no—
569C22×C32—41no—
570C22×C32—41no—
571C22×C32—41no—
572C22×C32D3×D412yescomplemented
573C22×C32D3×D412yescomplemented
574C22×C32C23×D311yescharacteristic
575C22×C32C23×D311yescharacteristic
576C2×C3⋊D3—21no—
577C2×C3⋊D3—21no—
578C2×C3⋊D3—21no—
579C2×C3⋊D3—21no—
580C2×C3⋊D3—21no—
581C2×C3⋊D3—21no—
582C2×C3⋊D3—21no—
583C2×C3⋊D3—21no—
584C2×C3⋊D3—44no—
585C2×C3⋊D3D3×D412yescomplemented
586C2×C3×D3—32no—
587C2×C3×D3—32no—
588C2×C3×D3—32no—
589C2×C3×D3—32no—
590C2×C3×D3—32no—
591C2×C3×D3—62no—
592C2×C3×D3—62no—
593C2×C3×D3—62no—
594C2×C3×D3—62no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—62no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—61no—
615C2×C3×D3—61no—
616C2×C3×D3—61no—
617C2×C3×D3—61no—
618C2×C3×D3—121no—
619C2×C3×D3—121no—
620C2×C3×D3—121no—
621C2×C3×D3—121no—
622C2×C3×D3—124no—
623C2×C3×D3—124no—
624C2×C3×D3—124no—
625C2×C3×D3—124no—
626C2×C3×D3—124no—
627C2×C3×D3—128no—
628C2×C3×D3—128no—
629D32—124no—
630D32—124no—
631C32×C4—22no—
632C32×C4—21no—
633C32×C4—21no—
634C3⋊Dic3—21no—
635C3⋊Dic3—21no—
636C3⋊Dic3—21no—
637C3⋊Dic3—21no—
638C3⋊Dic3D3×D412yescomplemented
639C3×Dic3—32no—
640C3×Dic3—32no—
641C3×Dic3—32no—
642C3×Dic3—62no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C22×D4—91no—
648C22×D4—271no—
649C22×D4—271no—
650C22×D4—271no—
651#127—271no—
652#121—91no—
653#121—271no—
654#121—271no—
655#121—271no—
656#120—91no—
657#120—271no—
658#120—271no—
659#120—271no—
660C4×D4—271no—
661C4×D4—271no—
662H(3,𝔽3)D4211yescharacteristic, complemented, Sylow
663C23×C3—31no—
664C23×C3—31no—
665C23×C3—31no—
666C23×C3—31no—
667C23×C3—61no—
668C23×C3—61no—
669C23×C3—91no—
670C23×C3—91no—
671C23×C3—91no—
672C23×C3—91no—
673C23×C3—91no—
674C23×C3—91no—
675C23×C3—182no—
676C23×C3—182no—
677C23×C3—182no—
678C23×C3—182no—
679C23×C3—182no—
680C23×C3—182no—
681C23×C3—361no—
682C23×C3—361no—
683C23×C3—361no—
684C23×C3C2×D3211yescharacteristic
685C23×C3C2×D3211yescharacteristic
686C22×D3—31no—
687C22×D3—31no—
688C22×D3—31no—
689C22×D3—31no—
690C22×D3—31no—
691C22×D3—31no—
692C22×D3—31no—
693C22×D3—31no—
694C22×D3—31no—
695C22×D3—61no—
696C22×D3—61no—
697C22×D3—61no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—62no—
703C22×D3—62no—
704C22×D3—62no—
705C22×D3—62no—
706C22×D3—62no—
707C22×D3—64no—
708C22×D3—64no—
709C22×D3—62no—
710C22×D3—91no—
711C22×D3—91no—
712C22×D3—91no—
713C22×D3—122no—
714C22×D3—122no—
715C22×D3—121no—
716C22×D3—121no—
717C22×D3—121no—
718C22×D3—121no—
719C22×D3—121no—
720C22×D3—122no—
721C22×D3—122no—
722C22×D3—182no—
723C22×D3—182no—
724C22×D3—182no—
725C22×D3—182no—
726C22×D3—182no—
727C22×D3—182no—
728C22×D3—182no—
729C22×D3—182no—
730C22×D3—361no—
731C22×D3—361no—
732C22×D3—361no—
733C22×D3—361no—
734C3×D4—22no—
735C3×D4—62no—
736C3×D4—62no—
737C3×D4—64no—
738C3×D4—94no—
739C3×D4—182no—
740C3×D4—182no—
741C3×D4—182no—
742C3×D4—182no—
743C3×D4—182no—
744C3×D4—361no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—61no—
748C2×C3×C4—91no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—182no—
755C2×C3×C4—182no—
756C2×C3×C4C2×D3211yescharacteristic
757#67—34no—
758#67—34no—
759#67—64no—
760#67—62no—
761#67—62no—
762#67—62no—
763#67—62no—
764#67—64no—
765#67—62no—
766#67—94no—
767#67—94no—
768#67—121no—
769#67—182no—
770#67—182no—
771#67—182no—
772#67—182no—
773#67—182no—
774#67—182no—
775#67—182no—
776#67—182no—
777#67—182no—
778#67—182no—
779#67—182no—
780#67—182no—
781#67—182no—
782#67—182no—
783#67—182no—
784#67—361no—
785#67—361no—
786#67—361no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—61no—
795C2×Dic3—62no—
796C2×Dic3—91no—
797C2×Dic3—91no—
798C2×Dic3—91no—
799C2×Dic3—91no—
800C2×Dic3—91no—
801C2×Dic3—182no—
802C2×Dic3—182no—
803C2×Dic3—182no—
804D12—62no—
805D12—62no—
806D12—64no—
807D12—94no—
808D12—182no—
809D12—182no—
810D12—182no—
811D12—182no—
812D12—182no—
813D12—182no—
814D12—361no—
815C4×D3—62no—
816C4×D3—62no—
817C4×D3—64no—
818C4×D3—182no—
819C4×D3—182no—
820C4×D3—182no—
821C4×D3—182no—
822C2×C32—22no—
823C2×C32—22no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—42no—
828C2×C32—42no—
829C2×C32—41no—
830C2×C32—41no—
831C2×C32C2×D3×D411yescharacteristic
832C2×C32C2×D3×D411yescharacteristic
833C2×C32C2×D3×D411yescharacteristic
834C2×C32C2×D3×D411yescharacteristic
835C2×C32#100411yescharacteristic
836C2×C32#100911yescharacteristic
837C3⋊D3—22no—
838C3⋊D3—41no—
839C3⋊D3—41no—
840C3×D3—64no—
841C3×D3—62no—
842C3×D3—62no—
843C3×D3—62no—
844C3×D3—62no—
845C3×D3—62no—
846C3×D3—122no—
847C3×D3—122no—
848C3×D3—121no—
849C3×D3—121no—
850C3×D3—121no—
851C3×D3—121no—
852C24—91no—
853C24—91no—
854C24—91no—
855C24—271no—
856C2×D4—91no—
857C2×D4—91no—
858C2×D4—91no—
859C2×D4—91no—
860C2×D4—91no—
861C2×D4—91no—
862C2×D4—91no—
863C2×D4—184no—
864C2×D4—271no—
865C2×D4—271no—
866C2×D4—271no—
867C2×D4—271no—
868C2×D4—271no—
869C2×D4—271no—
870C2×D4—271no—
871C2×D4—271no—
872C2×D4—544no—
873C2×D4—544no—
874C2×D4—544no—
875C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
876C22×C4—91no—
877C22×C4—91no—
878C22×C4—271no—
879C22×C4—271no—
880C4⋊C4—91no—
881C4⋊C4—271no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C42—271no—
891C22×C3—21no—
892C22×C3—21no—
893C22×C3—21no—
894C22×C3—21no—
895C22×C3—21no—
896C22×C3—31no—
897C22×C3—31no—
898C22×C3—32no—
899C22×C3—32no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—61no—
910C22×C3—62no—
911C22×C3—61no—
912C22×C3—62no—
913C22×C3—92no—
914C22×C3—92no—
915C22×C3—92no—
916C22×C3—121no—
917C22×C3—121no—
918C22×C3—121no—
919C22×C3—121no—
920C22×C3—181no—
921C22×C3—181no—
922C22×C3—181no—
923C22×C3—181no—
924C22×C3—181no—
925C22×C3—181no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3—181no—
930C22×C3—181no—
931C22×C3—181no—
932C22×C3—181no—
933C22×C3—181no—
934C22×C3—181no—
935C22×C3—364no—
936C22×C3—364no—
937C22×C3—364no—
938C22×C3#381112yes—
939C22×C3C22×D3211yescharacteristic
940C2×D3—32no—
941C2×D3—32no—
942C2×D3—32no—
943C2×D3—32no—
944C2×D3—32no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—62no—
956C2×D3—62no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—62no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—92no—
973C2×D3—121no—
974C2×D3—121no—
975C2×D3—121no—
976C2×D3—121no—
977C2×D3—124no—
978C2×D3—124no—
979C2×D3—124no—
980C2×D3—124no—
981C2×D3—124no—
982C2×D3—128no—
983C2×D3—128no—
984C2×D3—181no—
985C2×D3—181no—
986C2×D3—181no—
987C2×D3—181no—
988C2×D3—181no—
989C2×D3—181no—
990C2×D3—181no—
991C2×D3—181no—
992C2×D3—364no—
993C2×D3—364no—
994C2×D3—364no—
995C2×D3—364no—
996C3×C4—21no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—62no—
1000C3×C4—92no—
1001C3×C4—92no—
1002C3×C4—181no—
1003C3×C4—181no—
1004C3×C4—181no—
1005C3×C4—181no—
1006Dic3—32no—
1007Dic3—32no—
1008Dic3—32no—
1009Dic3—62no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—92no—
1015Dic3—181no—
1016Dic3—181no—
1017Dic3—181no—
1018Dic3—181no—
1019C32—21no—
1020C32#559011yescharacteristic, complemented
1021C32#560911yescharacteristic, complemented
1022C23—91no—
1023C23—91no—
1024C23—91no—
1025C23—91no—
1026C23—91no—
1027C23—91no—
1028C23—182no—
1029C23—182no—
1030C23—182no—
1031C23—182no—
1032C23—182no—
1033C23—182no—
1034C23—361no—
1035C23—361no—
1036C23—361no—
1037C23—542no—
1038C23—542no—
1039C23—1081no—
1040C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1041C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1042D4—22no—
1043D4—94no—
1044D4—182no—
1045D4—182no—
1046D4—182no—
1047D4—182no—
1048D4—182no—
1049D4—274no—
1050D4—361no—
1051D4—542no—
1052D4—542no—
1053D4—542no—
1054D4—542no—
1055D4—542no—
1056D4—542no—
1057D4—1081no—
1058C2×C4—91no—
1059C2×C4—91no—
1060C2×C4—91no—
1061C2×C4—91no—
1062C2×C4—91no—
1063C2×C4—91no—
1064C2×C4—182no—
1065C2×C4—182no—
1066C2×C4—542no—
1067C2×C4—542no—
1068C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1069C2×C3—22no—
1070C2×C3—31no—
1071C2×C3—31no—
1072C2×C3—31no—
1073C2×C3—31no—
1074C2×C3—31no—
1075C2×C3—31no—
1076C2×C3—41no—
1077C2×C3—62no—
1078C2×C3—62no—
1079C2×C3—61no—
1080C2×C3—61no—
1081C2×C3—61no—
1082C2×C3—122no—
1083C2×C3—121no—
1084C2×C3—121no—
1085C2×C3—122no—
1086C2×C3—182no—
1087C2×C3—182no—
1088C2×C3—182no—
1089C2×C3—361no—
1090C2×C3—361no—
1091C2×C3—361no—
1092C2×C3D32×D411yescharacteristic
1093C2×C3#6431411yescharacteristic
1094C2×C3C2×#381111yescharacteristic
1095D3—62no—
1096D3—62no—
1097D3—62no—
1098D3—62no—
1099D3—64no—
1100D3—62no—
1101D3—122no—
1102D3—121no—
1103D3—121no—
1104D3—122no—
1105D3—121no—
1106D3—121no—
1107D3—182no—
1108D3—361no—
1109D3—361no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—92no—
1116C22—92no—
1117C22—92no—
1118C22—181no—
1119C22—181no—
1120C22—181no—
1121C22—181no—
1122C22—181no—
1123C22—181no—
1124C22—181no—
1125C22—181no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—181no—
1132C22—181no—
1133C22—364no—
1134C22—364no—
1135C22—364no—
1136C22—1084no—
1137C22#8867712yescomplemented
1138C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1139C4—21no—
1140C4—92no—
1141C4—92no—
1142C4—181no—
1143C4—181no—
1144C4—181no—
1145C4—181no—
1146C3—31no—
1147C3—31no—
1148C3—61no—
1149C3#1059529211yescharacteristic
1150C2—22no—
1151C2—41no—
1152C2—182no—
1153C2—182no—
1154C2—182no—
1155C2—361no—
1156C2—361no—
1157C2—361no—
1158C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
1159C2#1172250711yescharacteristic
1160C2C2×#8867711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)D42
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×#272C2semidirect
2. C2×#88677C2semidirect
3. C2×#88676C2semidirect
4. C22×#6200C2semidirect
5. #64148⋊C3C2semidirect
6. #64146⋊C3C2semidirect
7. #11721323C2semidirect
8. #11721323C2semidirect
9. #11721317C2semidirect
10. #11721312C2semidirect
11. #11721293C2semidirect
12. #11721163C2semidirect
13. #11721157C2semidirect
14. #11721142C2semidirect
15. #11721124C2semidirect
18. C23×#272C22semidirect
19. C23×#272C22semidirect
20. C23×(C3⋊D3)⋊C3C22semidirect
21. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
22. C2×D4×H(3,𝔽3)C22semidirect
24. C2×#6235C22semidirect
26. C2×C4⋊#272C22semidirect
27. C2×C4×#272C22semidirect
28. C2×#638⋊C3C22semidirect
29. C2×#638⋊C3C22semidirect
30. C2×#638⋊C3C22semidirect
31. C2×#638⋊C3C22semidirect
32. C22×(C3⋊Dic3)⋊C3C22semidirect
37. C2×#6200C22semidirect
38. C2×#6200C22semidirect
39. C2×#6200C22semidirect
40. C2×#6200C22semidirect
41. C2×#6200C22semidirect
42. C2×#6200C22semidirect
43. C2×#6199C22semidirect
44. C2×#6198C22semidirect
45. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
46. #3757⋊C3C22semidirect
47. #3757⋊C3C22semidirect
48. #3752⋊C3C22semidirect
49. #3752⋊C3C22semidirect
50. #3752⋊C3C22semidirect
51. #3750⋊C3C22semidirect
52. #88451C22semidirect
53. #88451C22semidirect
54. #88451C22semidirect
55. #88449C22semidirect
56. #88447C22semidirect
66. #64148D3semidirect
67. #64146D3semidirect
111. #6235D4semidirect
131. #6200D4semidirect
138. C23×C3⋊D3C2×D3semidirect
149. C2×C32×D4C2×D3semidirect
150. C2×C32×D4C2×D3semidirect
151. C2×#638C2×D3semidirect
152. C2×#638C2×D3semidirect
153. C2×#638C2×D3semidirect
154. C2×#638C2×D3semidirect
155. C22×C3⋊Dic3C2×D3semidirect
202. #3757C2×D3semidirect
203. #3757C2×D3semidirect
204. #3752C2×D3semidirect
205. #3752C2×D3semidirect
206. #3752C2×D3semidirect
207. #3750C2×D3semidirect
229. C22×H(3,𝔽3)C2×D4semidirect
240. C2×#272C2×D4semidirect
241. C2×#272C2×D4semidirect
251. C2×(C3⋊D3)⋊C3C2×D4semidirect
254. #1084C2×D4semidirect
259. (C3⋊Dic3)⋊C3C2×D4semidirect
572. C22×C32D3×D4semidirect
573. C22×C32D3×D4semidirect
585. C2×C3⋊D3D3×D4semidirect
638. C3⋊Dic3D3×D4semidirect
662. H(3,𝔽3)D42semidirect
875. C2×D4((C3⋊D3)⋊C3)⋊C2semidirect
1020. C32#5590semidirect
1021. C32#5609semidirect
1137. C22#88677semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#2722
C2×#886772
C2×#886762
C22×#62002
#64148⋊C32
#64146⋊C32
#117213232
#117213172
#117213122
#117212932
#117211632
#117211572
#117211422
#117211242
#105952913
#105952873