Finite Group Databasebeta

← #13151437

Subgroups — #13151437

Order 1728.

1285 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6199C211yesmaximal, characteristic, complemented
2C2×#88671C211yesmaximal, characteristic, complemented
3#11721847C211yesmaximal, characteristic, complemented
4#64148⋊C3C211yesmaximal, characteristic, complemented
5D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
6#11721323C211yesmaximal, characteristic, complemented
7#11721319C211yesmaximal, characteristic, complemented
8#11721314C211yesmaximal, characteristic, complemented
9#11721303C211yesmaximal, characteristic, complemented
10#11721299C211yesmaximal, characteristic, complemented
11#11721293C211yesmaximal, characteristic, complemented
12#11721150C211yesmaximal, characteristic, complemented
13#11721123C211yesmaximal, characteristic, complemented
14#11721102C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10595130—31nomaximal
17#10595129—31nomaximal
18C23×#272C2211yescharacteristic
19C2×D4×H(3,𝔽3)C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C2×#6235C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic, complemented
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
26C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
27C2×#6200C2211yescharacteristic
28C2×#6200C2211yescharacteristic
29C2×#6199—24no—
30C2×#6199C2211yescharacteristic
31C2×#6199C2211yescharacteristic
32C2×#6199C2211yescharacteristic
33C2×#6199C2211yescharacteristic
34#88671—24no—
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
36C2×#6196C2211yescharacteristic, complemented
37#88552C2211yescharacteristic
38#88542C2211yescharacteristic
39#88542C2211yescharacteristic
40#3757⋊C3C2211yescharacteristic
41#3757⋊C3C2211yescharacteristic, complemented
42#3757⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
45#3750⋊C3C2211yescharacteristic, complemented
46C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
47#88451C2211yescharacteristic
48#88451C2211yescharacteristic
49#88450C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C2×#3805—31no—
56C2×#3804—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59#64148D311yescharacteristic, complemented
60D4×C3⋊Dic3D311yescharacteristic, complemented
61C3×#939—31no—
62C3×#937—31no—
63C3×#937—31no—
64C3×#937—61no—
65C3×D4×Dic3—31no—
66#63982—31no—
67#63977—31no—
68#63976—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—31no—
71Dic3×#67—31no—
72#63971—31no—
73#63970—31no—
74#63969—31no—
75#63969—31no—
76#63964—31no—
77#63952—31no—
78#63902—31no—
79#63899—31no—
80#63893—31no—
81#63891—31no—
82#63890—31no—
83#63880—31no—
84#63878—31no—
85#63877—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C23×H(3,𝔽3)C2311yescharacteristic
88C22×#272—22no—
89C22×#272—22no—
90C22×#272—22no—
91C22×#272C2311yescharacteristic
92C22×#272C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94D4×H(3,𝔽3)—22no—
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96#6235—22no—
97#6235—22no—
98C2×#1084C2311yescharacteristic
99C2×#1084C2311yescharacteristic
100#638⋊C3—22no—
101#638⋊C3—22no—
102C2×(C3⋊Dic3)⋊C3—22no—
103C2×(C3⋊Dic3)⋊C3—22no—
104C2×(C3⋊Dic3)⋊C3—22no—
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112#6200—22no—
113#6200—22no—
114#6199—22no—
115#6199—22no—
116#6199—22no—
117#6199D414yescomplemented
118((C3⋊D3)⋊C3)⋊C4—22no—
119#6196—22no—
120#5606—91no—
121#5586—91no—
122#5547—91no—
123C23×C3×D3—31no—
124C23×C3×D3—31no—
125C23×C3×D3—61no—
126C2×C32×D4—21no—
127C2×C32×D4C2×D311yescharacteristic
128C2×C32×D4C2×D311yescharacteristic
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic, complemented
131C22×C3⋊Dic3C2×D311yescharacteristic
132C22×C3⋊Dic3C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic, complemented
134C2×C3×#67—31no—
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—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—31no—
145C2×#627—31no—
146C2×#627—31no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#625—31no—
150C2×#625—31no—
151C2×#624—31no—
152#3805—64no—
153#3804—64no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—64no—
164C2×D3×Dic3—64no—
165#3757C2×D311yescharacteristic
166#3757C2×D311yescharacteristic, complemented
167#3757C2×D311yescharacteristic, complemented
168#3752C2×D311yescharacteristic, complemented
169C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
170#3750C2×D311yescharacteristic, complemented
171C4×C3⋊Dic3C2×D311yescharacteristic, complemented
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×#217—61no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—61no—
184C3×(C2×D3)⋊C4—61no—
185C3×C4⋊Dic3—31no—
186C3×Dic3⋊C4—31no—
187C3×C4×Dic3—31no—
188#3724—31no—
189#3724—31no—
190#3724—31no—
191Dic3⋊Dic3—31no—
192Dic3⋊Dic3—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195Dic3⋊Dic3—31no—
196#3722—31no—
197(C2×D3)⋊Dic3—31no—
198(C2×D3)⋊Dic3—31no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202Dic32—31no—
203Dic32—31no—
204C22×H(3,𝔽3)—21no—
205C22×H(3,𝔽3)—21no—
206C22×H(3,𝔽3)—21no—
207C22×H(3,𝔽3)—21no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)#4112yescomplemented
210C22×H(3,𝔽3)C2411yescharacteristic
211C2×#272—28no—
212C2×#272—21no—
213C2×#272—21no—
214C2×#272—21no—
215C2×#272—21no—
216C2×#272C2×D412yes—
217C2×#272#4112yescomplemented
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C4×H(3,𝔽3)—21no—
222#1084—21no—
223#1084—21no—
224(C3⋊Dic3)⋊C3—21no—
225(C3⋊Dic3)⋊C3—21no—
226(C3⋊Dic3)⋊C3—21no—
227(C3⋊Dic3)⋊C3—21no—
228(C3⋊Dic3)⋊C3—21no—
229(C3⋊Dic3)⋊C3C2×D412yes—
230(C3⋊Dic3)⋊C3C2×D412yes—
231C23×Dic3—91no—
232C2×#237—91no—
233C2×#237—91no—
234C2×#235—91no—
235C22×C4×D3—91no—
236C22×C4×D3—91no—
237C3×#121—91no—
238C3×#120—91no—
239C3×C4×D4—91no—
240#953—91no—
241#939—31no—
242#939—91no—
243#939—91no—
244#938—91no—
245#937—31no—
246#937—31no—
247#937—61no—
248#937—91no—
249#935—91no—
250D4×Dic3—31no—
251D4×Dic3—91no—
252D4×Dic3—91no—
253D4×Dic3—91no—
254C4×#67—91no—
255C4×#67—91no—
256#924—91no—
257#897—91no—
258#896—91no—
259#894—91no—
260#892—91no—
261#886—91no—
262#884—91no—
263#883—91no—
264#883—91no—
265#883—91no—
266#882—91no—
267#67⋊C4—91no—
268#67⋊C4—91no—
269#67⋊C4—91no—
270#67⋊C4—91no—
271#878—91no—
272#878—91no—
273#878—91no—
274#877—91no—
275C4×D12—91no—
276#872—91no—
277C23×C32—21no—
278C23×C32—21no—
279C23×C32C22×D311yescharacteristic
280C23×C32C22×D311yescharacteristic
281C23×C32C22×D311yescharacteristic
282C23×C32C22×D311yescharacteristic
283C22×C3⋊D3C22×D311yescharacteristic
284C22×C3×D3—31no—
285C22×C3×D3—31no—
286C22×C3×D3—31no—
287C22×C3×D3—31no—
288C22×C3×D3—31no—
289C22×C3×D3—61no—
290C22×C3×D3—61no—
291C22×C3×D3—62no—
292C22×C3×D3—62no—
293C22×C3×D3—62no—
294C22×C3×D3—62no—
295C22×C3×D3—62no—
296C22×C3×D3—62no—
297C22×C3×D3—122no—
298C22×C3×D3—122no—
299C22×C3×D3—122no—
300C32×D4—22no—
301C32×D4—22no—
302C32×D4—42no—
303C2×C32×C4—21no—
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C22×D311yescharacteristic
306#638—22no—
307#638—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3—22no—
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D311yescharacteristic
313C2×C3⋊Dic3C22×D311yescharacteristic
314C2×C3⋊Dic3C22×D311yescharacteristic
315C2×C3⋊Dic3C22×D311yescharacteristic
316C2×C3⋊Dic3C22×D311yescharacteristic
317C2×C3⋊Dic3C22×D311yescharacteristic
318C3×#67—62no—
319C3×#67—62no—
320C3×#67—62no—
321C3×#67—62no—
322C3×#67—62no—
323C3×#67—62no—
324C3×#67—122no—
325C3×#67—122no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—31no—
333C2×C3×Dic3—31no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
337C2×C3×Dic3—61no—
338C2×C3×Dic3—61no—
339C2×C3×Dic3—62no—
340C2×C3×Dic3—62no—
341C2×C3×Dic3—62no—
342#627—62no—
343#627—62no—
344#626—62no—
345#626—62no—
346#625—62no—
347#625—62no—
348#624—62no—
349D3×Dic3—34no—
350D3×Dic3—34no—
351D3×Dic3—62no—
352D3×Dic3—62no—
353D3×Dic3—62no—
354D3×Dic3—62no—
355D3×Dic3—62no—
356D3×Dic3—62no—
357D3×Dic3—62no—
358#525—271noSylow
359C2×H(3,𝔽3)—22no—
360C2×H(3,𝔽3)—41no—
361C2×H(3,𝔽3)C22×D411yescharacteristic
362C2×H(3,𝔽3)C2×#4111yescharacteristic
363C2×H(3,𝔽3)C2×#4111yescharacteristic
364#272—22no—
365#272—22no—
366(C3⋊D3)⋊C3—41no—
367C24×C3—91no—
368C23×D3—31no—
369C23×D3—31no—
370C23×D3—61no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—61no—
374C2×C3×D4—91no—
375C2×C3×D4—91no—
376C2×C3×D4—91no—
377C2×C3×D4—91no—
378C2×C3×D4D3211yescharacteristic
379C22×C3×C4—91no—
380C22×C3×C4—91no—
381C22×C3×C4—91no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—31no—
385C2×#67—31no—
386C2×#67—31no—
387C2×#67—31no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—91no—
400C22×Dic3—91no—
401C22×Dic3—91no—
402C22×Dic3—91no—
403C22×Dic3—91no—
404C22×Dic3—91no—
405C22×Dic3—91no—
406C22×Dic3—91no—
407C22×Dic3—184no—
408#237—184no—
409#237—184no—
410#235—184no—
411C2×D12—91no—
412C2×D12—91no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×C4×D3—91no—
417C2×C4×D3—91no—
418C2×C4×D3—91no—
419C2×C4×D3—91no—
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×C4×D3—91no—
423C2×C4×D3—184no—
424C2×C4×D3—184no—
425C2×Dic6—91no—
426C2×Dic6—91no—
427C2×Dic6—91no—
428C3×C4⋊C4—91no—
429C3×C4⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4—91no—
433C3×C22⋊C4—91no—
434C3×C22⋊C4—91no—
435C3×C22⋊C4—91no—
436C3×C22⋊C4—91no—
437C3×C42—91no—
438#217—31no—
439#217—31no—
440#217—31no—
441#217—31no—
442#217—31no—
443#217—61no—
444#217—91no—
445#217—91no—
446#217—91no—
447#217—91no—
448#217—91no—
449#217—91no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—31no—
452(C2×D3)⋊C4—31no—
453(C2×D3)⋊C4—31no—
454(C2×D3)⋊C4—31no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4—91no—
458(C2×D3)⋊C4—91no—
459(C2×D3)⋊C4—91no—
460(C2×D3)⋊C4—91no—
461(C2×D3)⋊C4—91no—
462(C2×D3)⋊C4—91no—
463(C2×D3)⋊C4—91no—
464C4⋊Dic3—31no—
465C4⋊Dic3—91no—
466C4⋊Dic3—91no—
467C4⋊Dic3—91no—
468C4⋊Dic3—91no—
469C4⋊Dic3—91no—
470Dic3⋊C4—31no—
471Dic3⋊C4—91no—
472Dic3⋊C4—91no—
473Dic3⋊C4—91no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—91no—
477Dic3⋊C4—91no—
478Dic3⋊C4—91no—
479Dic3⋊C4—91no—
480C4×Dic3—31no—
481C4×Dic3—91no—
482C4×Dic3—91no—
483C4×Dic3—91no—
484C4×Dic3—91no—
485C22×C32—21no—
486C22×C32—21no—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—21no—
490C22×C32—21no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—22no—
497C22×C32—41no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32#23512yescomplemented
503C22×C32#23712yescomplemented
504C22×C32C23×D311yescharacteristic
505C22×C32C23×D311yescharacteristic
506C2×C3⋊D3—21no—
507C2×C3⋊D3—21no—
508C2×C3⋊D3—21no—
509C2×C3×D3—32no—
510C2×C3×D3—32no—
511C2×C3×D3—32no—
512C2×C3×D3—32no—
513C2×C3×D3—62no—
514C2×C3×D3—62no—
515C2×C3×D3—68no—
516C2×C3×D3—68no—
517C2×C3×D3—61no—
518C2×C3×D3—61no—
519C2×C3×D3—61no—
520C2×C3×D3—61no—
521C2×C3×D3—61no—
522C2×C3×D3—61no—
523C2×C3×D3—61no—
524C2×C3×D3—61no—
525C2×C3×D3—61no—
526C2×C3×D3—61no—
527C2×C3×D3—61no—
528C2×C3×D3—121no—
529C2×C3×D3—121no—
530C2×C3×D3—121no—
531C2×C3×D3—121no—
532C2×C3×D3—128no—
533C32×C4—21no—
534C32×C4—21no—
535C32×C4—41no—
536C3⋊Dic3—21no—
537C3⋊Dic3—21no—
538C3⋊Dic3—21no—
539C3⋊Dic3—21no—
540C3⋊Dic3—21no—
541C3⋊Dic3D3×D412yes—
542C3⋊Dic3D3×D412yes—
543C3×Dic3—32no—
544C3×Dic3—32no—
545C3×Dic3—61no—
546C3×Dic3—61no—
547C3×Dic3—61no—
548C3×Dic3—61no—
549C3×Dic3—61no—
550C3×Dic3—61no—
551C3×Dic3—61no—
552C3×Dic3—61no—
553C3×Dic3—61no—
554C3×Dic3—121no—
555C3×Dic3—121no—
556C2×#41—271no—
557C23×C4—271no—
558#123—271no—
559#123—271no—
560C22⋊Q8—271no—
561C22⋊Q8—271no—
562#121—91no—
563#121—271no—
564#120—91no—
565#120—271no—
566C4×D4—91no—
567C4×D4—271no—
568C4×D4—271no—
569C4×D4—271no—
570#117—271no—
571H(3,𝔽3)#52511yescharacteristic, complemented, Sylow
572C23×C3—31no—
573C23×C3—31no—
574C23×C3—31no—
575C23×C3—31no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—91no—
579C23×C3—91no—
580C23×C3—91no—
581C23×C3—182no—
582C23×C3—182no—
583C23×C3—182no—
584C23×C3C2×D3211yescharacteristic
585C23×C3C2×D3211yescharacteristic
586C22×D3—31no—
587C22×D3—31no—
588C22×D3—31no—
589C22×D3—31no—
590C22×D3—31no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—91no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3—122no—
603C3×D4—22no—
604C3×D4—62no—
605C3×D4—62no—
606C3×D4—122no—
607C3×D4—182no—
608C3×D4—182no—
609C3×D4—182no—
610C3×D4—182no—
611C2×C3×C4—31no—
612C2×C3×C4—31no—
613C2×C3×C4—61no—
614C2×C3×C4—91no—
615C2×C3×C4—91no—
616C2×C3×C4—91no—
617C2×C3×C4—91no—
618C2×C3×C4—91no—
619C2×C3×C4—91no—
620C2×C3×C4—91no—
621C2×C3×C4—91no—
622C2×C3×C4—91no—
623C2×C3×C4—182no—
624C2×C3×C4—182no—
625C2×C3×C4—182no—
626C2×C3×C4C2×D3211yescharacteristic
627#67—62no—
628#67—62no—
629#67—62no—
630#67—62no—
631#67—62no—
632#67—62no—
633#67—122no—
634#67—122no—
635#67—182no—
636#67—182no—
637#67—182no—
638#67—182no—
639#67—182no—
640#67—182no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—31no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—91no—
658C2×Dic3—91no—
659C2×Dic3—91no—
660C2×Dic3—91no—
661C2×Dic3—91no—
662C2×Dic3—91no—
663C2×Dic3—91no—
664C2×Dic3—94no—
665C2×Dic3—182no—
666C2×Dic3—182no—
667C2×Dic3—182no—
668C2×Dic3—182no—
669C2×Dic3—182no—
670C2×Dic3—182no—
671C2×Dic3—182no—
672D12—182no—
673D12—182no—
674C4×D3—94no—
675C4×D3—94no—
676C4×D3—182no—
677C4×D3—182no—
678C4×D3—182no—
679C4×D3—182no—
680C4×D3—182no—
681C4×D3—182no—
682C4×D3—182no—
683C4×D3—182no—
684Dic6—182no—
685Dic6—182no—
686Dic6—182no—
687C2×C32—22no—
688C2×C32—22no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—42no—
693C2×C32—41no—
694C2×C32—41no—
695C2×C32—81no—
696C2×C32C2×#23511yescharacteristic
697C2×C32C2×D3×D411yescharacteristic
698C2×C32C2×D3×D411yescharacteristic
699C2×C32C2×#23711yescharacteristic
700C2×C32D3×#4111yescharacteristic
701C2×C32D3×#4111yescharacteristic
702C3⋊D3—41no—
703C3×D3—62no—
704C3×D3—62no—
705C3×D3—62no—
706C3×D3—62no—
707C3×D3—122no—
708C3×D3—122no—
709C3×D3—121no—
710C24—91no—
711#41—544no—
712C2×Q8—271no—
713C2×D4—91no—
714C2×D4—91no—
715C2×D4—91no—
716C2×D4—91no—
717C2×D4—271no—
718C2×D4—271no—
719C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic
720C22×C4—91no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—271no—
726C22×C4—271no—
727C22×C4—271no—
728C22×C4—544no—
729C4⋊C4—91no—
730C4⋊C4—91no—
731C4⋊C4—271no—
732C4⋊C4—271no—
733C4⋊C4—271no—
734C4⋊C4—271no—
735C22⋊C4—91no—
736C22⋊C4—91no—
737C22⋊C4—91no—
738C22⋊C4—91no—
739C22⋊C4—91no—
740C22⋊C4—91no—
741C22⋊C4—91no—
742C22⋊C4—271no—
743C22⋊C4—271no—
744C22⋊C4—271no—
745C42—91no—
746C42—271no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—31no—
753C22×C3—31no—
754C22×C3—32no—
755C22×C3—32no—
756C22×C3—61no—
757C22×C3—61no—
758C22×C3—61no—
759C22×C3—61no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—62no—
768C22×C3—92no—
769C22×C3—92no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—188no—
776C22×C3—181no—
777C22×C3—181no—
778C22×C3—181no—
779C22×C3—181no—
780C22×C3—181no—
781C22×C3—181no—
782C22×C3—181no—
783C22×C3#380412yes—
784C22×C3C22×D3211yescharacteristic
785C2×D3—32no—
786C2×D3—32no—
787C2×D3—32no—
788C2×D3—32no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—68no—
800C2×D3—68no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—128no—
809C2×D3—181no—
810C2×D3—181no—
811C2×D3—181no—
812C3×C4—21no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—92no—
816C3×C4—92no—
817C3×C4—121no—
818C3×C4—181no—
819C3×C4—181no—
820C3×C4—181no—
821C3×C4—181no—
822C3×C4—181no—
823C3×C4—181no—
824C3×C4—181no—
825Dic3—32no—
826Dic3—32no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—61no—
836Dic3—92no—
837Dic3—92no—
838Dic3—121no—
839Dic3—121no—
840Dic3—181no—
841Dic3—181no—
842Dic3—181no—
843Dic3—181no—
844Dic3—181no—
845C32—21no—
846C32#554711yescharacteristic, complemented
847C32#560611yescharacteristic, complemented
848C23—91no—
849C23—91no—
850C23—91no—
851C23—182no—
852C23—182no—
853C23—182no—
854C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
855C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
856Q8—542no—
857D4—22no—
858D4—182no—
859D4—182no—
860D4—182no—
861D4—182no—
862D4—542no—
863D4—542no—
864C2×C4—91no—
865C2×C4—91no—
866C2×C4—91no—
867C2×C4—91no—
868C2×C4—91no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—91no—
872C2×C4—91no—
873C2×C4—182no—
874C2×C4—182no—
875C2×C4—182no—
876C2×C4—274no—
877C2×C4—542no—
878C2×C4—542no—
879C2×C4—542no—
880C2×C4—542no—
881C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
882C2×C3—22no—
883C2×C3—31no—
884C2×C3—31no—
885C2×C3—31no—
886C2×C3—31no—
887C2×C3—31no—
888C2×C3—31no—
889C2×C3—41no—
890C2×C3—62no—
891C2×C3—62no—
892C2×C3—61no—
893C2×C3—61no—
894C2×C3—61no—
895C2×C3—122no—
896C2×C3—121no—
897C2×C3—121no—
898C2×C3—182no—
899C2×C3—182no—
900C2×C3—241no—
901C2×C3—361no—
902C2×C3D32×D411yescharacteristic
903C2×C3#6431211yescharacteristic
904C2×C3C2×#380411yescharacteristic
905D3—62no—
906D3—62no—
907D3—62no—
908D3—62no—
909D3—122no—
910D3—122no—
911D3—121no—
912D3—361no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—92no—
919C22—92no—
920C22—188no—
921C22—181no—
922C22—181no—
923C22—181no—
924C22—181no—
925C22—181no—
926C22—181no—
927C22—181no—
928C22#8867112yescomplemented
929C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
930C4—21no—
931C4—92no—
932C4—92no—
933C4—181no—
934C4—181no—
935C4—181no—
936C4—181no—
937C4—181no—
938C4—181no—
939C4—181no—
940C3—31no—
941C3—31no—
942C3—61no—
943C3#1059513811yescharacteristic
944C2—22no—
945C2—41no—
946C2—182no—
947C2—182no—
948C2—361no—
949C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
950C2#1172250511yescharacteristic
951C2C2×#8867111yescharacteristic
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)#525
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. C22×#6199C2semidirect
2. C2×#88671C2semidirect
3. #11721847C2semidirect
4. #64148⋊C3C2semidirect
5. D4×(C3⋊Dic3)⋊C3C2semidirect
6. #11721323C2semidirect
7. #11721319C2semidirect
8. #11721314C2semidirect
9. #11721303C2semidirect
10. #11721299C2semidirect
11. #11721293C2semidirect
12. #11721150C2semidirect
13. #11721123C2semidirect
14. #11721102C2semidirect
15. #11721076C2semidirect
23. C2×#638⋊C3C22semidirect
26. C22×(C3⋊Dic3)⋊C3C22semidirect
35. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
36. C2×#6196C22semidirect
41. #3757⋊C3C22semidirect
42. #3757⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
45. #3750⋊C3C22semidirect
46. C4×(C3⋊Dic3)⋊C3C22semidirect
49. #88450C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88448C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
59. #64148D3semidirect
60. D4×C3⋊Dic3D3semidirect
117. #6199D4semidirect
130. C2×#638C2×D3semidirect
133. C22×C3⋊Dic3C2×D3semidirect
166. #3757C2×D3semidirect
167. #3757C2×D3semidirect
168. #3752C2×D3semidirect
169. C4⋊(C3⋊Dic3)C2×D3semidirect
170. #3750C2×D3semidirect
171. C4×C3⋊Dic3C2×D3semidirect
209. C22×H(3,𝔽3)#41semidirect
217. C2×#272#41semidirect
502. C22×C32#235semidirect
503. C22×C32#237semidirect
571. H(3,𝔽3)#525semidirect
846. C32#5547semidirect
847. C32#5606semidirect
928. C22#88671semidirect

Maximal subgroups

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

subgroupindex
C22×#61992
C2×#886712
#117218472
#64148⋊C32
D4×(C3⋊Dic3)⋊C32
#117213232
#117213192
#117213142
#117213032
#117212992
#117212932
#117211502
#117211232
#117211022
#117210762
#105951303
#105951293