Finite Group Databasebeta

← #13148520

Subgroups — #13148520

Order 1728.

872 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721734C211yesmaximal, characteristic, complemented
2#64090⋊C3C211yesmaximal, characteristic
3#64087⋊C3C211yesmaximal, characteristic, complemented
4#11721315C211yesmaximal, characteristic
5#11721314C211yesmaximal, characteristic
6C2×#88449C211yesmaximal, characteristic, complemented
7#11721299C211yesmaximal, characteristic, complemented
8#11721135C211yesmaximal, characteristic, complemented
9#11721134C211yesmaximal, characteristic, complemented
10#11721119C211yesmaximal, characteristic, complemented
11#11721106C211yesmaximal, characteristic, complemented
12#11721091C211yesmaximal, characteristic, complemented
13#11721085C211yesmaximal, characteristic, complemented
14#11721083C211yesmaximal, characteristic, complemented
15#11721079C211yesmaximal, characteristic, complemented
16#10594141—31nomaximal
17#10594133—31nomaximal
18C22×#1084C2211yescharacteristic
19C2×#6229C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic
25C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×#6196C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29#88552C2211yescharacteristic
30C4⋊#1084C2211yescharacteristic
31#88540C2211yescharacteristic
32#88540C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
39C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
40#88450C2211yescharacteristic
41#88450C2211yescharacteristic
42#88449C2211yescharacteristic
43#88449C2211yescharacteristic
44#88449C2211yescharacteristic
45#88449C2211yescharacteristic
46#88449C2211yescharacteristic
47#88448C2211yescharacteristic
48#88448C2211yescharacteristic
49#88448C2211yescharacteristic
50#88448C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53#64090D311yescharacteristic
54#64087D311yescharacteristic, complemented
55C3×#67⋊C4—31no—
56C3×#878—31no—
57C3×#878—31no—
58C3×#878—31no—
59C3×#878—61no—
60#63982—31no—
61#67⋊Dic3—31no—
62Dic3×#67—31no—
63C2×Dic3⋊Dic3—31no—
64C2×Dic3⋊Dic3—31no—
65#63964—31no—
66#63952—31no—
67#63952—31no—
68#63895—31no—
69#63893—31no—
70#63888—31no—
71#63887—31no—
72#63883—31no—
73D3×Dic3⋊C4—31no—
74#63871—31no—
75#63870—31no—
76#63867—31no—
77#63857—31no—
78#63847—31no—
79#63846—31no—
80#63843—31no—
81Dic3×Dic6—31no—
82#63840—31no—
83#63839—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×#1084—22no—
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92C2×#1084C2311yescharacteristic
93#6229—22no—
94#638⋊C3Q814yescomplemented
95C2×(C3⋊Dic3)⋊C3—41no—
96C2×(C3⋊Dic3)⋊C3—41no—
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C4×(C3⋊D3)⋊C3—41no—
105#634⋊C3—41no—
106((C3⋊D3)⋊C3)⋊C4—22no—
107((C3⋊D3)⋊C3)⋊C4—41no—
108#6196—41no—
109#5636—91no—
110#5635—91no—
111#5539—91no—
112C2×#638C2×D311yescharacteristic
113C22×C3⋊Dic3C2×D311yescharacteristic
114C22×C3⋊Dic3C2×D311yescharacteristic
115C2×C4×C3⋊D3C2×D311yescharacteristic
116C2×#634C2×D311yescharacteristic
117C2×C3×#67—31no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3—61no—
123C2×C3×C4×D3—31no—
124C2×C3×Dic6—31no—
125C2×C3×Dic6—31no—
126C2×C3×Dic6—31no—
127C2×C3×Dic6—61no—
128C2×#627—31no—
129C2×#627—31no—
130C2×#624—31no—
131C2×#624—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C32×C22⋊C4—21no—
135C32×C22⋊C4C2×D311yescharacteristic
136C32×C22⋊C4C2×D311yescharacteristic
137#3757C2×D311yescharacteristic
138#3752C2×D311yescharacteristic
139C4⋊(C3⋊Dic3)C2×D311yescharacteristic
140#3750C2×D311yescharacteristic
141#3750C2×D311yescharacteristic
142#3750C2×D311yescharacteristic
143C4×C3⋊Dic3C2×D311yescharacteristic
144C3×#217—31no—
145C3×#217—31no—
146C3×#217—31no—
147C3×#217—61no—
148C3×(C2×D3)⋊C4—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—31no—
152C3×C4⋊Dic3—61no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4—31no—
158C3×Dic3⋊C4—31no—
159C3×Dic3⋊C4—31no—
160C3×Dic3⋊C4—61no—
161C3×Dic3⋊C4—61no—
162C3×C4×Dic3—31no—
163#3724—31no—
164#3724—31no—
165#3724—31no—
166#3724—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179Dic3⋊Dic3—31no—
180Dic3⋊Dic3—31no—
181#3722—31no—
182#3722—31no—
183(C2×D3)⋊Dic3—31no—
184(C2×D3)⋊Dic3—31no—
185Dic32—31no—
186Dic32—31no—
187Dic32—31no—
188Dic32—31no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)—21no—
191C22×H(3,𝔽3)C2×Q812yes—
192C22×H(3,𝔽3)C2411yescharacteristic
193C2×(C3⋊D3)⋊C3—21no—
194C2×(C3⋊D3)⋊C3—21no—
195C2×(C3⋊D3)⋊C3C2×Q812yes—
196C4×H(3,𝔽3)—21no—
197C4×H(3,𝔽3)—21no—
198#1084—21no—
199#1084—21no—
200#1084—21no—
201#1084#4112yes—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3—21no—
208(C3⋊Dic3)⋊C3C2×Q812yes—
209C3×C22⋊Q8—91no—
210C3×C22⋊Q8—91no—
211C3×C4×D4—91no—
212#946—91no—
213#946—91no—
214Q8×Dic3—91no—
215#944—91no—
216D4×Dic3—91no—
217D4×Dic3—91no—
218C4×#67—91no—
219C4×#67—91no—
220C2×C4⋊Dic3—91no—
221#924—91no—
222#924—91no—
223C2×Dic3⋊C4—91no—
224C2×Dic3⋊C4—91no—
225C2×Dic3⋊C4—91no—
226#897—91no—
227#897—91no—
228#896—91no—
229#896—91no—
230D3×C4⋊C4—91no—
231D3×C4⋊C4—91no—
232#890—91no—
233#889—91no—
234#889—91no—
235#889—91no—
236#889—91no—
237#888—91no—
238#888—91no—
239#887—91no—
240#67⋊C4—31no—
241#67⋊C4—91no—
242#67⋊C4—91no—
243#67⋊C4—91no—
244#878—31no—
245#878—31no—
246#878—31no—
247#878—61no—
248#878—91no—
249#878—91no—
250#878—91no—
251#878—91no—
252#878—91no—
253#870—91no—
254C4×Dic6—91no—
255C23×C32—21no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3C22×D311yescharacteristic
259C22×C3×D3—31no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266#638Dic614yescomplemented
267C2×C3⋊Dic3—41no—
268C2×C3⋊Dic3—41no—
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D311yescharacteristic
275C2×C3⋊Dic3C22×D311yescharacteristic
276C4×C3⋊D3—41no—
277#634—41no—
278C3×#67—34no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—122no—
301C2×C3×Dic3—121no—
302C2×C3×Dic3—121no—
303C3×C4×D3—121no—
304C3×Dic6—62no—
305C3×Dic6—62no—
306C3×Dic6—122no—
307C3×Dic6—121no—
308#627—121no—
309#627—121no—
310#624—62no—
311#624—121no—
312D3×Dic3—62no—
313D3×Dic3—121no—
314#554—271noSylow
315C2×H(3,𝔽3)—22no—
316C2×H(3,𝔽3)C22×Q811yescharacteristic
317C2×H(3,𝔽3)C2×#4111yescharacteristic
318C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
319(C3⋊D3)⋊C3—22no—
320C2×C3×Q8—91no—
321C2×C3×Q8—91no—
322C2×C3×D4—91no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C22×C3×C4—91no—
327C2×#67—31no—
328C2×#67—91no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—91no—
337C22×Dic3—91no—
338C2×C4×D3—31no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C3×C4⋊C4—91no—
353C3×C4⋊C4—91no—
354C3×C4⋊C4—91no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4D3211yescharacteristic
366C3×C42—91no—
367#217—31no—
368#217—31no—
369#217—31no—
370#217—61no—
371#217—91no—
372#217—91no—
373#217—91no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—91no—
385C4⋊Dic3—91no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—91no—
389C4⋊Dic3—91no—
390C4⋊Dic3—91no—
391C4⋊Dic3—91no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424C4×Dic3—31no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—22no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32C2×Dic612yes—
441C22×C32D3×Q812yes—
442C22×C32C23×D311yescharacteristic
443C22×C32C23×D311yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3C2×Dic612yes—
447C2×C3×D3—32no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—41no—
455C32×C4—41no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3C2×Dic612yes—
463C3×Dic3—32no—
464C3×Dic3—32no—
465C3×Dic3—32no—
466C3×Dic3—62no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—121no—
480C3×Dic3—121no—
481C3×Dic3—121no—
482C4⋊Q8—271no—
483#125—271no—
484#125—271no—
485C22⋊Q8—91no—
486C22⋊Q8—91no—
487C22⋊Q8—271no—
488C22⋊Q8—271no—
489C22⋊Q8—271no—
490C22⋊Q8—271no—
491C4×Q8—271no—
492C4×D4—91no—
493C4×D4—271no—
494C4×D4—271no—
495C2×C4⋊C4—271no—
496C2×C4⋊C4—271no—
497H(3,𝔽3)#55411yescharacteristic, complemented, Sylow
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—61no—
501C23×C3—91no—
502C23×C3C2×D3211yescharacteristic
503C22×D3—31no—
504C22×D3—91no—
505C3×Q8—182no—
506C3×Q8—361no—
507C3×D4—94no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—182no—
526C2×C3×C4—361no—
527C2×C3×C4—361no—
528C2×C3×C4—361no—
529C2×C3×C4C2×D3211yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531#67—34no—
532#67—94no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—122no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—182no—
565C2×Dic3—361no—
566C2×Dic3—361no—
567C2×Dic3—361no—
568C4×D3—121no—
569C4×D3—182no—
570C4×D3—182no—
571C4×D3—361no—
572C4×D3—361no—
573C4×D3—361no—
574Dic6—62no—
575Dic6—62no—
576Dic6—122no—
577Dic6—121no—
578Dic6—361no—
579Dic6—361no—
580Dic6—361no—
581Dic6—361no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—42no—
588C2×C32C22×Dic611yescharacteristic
589C2×C32#100411yescharacteristic
590C2×C32#100411yescharacteristic
591C2×C32C2×D3×Q811yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C2×C32D3×#4111yescharacteristic
594C3⋊D3—22no—
595C3×D3—62no—
596C2×Q8—91no—
597C2×Q8—91no—
598C2×Q8—271no—
599C2×D4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—91no—
603C22×C4—91no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C4⋊C4—271no—
617C4⋊C4—271no—
618C4⋊C4—271no—
619C4⋊C4—271no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—91no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
628C42—91no—
629C42—271no—
630C42—271no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—31no—
634C22×C3—31no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—92no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3D3×Dic612yes—
649C22×C3C22×D3211yescharacteristic
650C2×D3—32no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—92no—
654C2×D3—181no—
655C2×D3—181no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—92no—
663C3×C4—92no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—181no—
667C3×C4—181no—
668C3×C4—181no—
669C3×C4—181no—
670C3×C4—181no—
671C3×C4—181no—
672C3×C4—181no—
673C3×C4—181no—
674C3×C4—181no—
675Dic3—32no—
676Dic3—32no—
677Dic3—32no—
678Dic3—62no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—92no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—181no—
696Dic3—181no—
697Dic3—181no—
698Dic3—181no—
699Dic3—181no—
700Dic3—181no—
701C32—21no—
702C32#553911yescharacteristic, complemented
703C32#563611yescharacteristic, complemented
704C23—91no—
705C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
706Q8—182no—
707Q8—361no—
708Q8—1081no—
709D4—94no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—182no—
722C2×C4—361no—
723C2×C4—361no—
724C2×C4—361no—
725C2×C4—542no—
726C2×C4—1081no—
727C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
728C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
729C2×C3—22no—
730C2×C3—31no—
731C2×C3—31no—
732C2×C3—31no—
733C2×C3—31no—
734C2×C3—31no—
735C2×C3—31no—
736C2×C3—62no—
737C2×C3—62no—
738C2×C3—61no—
739C2×C3—61no—
740C2×C3—61no—
741C2×C3—122no—
742C2×C3—182no—
743C2×C3C2×D3×Dic611yescharacteristic
744C2×C3#6431211yescharacteristic
745C2×C3#6431311yescharacteristic
746D3—62no—
747D3—182no—
748C22—21no—
749C22—21no—
750C22—92no—
751C22—181no—
752C22—181no—
753C22((C3⋊D3)⋊C3)⋊Q812yes—
754C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
755C4—21no—
756C4—21no—
757C4—92no—
758C4—92no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—181no—
763C4—181no—
764C4—181no—
765C4—181no—
766C4—181no—
767C4—181no—
768C3—31no—
769C3—31no—
770C3—61no—
771C3#1059415611yescharacteristic
772C2—22no—
773C2—182no—
774C2C2×((C3⋊D3)⋊C3)⋊Q811yescharacteristic
775C2#1172250511yescharacteristic
776C2#1172250611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC2×#638⋊C3C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#554
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. #11721734C2semidirect
3. #64087⋊C3C2semidirect
6. C2×#88449C2semidirect
7. #11721299C2semidirect
8. #11721135C2semidirect
9. #11721134C2semidirect
10. #11721119C2semidirect
11. #11721106C2semidirect
12. #11721091C2semidirect
13. #11721085C2semidirect
14. #11721083C2semidirect
15. #11721079C2semidirect
54. #64087D3semidirect
94. #638⋊C3Q8semidirect
266. #638Dic6semidirect
497. H(3,𝔽3)#554semidirect
702. C32#5539semidirect
703. C32#5636semidirect

Maximal subgroups

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

subgroupindex
#117217342
#64090⋊C32
#64087⋊C32
#117213152
#117213142
C2×#884492
#117212992
#117211352
#117211342
#117211192
#117211062
#117210912
#117210852
#117210832
#117210792
#105941413
#105941333