Finite Group Databasebeta

← #13150728

Subgroups — #13150728

Order 1728.

825 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721826C211yesmaximal, characteristic, complemented
2#64138⋊C3C211yesmaximal, characteristic
3C2×#3750⋊C3C211yesmaximal, characteristic, complemented
4#11721314C211yesmaximal, characteristic
5#11721306C211yesmaximal, characteristic
6#11721299C211yesmaximal, characteristic, complemented
7#11721296C211yesmaximal, characteristic, complemented
8#11721133C211yesmaximal, characteristic, complemented
9#11721121C211yesmaximal, characteristic, complemented
10#11721112C211yesmaximal, characteristic, complemented
11#11721111C211yesmaximal, characteristic, complemented
12#11721098C211yesmaximal, characteristic, complemented
13#11721085C211yesmaximal, characteristic, complemented
14#11721085C211yesmaximal, characteristic, complemented
15#11721078C211yesmaximal, characteristic, complemented
16#10594960—31nomaximal
17#10594807—31nomaximal
18C22×C4×H(3,𝔽3)C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
23C2×#6196C2211yescharacteristic
24#88552C2211yescharacteristic
25#88552C2211yescharacteristic
26C4⋊#1084C2211yescharacteristic
27C4⋊#1084C2211yescharacteristic
28C4×#1084C2211yescharacteristic
29C4×#1084C2211yescharacteristic
30#3757⋊C3C2211yescharacteristic
31#3752⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic
33#3750⋊C3C2211yescharacteristic
34#3750⋊C3C2211yescharacteristic
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2211yescharacteristic
37#3750⋊C3C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
39#88450C2211yescharacteristic
40#88450C2211yescharacteristic
41#88450C2211yescharacteristic
42#88449C2211yescharacteristic
43#88449C2211yescharacteristic
44#88449C2211yescharacteristic
45#88448C2211yescharacteristic
46#88448C2211yescharacteristic
47#88448C2211yescharacteristic
48#88448C2211yescharacteristic
49#88448C2211yescharacteristic
50#88447C2211yescharacteristic
51#88447C2211yescharacteristic
52#88447C2211yescharacteristic
53#64138D311yescharacteristic
54C2×#3750D311yescharacteristic, complemented
55C3×#929—31no—
56C3×#926—31no—
57C3×#926—31no—
58C3×#926—61no—
59C2×C3×Dic3⋊C4—31no—
60#63982—31no—
61#67⋊Dic3—31no—
62#63966—31no—
63#63964—31no—
64#63962—31no—
65#63957—31no—
66#63955—31no—
67#63952—31no—
68#63899—31no—
69#63895—31no—
70#63877—31no—
71#63868—31no—
72#63867—31no—
73#63867—31no—
74#63859—31no—
75#63858—31no—
76#63848—31no—
77#63847—31no—
78#63847—31no—
79#63846—31no—
80#63846—31no—
81#63837—31no—
82#63837—31no—
83#63836—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C2×C4×H(3,𝔽3)—22no—
87C2×C4×H(3,𝔽3)C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×#1084C2311yescharacteristic
90C2×#1084C2311yescharacteristic
91C2×#1084C2311yescharacteristic
92C2×#1084C2311yescharacteristic
93#638⋊C3—22no—
94C2×(C3⋊Dic3)⋊C3—22no—
95C2×(C3⋊Dic3)⋊C3—22no—
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103((C3⋊D3)⋊C3)⋊C4—22no—
104#6196—22no—
105#5650—91no—
106#5531—91no—
107#5513—91no—
108C22×C32×C4—21no—
109C22×C32×C4C2×D311yescharacteristic
110C22×C32×C4C2×D311yescharacteristic
111C2×#638C2×D311yescharacteristic
112C22×C3⋊Dic3C2×D311yescharacteristic
113C22×C3⋊Dic3C2×D311yescharacteristic
114C2×C3×#67—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C2×#627—31no—
118C2×#627—31no—
119C2×#624—31no—
120C2×D3×Dic3—31no—
121#3757C2×D311yescharacteristic
122#3752C2×D311yescharacteristic
123#3752C2×D311yescharacteristic
124#3750C2×D311yescharacteristic
125#3750C2×D311yescharacteristic
126#3750C2×D311yescharacteristic
127#3750C2×D311yescharacteristic
128#3750C2×D311yescharacteristic
129#3750C2×D311yescharacteristic
130C3×#217—31no—
131C3×#217—31no—
132C3×#217—31no—
133C3×#217—31no—
134C3×#217—31no—
135C3×#217—61no—
136C3×#217—61no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—61no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—61no—
156C3×C4×Dic3—61no—
157#3724—31no—
158#3724—31no—
159#3724—31no—
160#3724—31no—
161#3724—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173#3722—31no—
174#3722—31no—
175#3722—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179Dic32—31no—
180Dic32—31no—
181Dic32—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—31no—
185C22×H(3,𝔽3)—21no—
186C22×H(3,𝔽3)—21no—
187C22×H(3,𝔽3)#4112yes—
188C22×H(3,𝔽3)C2411yescharacteristic
189C2×(C3⋊D3)⋊C3—21no—
190C2×(C3⋊D3)⋊C3—21no—
191C2×(C3⋊D3)⋊C3—21no—
192C4×H(3,𝔽3)—21no—
193C4×H(3,𝔽3)—21no—
194#1084—21no—
195#1084—21no—
196#1084—21no—
197#1084—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200(C3⋊Dic3)⋊C3—21no—
201(C3⋊Dic3)⋊C3—21no—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3#4112yes—
205C3×#123—91no—
206C3×#117—91no—
207C2×C3×C4⋊C4—91no—
208#935—91no—
209D4×Dic3—91no—
210#929—31no—
211#929—91no—
212#929—91no—
213C4×#67—91no—
214#926—31no—
215#926—31no—
216#926—61no—
217#926—91no—
218#924—91no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—91no—
221#898—91no—
222#898—91no—
223#898—91no—
224#897—91no—
225#896—91no—
226#892—91no—
227#890—91no—
228#890—91no—
229#889—91no—
230#889—91no—
231#889—91no—
232#889—91no—
233#889—91no—
234#889—91no—
235#887—91no—
236#887—91no—
237#886—91no—
238#67⋊C4—91no—
239#879—91no—
240#879—91no—
241#878—91no—
242#878—91no—
243#878—91no—
244#877—91no—
245#877—91no—
246#877—91no—
247#876—91no—
248#872—91no—
249#870—91no—
250C4×Dic6—91no—
251C23×C32—21no—
252C23×C32C22×D311yescharacteristic
253C23×C32C22×D311yescharacteristic
254C22×C3⋊D3C22×D311yescharacteristic
255C22×C3×D3—31no—
256C2×C32×C4—24no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265#638—22no—
266C2×C3⋊Dic3—22no—
267C2×C3⋊Dic3—22no—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D311yescharacteristic
275C3×#67—62no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
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—61no—
292C2×C3×Dic3—61no—
293C2×C3×Dic3—61no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—62no—
297#627—62no—
298#627—62no—
299#624—62no—
300D3×Dic3—62no—
301#552—271noSylow
302C2×H(3,𝔽3)—22no—
303C2×H(3,𝔽3)C2×#4111yescharacteristic
304C2×H(3,𝔽3)C2×#4111yescharacteristic
305C2×H(3,𝔽3)2−1+411yescharacteristic
306(C3⋊D3)⋊C3—41no—
307C2×C3×D4—91no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—91no—
312C22×C3×C4—91no—
313C22×C3×C4D3211yescharacteristic
314C2×#67—31no—
315C2×#67—91no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—91no—
319C22×Dic3—91no—
320C22×Dic3—91no—
321C2×C4×D3—91no—
322C2×C4×D3—91no—
323C2×Dic6—91no—
324C2×Dic6—91no—
325C2×Dic6—91no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4—91no—
337C3×C22⋊C4—91no—
338C3×C22⋊C4—91no—
339C3×C42—91no—
340C3×C42—91no—
341#217—31no—
342#217—31no—
343#217—31no—
344#217—31no—
345#217—31no—
346#217—61no—
347#217—61no—
348#217—91no—
349#217—91no—
350#217—91no—
351#217—91no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—91no—
355(C2×D3)⋊C4—91no—
356(C2×D3)⋊C4—91no—
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—91no—
369C4⋊Dic3—91no—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—22no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32#23712yes—
428C22×C32#23712yes—
429C22×C32C23×D311yescharacteristic
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—21no—
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3#23512yes—
450C3×Dic3—32no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—121no—
466C3×Dic3—121no—
467C3×Dic3—121no—
468C3×Dic3—121no—
469#126—271no—
470#126—271no—
471#125—271no—
472#125—271no—
473#125—271no—
474#123—91no—
475#123—271no—
476C22⋊Q8—271no—
477C22⋊Q8—271no—
478C4×Q8—271no—
479C4×D4—271no—
480#117—91no—
481#117—271no—
482#117—271no—
483C2×C4⋊C4—91no—
484H(3,𝔽3)#55211yescharacteristic, complemented, Sylow
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—91no—
489C23×C3C2×D3211yescharacteristic
490C22×D3—31no—
491C22×D3—91no—
492C3×D4—182no—
493C2×C3×C4—22no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—64no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—182no—
515C2×C3×C4—182no—
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518#67—62no—
519#67—182no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—182no—
549C2×Dic3—182no—
550C2×Dic3—182no—
551C4×D3—182no—
552C4×D3—182no—
553Dic6—182no—
554Dic6—182no—
555Dic6—182no—
556C2×C32—22no—
557C2×C32—22no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—42no—
562C2×C32C2×#23511yescharacteristic
563C2×C32C2×#23711yescharacteristic
564C2×C32C2×#23711yescharacteristic
565C2×C32#100711yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C2×C32#101011yescharacteristic
568C3⋊D3—41no—
569C3×D3—121no—
570C2×Q8—271no—
571C2×D4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—271no—
575C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4—271no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C42—91no—
601C42—91no—
602C42—271no—
603C42—271no—
604C42—271no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—31no—
608C22×C3—31no—
609C22×C3—32no—
610C22×C3—32no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—62no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3#380512yes—
623C22×C3C22×D3211yescharacteristic
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—181no—
628C2×D3—181no—
629C2×D3—181no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—92no—
639C3×C4—181no—
640C3×C4—181no—
641C3×C4—181no—
642C3×C4—181no—
643C3×C4—181no—
644C3×C4—181no—
645C3×C4—181no—
646C3×C4—181no—
647C3×C4—181no—
648C3×C4—181no—
649Dic3—32no—
650Dic3—61no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—61no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—92no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675C32—21no—
676C32#551311yescharacteristic, complemented
677C32#565011yescharacteristic, complemented
678C23—91no—
679C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
680Q8—542no—
681D4—182no—
682C2×C4—22no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—182no—
695C2×C4—182no—
696C2×C4—542no—
697C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
698C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
699C2×C3—22no—
700C2×C3—31no—
701C2×C3—31no—
702C2×C3—31no—
703C2×C3—31no—
704C2×C3—31no—
705C2×C3—31no—
706C2×C3—62no—
707C2×C3—62no—
708C2×C3—61no—
709C2×C3—61no—
710C2×C3—61no—
711C2×C3—122no—
712C2×C3—361no—
713C2×C3#6429711yescharacteristic
714C2×C3D3×#23511yescharacteristic
715C2×C3C2×#380511yescharacteristic
716D3—121no—
717D3—361no—
718C22—21no—
719C22—21no—
720C22—181no—
721C22—181no—
722C22—181no—
723C22#8867212yes—
724C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
725C4—21no—
726C4—21no—
727C4—92no—
728C4—181no—
729C4—181no—
730C4—181no—
731C4—181no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—181no—
738C3—31no—
739C3—31no—
740C3—61no—
741C3#1059495211yescharacteristic
742C2—22no—
743C2—361no—
744C2#1172248211yescharacteristic
745C2#1172249011yescharacteristic
746C2C2×#8867211yescharacteristic
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)#552
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. #11721826C2semidirect
3. C2×#3750⋊C3C2semidirect
6. #11721299C2semidirect
7. #11721296C2semidirect
8. #11721133C2semidirect
9. #11721121C2semidirect
10. #11721112C2semidirect
11. #11721111C2semidirect
12. #11721098C2semidirect
13. #11721085C2semidirect
14. #11721085C2semidirect
15. #11721078C2semidirect
54. C2×#3750D3semidirect
484. H(3,𝔽3)#552semidirect
676. C32#5513semidirect
677. C32#5650semidirect

Maximal subgroups

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

subgroupindex
#117218262
#64138⋊C32
C2×#3750⋊C32
#117213142
#117213062
#117212992
#117212962
#117211332
#117211212
#117211122
#117211112
#117210982
#117210852
#117210782
#105949603
#105948073