Finite Group Databasebeta

← #10846092

Subgroups — #10846092

Order 768.

984 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2542C211yesmaximal, characteristic
2C2×#5090C211yesmaximal, characteristic, complemented
3C2×#5052C211yesmaximal, characteristic, complemented
4C2×#5051C211yesmaximal, characteristic, complemented
5#82375C211yesmaximal, characteristic
6C2×#5011C211yesmaximal, characteristic
7#71786C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#71697C211yesmaximal, characteristic, complemented
11#71696C211yesmaximal, characteristic, complemented
12#71695C211yesmaximal, characteristic, complemented
13#71694C211yesmaximal, characteristic, complemented
14#69475C211yesmaximal, characteristic, complemented
15#69468C211yesmaximal, characteristic, complemented
16#25398—31nomaximal, Sylow
17C2×C3×C4⋊Q8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×#208C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C3×#399—21no—
31C3×#399—21no—
32C3×#390—21no—
33C3×#384—21no—
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5222—21no—
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5090—24no—
47#5052—24no—
48#5051—24no—
49#5011—24no—
50#4983—21no—
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4944—21no—
56#4944—21no—
57#4936C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#470—31no—
65C2×#467—31no—
66C2×#462—31no—
67C2×#435—31no—
68#2542D311yescharacteristic
69#2536—31no—
70#2036—31no—
71#2035—31no—
72#2001—31no—
73#2001—31no—
74#1960—31no—
75#1949—31no—
76#1894—31no—
77#1892—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4D411yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×Dic6C2311yescharacteristic
85C3×C4⋊Q8—22no—
86C3×C4⋊Q8—22no—
87C3×C22⋊Q8—22no—
88C3×C22⋊Q8—22no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—41no—
92C3×C22⋊Q8—41no—
93C3×C22⋊Q8—41no—
94C3×C22⋊Q8—41no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4D411yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4D411yescharacteristic
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C42—21no—
113C2×C3×C42C2311yescharacteristic
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#216—22no—
121C2×#216—22no—
122C2×#216—41no—
123C2×#216—41no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924—22no—
129#924—41no—
130#924—41no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×#208—22no—
136C2×#208—22no—
137C2×#208—41no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C4×Dic6—22no—
146C4×Dic6—22no—
147C3×#95—21no—
148#835—22no—
149#835—22no—
150#835—22no—
151#835—22no—
152#835—41no—
153#835—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—22no—
159#830—22no—
160#810—22no—
161#810D414yescomplemented
162#808—22no—
163#807—22no—
164C4⋊(C3⋊C8)D414yes—
165#803—22no—
166C22×Q16—31no—
167C22×Q16—31no—
168C22×M16—31no—
169C23×C8—31no—
170C2×C4⋊Q8C2×D311yescharacteristic
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×C22⋊Q8C2×D311yescharacteristic
176C2×C22⋊Q8C2×D311yescharacteristic
177C2×C4×Q8—31no—
178C2×C4×D4C2×D311yescharacteristic
179#470—64no—
180#467—64no—
181#462—64no—
182#435—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—21no—
198#399—21no—
199#398—61no—
200#394—61no—
201#390—21no—
202#388—61no—
203#388—61no—
204#384—21no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×D4—22no—
228C2×C3×D4—22no—
229C2×C3×D4—41no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2411yescharacteristic
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6C2×D412yes—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4—42no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4C2×D412yes—
271C3×C4⋊C4#4112yes—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C42—42no—
279C3×C42C2×D412yes—
280C3×C42#4112yes—
281#217—42no—
282#217—42no—
283#217—42no—
284#217—42no—
285#216—44no—
286#216—44no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293Dic3⋊C4—42no—
294Dic3⋊C4—42no—
295Dic3⋊C4—42no—
296C4×Dic3—42no—
297#208—44no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—44no—
308C2×C3⋊C8C2×D412yes—
309C2×C3⋊C8C2×D412yes—
310C2×C3⋊C8C2×D412yes—
311C22×Q8—31no—
312C22×Q8C22×D311yescharacteristic
313C22×Q8C22×D311yescharacteristic
314C22×D4#6711yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×Q16—62no—
318C2×Q16—62no—
319C2×Q16—62no—
320C2×Q16—62no—
321C2×Q16—121no—
322C2×Q16—121no—
323C2×M16—62no—
324C2×M16—62no—
325C2×M16—121no—
326C22×C8—31no—
327C22×C8—31no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8—62no—
331C22×C8—62no—
332C22×C8—121no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—41no—
340C22⋊Q8—41no—
341C22⋊Q8—41no—
342C22⋊Q8—41no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C4×Q8—62no—
348C4×Q8—62no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4#6711yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4#6711yescharacteristic
375C2×C22⋊C4#6711yescharacteristic
376C2×C42—21no—
377C2×C42—61no—
378C2×C42C22×D311yescharacteristic
379#107—62no—
380#106—62no—
381C4⋊C8—34no—
382#103—34no—
383#103—62no—
384#103—62no—
385#103—62no—
386#103—62no—
387#103—62no—
388#103—121no—
389#103—121no—
390C22⋊C8—62no—
391C22⋊C8—62no—
392#97—62no—
393#95—21no—
394#95—61no—
395#95—61no—
396#95—61no—
397#95—61no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3#13712yes—
412C23×C3C22×D411yescharacteristic
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×D4—44no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4#12112yes—
453C2×C3×C4#12112yes—
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4H(5,𝔽2)11yescharacteristic
459C2×C3×C4H(5,𝔽2)11yescharacteristic
460C2×Dic3—22no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472Dic6—22no—
473Dic6—22no—
474Dic6—41no—
475Dic6—41no—
476C3⋊C8—22no—
477C3⋊C8—22no—
478C3⋊C8—22no—
479C3⋊C8—41no—
480C24C2×#6711yescharacteristic
481C24C2×#6711yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—32no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—41no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4C2×#6711yescharacteristic
524C22×C4C2×#6711yescharacteristic
525C22×C4C2×#6711yescharacteristic
526C22×C4C2×#6711yescharacteristic
527C22×C4C23×D311yescharacteristic
528Q16—124no—
529Q16—124no—
530M16—124no—
531C2×C8—32no—
532C2×C8—32no—
533C2×C8—32no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—124no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—122no—
560C4⋊C4—122no—
561C4⋊C4—122no—
562C4⋊C4D3×D412yes—
563C4⋊C4#23712yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—122no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C42—42no—
575C42—122no—
576C42D3×D412yes—
577C42#23712yes—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3C2×#12111yescharacteristic
593C22×C3D4211yescharacteristic
594C22×C3#54611yescharacteristic
595C22×C3C2×#13711yescharacteristic
596C22×C3#57511yescharacteristic
597C22×C3#57811yescharacteristic
598C22×C3#57811yescharacteristic
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—81no—
606C3×C4—81no—
607C3×C4#53211yescharacteristic
608C3×C4#54011yescharacteristic
609C3×C4D4211yescharacteristic
610C3×C4#55011yescharacteristic
611Dic3—42no—
612Dic3—81no—
613Dic3—81no—
614Dic3—81no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23#94212yes—
629C23C22×#6711yescharacteristic
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—62no—
639Q8—62no—
640Q8—121no—
641Q8—121no—
642D4—44no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—62no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4#93912yes—
686C2×C4#93912yes—
687C2×C4C2×D3×D411yescharacteristic
688C2×C4C2×D3×D411yescharacteristic
689C2×C4C2×#23711yescharacteristic
690C2×C4C2×#23711yescharacteristic
691C2×C4#100411yescharacteristic
692C2×C4#100411yescharacteristic
693C8—62no—
694C8—62no—
695C8—62no—
696C8—121no—
697C2×C3—42no—
698C2×C3—81no—
699C2×C3#242811yescharacteristic
700C2×C3#305611yescharacteristic
701C2×C3#305911yescharacteristic
702C2×C3#326911yescharacteristic
703C2×C3#327011yescharacteristic
704C2×C3#331211yescharacteristic
705C2×C3#331511yescharacteristic
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22D4×#6711yescharacteristic
721C22C2×#93911yescharacteristic
722C22#580611yescharacteristic
723C22C2×#94211yescharacteristic
724C22#582211yescharacteristic
725C22#583811yescharacteristic
726C22#583811yescharacteristic
727C4—22no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—122no—
736C4—241no—
737C4—241no—
738C4—241no—
739C4#571611yescharacteristic
740C4#571711yescharacteristic
741C4#571811yescharacteristic
742C4#571911yescharacteristic
743C3#2539811yescharacteristic, complemented, Sylow
744C2—42no—
745C2—81no—
746C2#8273211yescharacteristic
747C2#8318611yescharacteristic
748C2#8339911yescharacteristic
749C2#8351311yescharacteristic
750C2#8352811yescharacteristic
751C2#8355211yescharacteristic
752C2#8356511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2542C2
socleC23×C3C22×D4
prime radicalC22×C3×D4D4
hypercenter#2542D3
hypocenterC3#25398
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
2. C2×#5090C2semidirect
3. C2×#5052C2semidirect
4. C2×#5051C2semidirect
7. #71786C2semidirect
8. #71700C2semidirect
9. #71700C2semidirect
10. #71697C2semidirect
11. #71696C2semidirect
12. #71695C2semidirect
13. #71694C2semidirect
14. #69475C2semidirect
15. #69468C2semidirect
161. #810D4semidirect
743. C3#25398semidirect

Maximal subgroups

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

subgroupindex
C3×#25422
C2×#50902
C2×#50522
C2×#50512
#823752
C2×#50112
#717862
#717002
#716972
#716962
#716952
#716942
#694752
#694682
#253983