Finite Group Databasebeta

← #10845997

Subgroups — #10845997

Order 768.

1020 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82499C211yesmaximal, characteristic, complemented
2C2×#5028C211yesmaximal, characteristic, complemented
3C2×#4816C211yesmaximal, characteristic, complemented
4C2×#4812C211yesmaximal, characteristic, complemented
5C2×#4688C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic
7C3×C4×#103C211yesmaximal, characteristic, complemented
8#70273C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#69773C211yesmaximal, characteristic, complemented
11#69468C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68884C211yesmaximal, characteristic, complemented
14#68825C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#25391—31nomaximal, Sylow
17C2×C3×C4×Q8C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×ΓL(1,𝔽25)C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#897C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#875C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×C4×C8C2211yescharacteristic
33C3×C4×C4⋊C4C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39C2×#816C2211yescharacteristic
40#5028—24no—
41#4991—21no—
42#4987C2211yescharacteristic
43#4987C2211yescharacteristic
44#4981—21no—
45C2×#810C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#808C2211yescharacteristic
48C2×#807C2211yescharacteristic
49#4940—21no—
50#4940—21no—
51#4939—21no—
52#4939—21no—
53#4936C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4816—24no—
56#4812—24no—
57#4688—24no—
58#4677—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#470—31no—
65C2×#468—31no—
66C2×#464—31no—
67C2×#436—31no—
68#2540—31no—
69#2536—31no—
70#2036—31no—
71#2034—31no—
72#2001—31no—
73#2000—31no—
74#1958—31no—
75#1949—31no—
76#1895—31no—
77#1894—31no—
78C4×#103D311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×D12—21no—
81C22×D12—21no—
82C22×D12D411yescharacteristic
83C22×D12C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4×Q8—22no—
90C3×C4×Q8—22no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42C2311yescharacteristic
98#946—22no—
99#946—22no—
100#946—41no—
101#946—41no—
102C2×#216—22no—
103C2×#216—22no—
104C2×#216—41no—
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—41no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4D411yescharacteristic
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3D411yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C22×C3⋊C8C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C2×ΓL(1,𝔽25)—22no—
130C2×ΓL(1,𝔽25)—22no—
131C2×ΓL(1,𝔽25)—22no—
132C2×ΓL(1,𝔽25)—22no—
133C2×ΓL(1,𝔽25)—41no—
134C2×ΓL(1,𝔽25)—41no—
135#897—22no—
136#897—22no—
137#897—41no—
138#897—41no—
139#895—22no—
140#895—22no—
141#895—41no—
142#895—41no—
143#875—22no—
144#875—22no—
145C4×D12—22no—
146C4×D12—22no—
147C3×#103—22no—
148C3×#103D414yescomplemented
149C3×C4×C8—22no—
150C3×#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—22no—
156#821—41no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160#816—41no—
161#810—22no—
162#809—22no—
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166C22×Q16—31no—
167C22×SD16—31no—
168C22×M16—31no—
169C22×M16—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—31no—
179#470—64no—
180#468—64no—
181#464—64no—
182#436—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8C2×D311yescharacteristic
197#399—61no—
198#398—61no—
199#394—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#388—61no—
204#388—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8C2×D412yes—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2411yescharacteristic
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3C2×D411yescharacteristic
233C22×Dic3C2×D411yescharacteristic
234C2×D12—22no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—41no—
242C2×D12—41no—
243C2×D12—42no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12—42no—
247C2×D12—81no—
248C2×D12—81no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8C2×D412yes—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4C2×D412yes—
279C3×C4⋊C4#4112yes—
280C3×C42—42no—
281C3×C42—81no—
282C3×C42C2×D412yes—
283C3×C42#4112yes—
284#216—44no—
285#215—44no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298C4⋊Dic3—22no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—42no—
304C4⋊Dic3—42no—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8C2×D412yes—
312C2×C3⋊C8C2×D412yes—
313ΓL(1,𝔽25)—44no—
314ΓL(1,𝔽25)—44no—
315C22×Q8—31no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4—61no—
321C23×C4—31no—
322C23×C4—31no—
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—121no—
329C2×M16—62no—
330C2×M16—62no—
331C2×M16—62no—
332C2×M16—62no—
333C2×M16—121no—
334C2×M16—121no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339#124—62no—
340#124—62no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349#121—62no—
350#121—62no—
351#121—121no—
352#121—121no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—62no—
356C4×D4—62no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C22⋊C4—31no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#106—62no—
385C4⋊C8—34no—
386#103—22no—
387#103—62no—
388#103—62no—
389#103—121no—
390#103D1214yescomplemented
391#102—62no—
392#102—62no—
393#102—121no—
394C22⋊C8—62no—
395C22⋊C8—62no—
396C4×C8—22no—
397#95—21no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3C22×D411yescharacteristic
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
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#12112yes—
445C2×C3×C4#12112yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4H(5,𝔽2)11yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467D12—44no—
468D12—41no—
469D12—41no—
470D12—41no—
471D12—41no—
472D12—84no—
473D12—84no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481C4×D3—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—22no—
487C3×C8—41no—
488C3⋊C8—22no—
489C3⋊C8—22no—
490C24—31no—
491C24—31no—
492C24—61no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8C2×D1212yes—
505C2×D4—62no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—121no—
513C2×D4—121no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—241no—
519C2×D4—241no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—124no—
546M16—124no—
547M16—124no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—32no—
554C2×C8—32no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8C2×D1212yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—62no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—122no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4—122no—
574C4⋊C4C2×D1212yes—
575C4⋊C4#23512yes—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C42—42no—
589C42—81no—
590C42#23512yes—
591C42D3×D412yes—
592C22×C3C2×#12111yescharacteristic
593C22×C3D4211yescharacteristic
594C22×C3#54611yescharacteristic
595C22×C3#57511yescharacteristic
596C22×C3#57511yescharacteristic
597C22×C3#57711yescharacteristic
598C22×C3#57811yescharacteristic
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—81no—
626C3×C4#53211yescharacteristic
627C3×C4#54011yescharacteristic
628C3×C4D4211yescharacteristic
629C3×C4#55011yescharacteristic
630Dic3—41no—
631Dic3—41no—
632Dic3—81no—
633Dic3—81no—
634Dic3—81no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665D4—124no—
666D4—121no—
667D4—121no—
668D4—121no—
669D4—121no—
670D4—244no—
671D4—244no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4#88412yes—
712C2×C4#88412yes—
713C2×C4C22×D1211yescharacteristic
714C2×C4C2×#23511yescharacteristic
715C2×C4C2×#23511yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4#100911yescharacteristic
718C2×C4#100911yescharacteristic
719C8—22no—
720C8—41no—
721C8—62no—
722C8—62no—
723C2×C3#242811yescharacteristic
724C2×C3#305411yescharacteristic
725C2×C3#306311yescharacteristic
726C2×C3#327511yescharacteristic
727C2×C3#327711yescharacteristic
728C2×C3#332311yescharacteristic
729C2×C3#332711yescharacteristic
730D3—81no—
731D3—81no—
732D3—161no—
733C22—121no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22C2×#88411yescharacteristic
755C22D4×D1211yescharacteristic
756C22#555011yescharacteristic
757C22#576211yescharacteristic
758C22#576611yescharacteristic
759C22#576811yescharacteristic
760C22#576811yescharacteristic
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—81no—
767C4—121no—
768C4—121no—
769C4—241no—
770C4—241no—
771C4—241no—
772C4#547711yescharacteristic
773C4#553511yescharacteristic
774C4D4×D1211yescharacteristic
775C4#555311yescharacteristic
776C3#2539111yescharacteristic, complemented, Sylow
777C2—241no—
778C2—241no—
779C2—481no—
780C2#7348711yescharacteristic
781C2#7880011yescharacteristic
782C2#7883911yescharacteristic
783C2#7967111yescharacteristic
784C2#7968211yescharacteristic
785C2#7973011yescharacteristic
786C2#7973811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C4×#103C2
socleC23×C3C22×D4
prime radical#73798C2
hypercenterC4×#103D3
hypocenterC3#25391
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. #82499C2semidirect
2. C2×#5028C2semidirect
3. C2×#4816C2semidirect
4. C2×#4812C2semidirect
5. C2×#4688C2semidirect
7. C3×C4×#103C2semidirect
8. #70273C2semidirect
9. #70272C2semidirect
10. #69773C2semidirect
11. #69468C2semidirect
12. #68885C2semidirect
13. #68884C2semidirect
14. #68825C2semidirect
15. #68823C2semidirect
78. C4×#103D3semidirect
148. C3×#103D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
390. #103D12semidirect
776. C3#25391semidirect

Maximal subgroups

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

subgroupindex
#824992
C2×#50282
C2×#48162
C2×#48122
C2×#46882
#737982
C3×C4×#1032
#702732
#702722
#697732
#694682
#688852
#688842
#688252
#688232
#253913