Finite Group Databasebeta

← #10801043

Subgroups — #10801043

Order 768.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5750C211yesmaximal, characteristic, complemented
2C2×#4894C211yesmaximal, characteristic, complemented
3#79074C211yesmaximal, characteristic, complemented
4C2×#4824C211yesmaximal, characteristic, complemented
5#78833C211yesmaximal, characteristic
6C3×#1866C211yesmaximal, characteristic, complemented
7#72010C211yesmaximal, characteristic, complemented
8#70713C211yesmaximal, characteristic, complemented
9#70545C211yesmaximal, characteristic, complemented
10#70380C211yesmaximal, characteristic, complemented
11#70290C211yesmaximal, characteristic, complemented
12#68755C211yesmaximal, characteristic, complemented
13#68739C211yesmaximal, characteristic, complemented
14#68695C211yesmaximal, characteristic, complemented
15#68649C211yesmaximal, characteristic, complemented
16#21468—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic
19C2×#950C2211yescharacteristic
20C2×#948C2211yescharacteristic
21#5750—24no—
22#5750—24no—
23C2×#907—21no—
24C2×#907C2211yescharacteristic
25C2×#907C2211yescharacteristic, complemented
26C2×D3×M16—21no—
27C2×D3×M16C2211yescharacteristic
28C2×#904C2211yescharacteristic
29C2×#901—21no—
30C2×#901C2211yescharacteristic
31C22×ΓL(1,𝔽25)—21no—
32C22×ΓL(1,𝔽25)C2211yescharacteristic
33#5524C2211yescharacteristic
34C2×C3×#108C2211yescharacteristic, complemented
35C3×#424C2211yescharacteristic, complemented
36C2×C3×#104C2211yescharacteristic
37C3×#416C2211yescharacteristic
38C2×#837C2211yescharacteristic
39C2×#825C2211yescharacteristic
40C2×#825C2211yescharacteristic, complemented
41#5126C2211yescharacteristic
42C2×#822C2211yescharacteristic, complemented
43#5110C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#815C2211yescharacteristic, complemented
46#5002C2211yescharacteristic
47#4997C2211yescharacteristic, complemented
48C4×(C2×D3)⋊C4C2211yescharacteristic
49C2×#805C2211yescharacteristic
50C2×#805C2211yescharacteristic, complemented
51C2×C4×C3⋊C8C2211yescharacteristic, complemented
52#4894—24no—
53#4838—21no—
54#4838—21no—
55#4836—21no—
56#4836—21no—
57#4824—24no—
58#4810C411yescharacteristic, complemented
59#4809C411yescharacteristic, complemented
60#4808C411yescharacteristic, complemented
61#4806C411yescharacteristic, complemented
62#4783C411yescharacteristic, complemented
63#4781C411yescharacteristic, complemented
64#4776C411yescharacteristic, complemented
65#4773C411yescharacteristic, complemented
66C3×#339C2211yescharacteristic, complemented
67C3×#336C2211yescharacteristic, complemented
68#4558C2211yescharacteristic, complemented
69#4552C2211yescharacteristic, complemented
70#4550C2211yescharacteristic, complemented
71#4532C2211yescharacteristic, complemented
72C2×#568—31no—
73#3002—31no—
74C2×#444—31no—
75C2×#443—31no—
76#2930—31no—
77#1876—31no—
78#1876—31no—
79#1871—31no—
80#1866—31no—
81#1866D311yescharacteristic, complemented
82#1855—31no—
83#1789—31no—
84#1765—31no—
85#1764—31no—
86#1753—31no—
87C2×C3×#41C2311yescharacteristic
88D3×#41—22no—
89D3×#41—22no—
90D3×#41—22no—
91D3×#41—22no—
92C2×#239C2×C411yescharacteristic
93C2×D3×Q8C2×C411yescharacteristic
94C2×#237—21no—
95C2×#237C2×C411yescharacteristic
96C2×D3×D4—21no—
97C2×D3×D4C2×C411yescharacteristic
98C2×#235—21no—
99C2×#235C2311yescharacteristic
100C2×#235C2311yescharacteristic
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C3×#131—22no—
104C3×#131—22no—
105C2×C3×M16—21no—
106C2×C3×M16C2311yescharacteristic
107C2×C3×M16C2311yescharacteristic
108C22×C3×C8—21no—
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×#117C2311yescharacteristic
112C2×C3×C42C2311yescharacteristic
113#950—22no—
114#950—22no—
115#948—22no—
116#948D414yescomplemented
117C2×#216C2×C411yescharacteristic
118C2×#215C2×C411yescharacteristic
119C2×#214C2×C411yescharacteristic
120C2×#213C2×C411yescharacteristic
121C2×(C2×D3)⋊C4—21no—
122C2×C4×Dic3C2311yescharacteristic
123C2×#208—21no—
124C2×#208C2311yescharacteristic
125C2×#208C2311yescharacteristic
126C22×C3⋊C8—21no—
127C22×C3⋊C8C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129#907—28no—
130#907—22no—
131#907—22no—
132#907—22no—
133#907D414yescomplemented
134D3×M16—28no—
135D3×M16—22no—
136D3×M16—22no—
137C2×Dic12C2×C411yescharacteristic
138#904—22no—
139#904—22no—
140C2×D24C2×C411yescharacteristic
141C2×#204C2×C411yescharacteristic
142C2×#204C2×C411yescharacteristic
143#901—28no—
144#901—22no—
145#901—22no—
146C2×ΓL(1,𝔽25)—28no—
147C2×ΓL(1,𝔽25)—21no—
148C2×ΓL(1,𝔽25)—21no—
149C2×ΓL(1,𝔽25)—21no—
150C2×ΓL(1,𝔽25)—22no—
151C2×ΓL(1,𝔽25)—22no—
152C2×ΓL(1,𝔽25)—21no—
153C2×ΓL(1,𝔽25)D411yescharacteristic
154C2×ΓL(1,𝔽25)D411yescharacteristic
155C2×ΓL(1,𝔽25)D411yescharacteristic
156C2×ΓL(1,𝔽25)D411yescharacteristic
157C2×D3×C8—21no—
158C2×D3×C8—21no—
159C2×D3×C8—21no—
160C2×D3×C8—21no—
161#897C2×C411yescharacteristic
162#897C2×C411yescharacteristic
163#895C2×C411yescharacteristic
164#895C2×C411yescharacteristic
165#886—21no—
166#882—21no—
167C4×D12—21no—
168C4×D12—21no—
169C3×#108—22no—
170C3×C4⋊C8—21no—
171C3×C4⋊C8—21no—
172C3×#104—22no—
173C3×#103C2×C411yescharacteristic
174C3×#103C2×C411yescharacteristic
175C3×#102C2×C411yescharacteristic
176C3×#102C2×C411yescharacteristic
177#837—22no—
178C3⋊#95—21no—
179#825—22no—
180#825—22no—
181#822—22no—
182(C2×D3)⋊C8—21no—
183(C2×D3)⋊C8—21no—
184(C2×D3)⋊C8—21no—
185(C2×D3)⋊C8—21no—
186(C2×D3)⋊C8C2×C411yescharacteristic
187(C2×D3)⋊C8C2×C411yescharacteristic
188(C2×D3)⋊C8C2×C411yescharacteristic
189(C2×D3)⋊C8C2×C411yescharacteristic
190#815—22no—
191#810C2×C411yescharacteristic
192#810C2×C411yescharacteristic
193#809C2×C411yescharacteristic
194#809C2×C411yescharacteristic
195#805—22no—
196#805—22no—
197#803—21no—
198C4×C3⋊C8—22no—
199C4×C3⋊C8—21no—
200C22×#41—31no—
201C2×#135—31no—
202C2×#135—31no—
203#568—64no—
204#568—64no—
205C2×#131—31no—
206C2×#131—31no—
207C2×#131—31no—
208C2×#131—31no—
209C2×#131—61no—
210C2×#131—61no—
211C2×#131C2×D311yescharacteristic
212C22×M16—31no—
213C22×M16—31no—
214C22×M16—61no—
215C22×M16—61no—
216#525—31no—
217#452—31no—
218#452—31no—
219#451—31no—
220#450—31no—
221#449—31no—
222#449—31no—
223#448—31no—
224#447—31no—
225#444—64no—
226#443—64no—
227#436—61no—
228#436—61no—
229#435—61no—
230#435—61no—
231C2×#108—31no—
232C2×#108C2×D311yescharacteristic, complemented
233#424C2×D311yescharacteristic, complemented
234C2×#104—31no—
235C2×#104—31no—
236C2×#104—31no—
237C2×#104—31no—
238C2×#104—31no—
239C2×#104C2×D311yescharacteristic
240#416—31no—
241#416C2×D311yescharacteristic
242#408—31no—
243#407—31no—
244C2×C22⋊C8—31no—
245#405—31no—
246C2×#97—31no—
247C2×C4×C8—31no—
248C4×C22⋊C4—31no—
249#341—31no—
250#341—31no—
251#339—31no—
252#339C2×D311yescharacteristic, complemented
253#336—31no—
254#336C2×D311yescharacteristic, complemented
255C23×D3—21no—
256C23×D3#4111yescharacteristic
257C3×#41—21no—
258C3×#41—21no—
259C3×#41C2×D412yes—
260C3×#41#4112yes—
261C2×C3×Q8C22×C411yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4C22×C411yescharacteristic
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4C2411yescharacteristic
267C2×#67—21no—
268C2×#67—21no—
269C2×#67—21no—
270C2×#67—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3#4111yescharacteristic
274#239—22no—
275#239—22no—
276D3×Q8—22no—
277D3×Q8—22no—
278#237—24no—
279#237—24no—
280#237—22no—
281#237—22no—
282D3×D4—24no—
283D3×D4—24no—
284D3×D4—22no—
285D3×D4—22no—
286#235—24no—
287#235—24no—
288#235—21no—
289#235—21no—
290#235—21no—
291#235—21no—
292#235—21no—
293#235—21no—
294#235C2×D412yes—
295#235#4112yes—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12C22×C411yescharacteristic
300C2×D12C22×C411yescharacteristic
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3C22×C411yescharacteristic
312C2×C4×D3C22×C411yescharacteristic
313C2×C4×D3C2×D411yescharacteristic
314C2×C4×D3C2×D411yescharacteristic
315C2×Dic6—21no—
316C2×Dic6C22×C411yescharacteristic
317C2×Dic6C22×C411yescharacteristic
318C3×M16—24no—
319C3×M16—21no—
320C3×M16—21no—
321C3×M16—21no—
322C3×M16C2×D412yes—
323C2×C3×C8—24no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8C22×C411yescharacteristic
331C2×C3×C8C22×C411yescharacteristic
332C2×C3×C8C2×D411yescharacteristic
333C2×C3×C8C2×D411yescharacteristic
334C3×C4⋊C4C22×C411yescharacteristic
335C3×C4⋊C4C22×C411yescharacteristic
336C3×C22⋊C4—21no—
337C3×C42—21no—
338C3×C42—21no—
339C3×C42—21no—
340#216—22no—
341#215—22no—
342#214—22no—
343#213—22no—
344(C2×D3)⋊C4—21no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—21no—
347(C2×D3)⋊C4—21no—
348(C2×D3)⋊C4—42no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4×Dic3—21no—
352C4×Dic3—21no—
353#208—21no—
354#208—24no—
355#208—21no—
356#208—21no—
357#208C2×D412yes—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—24no—
362C2×C3⋊C8—21no—
363C2×C3⋊C8C22×C411yescharacteristic
364C2×C3⋊C8C22×C411yescharacteristic
365C2×C3⋊C8C2×D411yescharacteristic
366C2×C3⋊C8C2×D412yes—
367C2×C3⋊C8C2×D411yescharacteristic
368C2×C3⋊C8C2×D412yes—
369Dic12—22no—
370D24—22no—
371#204—22no—
372#204—22no—
373ΓL(1,𝔽25)—24no—
374ΓL(1,𝔽25)—24no—
375ΓL(1,𝔽25)—22no—
376ΓL(1,𝔽25)—24no—
377ΓL(1,𝔽25)—22no—
378ΓL(1,𝔽25)—22no—
379ΓL(1,𝔽25)—22no—
380ΓL(1,𝔽25)—42no—
381D3×C8—24no—
382D3×C8—24no—
383D3×C8—24no—
384D3×C8—42no—
385C2×#41—31no—
386C2×#41—31no—
387C2×#41—31no—
388C2×#41—31no—
389C2×#41—61no—
390C2×#41—61no—
391C2×#41—62no—
392C2×#41—62no—
393C2×#41—62no—
394C2×#41—62no—
395C2×#41C22×D311yescharacteristic
396C22×Q8—31no—
397C22×D4—31no—
398C22×D4—61no—
399C23×C4—31no—
400C23×C4—61no—
401#135—62no—
402#135—62no—
403#135—62no—
404#135—62no—
405C2×Q16—31no—
406C2×Q16—31no—
407C2×SD16—31no—
408C2×SD16—31no—
409C2×SD16—31no—
410C2×SD16—31no—
411C2×D8—31no—
412C2×D8—31no—
413#131—22no—
414#131—22no—
415#131—34no—
416#131—34no—
417#131—62no—
418#131—62no—
419#131—68no—
420#131—62no—
421#131—62no—
422#131—62no—
423#131—62no—
424#131—68no—
425C2×M16—21no—
426C2×M16—31no—
427C2×M16—31no—
428C2×M16—31no—
429C2×M16—31no—
430C2×M16—31no—
431C2×M16—31no—
432C2×M16—62no—
433C2×M16—62no—
434C2×M16—61no—
435C2×M16—61no—
436C2×M16—61no—
437C2×M16—68no—
438C2×M16—61no—
439C2×M16—62no—
440C2×M16—68no—
441C2×M16—62no—
442C2×M16—61no—
443C2×M16C22×D311yescharacteristic
444C2×M16C22×D311yescharacteristic
445C22×C8—21no—
446C22×C8—31no—
447C22×C8—31no—
448C22×C8—61no—
449C22×C8—61no—
450C22×C8—61no—
451C22×C8—61no—
452C22×C8—61no—
453C22×C8C22×D311yescharacteristic
454C22×C8C22×D311yescharacteristic
455#123—61no—
456C22⋊Q8—31no—
457C22⋊Q8—31no—
458#121—31no—
459#121—31no—
460#120—61no—
461C4×D4—61no—
462C4×D4—61no—
463#117C22×D311yescharacteristic
464C2×C22⋊C4—61no—
465C2×C42—31no—
466C2×C42C22×D311yescharacteristic
467#108—22no—
468#108—62no—
469C4⋊C8—21no—
470C4⋊C8—21no—
471#104—22no—
472#104—62no—
473#104—62no—
474#104—62no—
475#104—62no—
476#104—62no—
477#103—31no—
478#103—31no—
479#103C4×D311yescharacteristic
480#103C4×D311yescharacteristic
481#102—31no—
482#102—31no—
483#102C4×D311yescharacteristic
484#102C4×D311yescharacteristic
485C22⋊C8—31no—
486C22⋊C8—31no—
487C22⋊C8—31no—
488C22⋊C8—31no—
489C22⋊C8—61no—
490C22⋊C8—61no—
491C22⋊C8—61no—
492C22⋊C8—61no—
493#97—61no—
494#97—62no—
495C4×C8—62no—
496C4×C8—61no—
497#95—61no—
498C23×C3—21no—
499C23×C3C2×#4111yescharacteristic
500C22×D3—21no—
501C22×D3—24no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—81no—
508C22×D3—81no—
509C22×D3C4×D411yescharacteristic
510C22×D3C4×D411yescharacteristic
511C3×Q8—21no—
512C3×Q8C4×D412yes—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—21no—
516C3×D4C4×D412yes—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4C23×C411yescharacteristic
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C2×#4111yescharacteristic
530C2×C3×C4C2×#4111yescharacteristic
531#67—24no—
532#67—24no—
533#67—22no—
534#67—22no—
535#67—41no—
536#67—41no—
537C2×Dic3—24no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3C4×D411yescharacteristic
546C2×Dic3C4×D411yescharacteristic
547D12—24no—
548D12—21no—
549D12—21no—
550D12—21no—
551D12—81no—
552D12—81no—
553D12C4×D412yes—
554C4×D3—24no—
555C4×D3—24no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—22no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—22no—
565C4×D3—21no—
566C4×D3—41no—
567C4×D3—41no—
568Dic6—24no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6C4×D412yes—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—22no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—41no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—22no—
582C3⋊C8—41no—
583C3⋊C8#12012yes—
584C3⋊C8#12012yes—
585C24—31no—
586C24—61no—
587#41—21no—
588#41—21no—
589#41—32no—
590#41—32no—
591#41—64no—
592#41—64no—
593#41—62no—
594#41—64no—
595#41—64no—
596#41—62no—
597#41—62no—
598#41—62no—
599#41—61no—
600#41—61no—
601#41—61no—
602#41—61no—
603#41—61no—
604#41—61no—
605#41D3×D412yes—
606#41#23912yes—
607C2×Q8—31no—
608C2×Q8—31no—
609C2×Q8—61no—
610C2×Q8—62no—
611C2×Q8—62no—
612C2×Q8C2×C4×D311yescharacteristic
613C2×D4—21no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—62no—
621C2×D4—64no—
622C2×D4—64no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4—62no—
626C2×D4—61no—
627C2×D4C2×C4×D311yescharacteristic
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—64no—
638C22×C4—64no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4C23×D311yescharacteristic
648Q16—62no—
649Q16—62no—
650SD16—62no—
651SD16—62no—
652SD16—62no—
653SD16—62no—
654D8—62no—
655D8—62no—
656M16—24no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—32no—
661M16—62no—
662M16—62no—
663M16—62no—
664M16—62no—
665M16—64no—
666M16—64no—
667M16—64no—
668M16—64no—
669M16—61no—
670M16—61no—
671M16—61no—
672M16—122no—
673M16D3×D412yes—
674C2×C8—24no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—32no—
682C2×C8—32no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—31no—
686C2×C8—31no—
687C2×C8—64no—
688C2×C8—64no—
689C2×C8—64no—
690C2×C8—64no—
691C2×C8—61no—
692C2×C8—61no—
693C2×C8—61no—
694C2×C8—61no—
695C2×C8—122no—
696C2×C8C2×C4×D311yescharacteristic
697C2×C8C2×C4×D311yescharacteristic
698C2×C8D3×D411yescharacteristic
699C2×C8D3×D411yescharacteristic
700C4⋊C4—61no—
701C4⋊C4—61no—
702C4⋊C4C2×C4×D311yescharacteristic
703C4⋊C4C2×C4×D311yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—122no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—61no—
714C42—61no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—22no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3C2×C4×D411yescharacteristic
721C22×C3#52511yescharacteristic
722C22×C3#52511yescharacteristic
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—81no—
736C2×D3—81no—
737C2×D3—84no—
738C3×C4—22no—
739C3×C4—42no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4C2×C4×D411yescharacteristic
743C3×C4C2×C4×D411yescharacteristic
744C3×C4C2×#12011yescharacteristic
745C3×C4#52511yescharacteristic
746Dic3—21no—
747Dic3—22no—
748Dic3—21no—
749Dic3—41no—
750Dic3—81no—
751C23—21no—
752C23—31no—
753C23—31no—
754C23—64no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—121no—
760C23—121no—
761C23—241no—
762C23—241no—
763C23D3×#4111yescharacteristic
764Q8—21no—
765Q8—32no—
766Q8—64no—
767Q8—61no—
768Q8—61no—
769Q8—61no—
770Q8#89312yes—
771D4—22no—
772D4—22no—
773D4—21no—
774D4—32no—
775D4—64no—
776D4—64no—
777D4—64no—
778D4—62no—
779D4—62no—
780D4—61no—
781D4—61no—
782D4—61no—
783D4—121no—
784D4—121no—
785D4—241no—
786D4—241no—
787D4#89312yes—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—64no—
799C2×C4—64no—
800C2×C4—64no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—62no—
814C2×C4—61no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4C22×C4×D311yescharacteristic
821C2×C4C2×D3×D411yescharacteristic
822C2×C4C2×D3×D411yescharacteristic
823C2×C4C2×D3×D411yescharacteristic
824C2×C4C2×#23911yescharacteristic
825C2×C4D3×#4111yescharacteristic
826C8—21no—
827C8—21no—
828C8—21no—
829C8—22no—
830C8—21no—
831C8—32no—
832C8—32no—
833C8—41no—
834C8—61no—
835C8—61no—
836C8—62no—
837C8—121no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3C4×#12011yescharacteristic
842C2×C3#295611yescharacteristic
843C2×C3#295711yescharacteristic
844D3—41no—
845D3—41no—
846D3—42no—
847D3—81no—
848C22—21no—
849C22—21no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—61no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—241no—
866C22—241no—
867C22—244no—
868C22C4×D3×D411yescharacteristic
869C22#562711yescharacteristic
870C22#565611yescharacteristic
871C4—22no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—61no—
876C4—61no—
877C4—62no—
878C4—121no—
879C4—241no—
880C4C2×#89311yescharacteristic
881C4C4×D3×D411yescharacteristic
882C4D3×#12011yescharacteristic
883C4#562711yescharacteristic
884C3#2146811yescharacteristic, complemented, Sylow
885C2—21no—
886C2—21no—
887C2—42no—
888C2—121no—
889C2—121no—
890C2—122no—
891C2—241no—
892C2#7437911yescharacteristic
893C2#7988911yescharacteristic
894C2#7989911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1866C2
socleC22×C3C2×C4×D4
prime radical#78833C2
cosocleC22×C3×C4C24
hypercenter#1866D3
hypocenterC3#21468
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
1. C2×#5750C2semidirect
2. C2×#4894C2semidirect
3. #79074C2semidirect
4. C2×#4824C2semidirect
6. C3×#1866C2semidirect
7. #72010C2semidirect
8. #70713C2semidirect
9. #70545C2semidirect
10. #70380C2semidirect
11. #70290C2semidirect
12. #68755C2semidirect
13. #68739C2semidirect
14. #68695C2semidirect
15. #68649C2semidirect
25. C2×#907C22semidirect
34. C2×C3×#108C22semidirect
35. C3×#424C22semidirect
40. C2×#825C22semidirect
42. C2×#822C22semidirect
43. #5110C22semidirect
45. C2×#815C22semidirect
47. #4997C22semidirect
50. C2×#805C22semidirect
51. C2×C4×C3⋊C8C22semidirect
58. #4810C4semidirect
59. #4809C4semidirect
60. #4808C4semidirect
61. #4806C4semidirect
62. #4783C4semidirect
63. #4781C4semidirect
64. #4776C4semidirect
65. #4773C4semidirect
66. C3×#339C22semidirect
67. C3×#336C22semidirect
68. #4558C22semidirect
69. #4552C22semidirect
70. #4550C22semidirect
71. #4532C22semidirect
81. #1866D3semidirect
116. #948D4semidirect
133. #907D4semidirect
232. C2×#108C2×D3semidirect
233. #424C2×D3semidirect
252. #339C2×D3semidirect
254. #336C2×D3semidirect
884. C3#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#57502
C2×#48942
#790742
C2×#48242
#788332
C3×#18662
#720102
#707132
#705452
#703802
#702902
#687552
#687392
#686952
#686492
#214683