Finite Group Databasebeta

← #11884279

Subgroups — #11884279

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64121C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3#10595248C211yesmaximal, characteristic, complemented
4#10595246C211yesmaximal, characteristic, complemented
5C3×#5152C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591468C211yesmaximal, characteristic, complemented
8#10591466C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591457C211yesmaximal, characteristic, complemented
12#10590897C211yesmaximal, characteristic, complemented
13#10590853C211yesmaximal, characteristic, complemented
14#10590843C211yesmaximal, characteristic, complemented
15#10590736C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#79879—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3830C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25#64121—24no—
26C2×#3746C2211yescharacteristic, complemented
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic, complemented
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#911—24no—
33C2×C3×#204C2211yescharacteristic
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
35#63978—21no—
36#63978—21no—
37#63977—21no—
38#63966—21no—
39C2×Dic3⋊Dic3—21no—
40#63962—21no—
41#63962—21no—
42C2×(C2×D3)⋊Dic3—21no—
43#63916C2211yescharacteristic
44C4×#626C2211yescharacteristic
45#63871C2211yescharacteristic, complemented
46#63866C2211yescharacteristic, complemented
47#63860C2211yescharacteristic
48#63857C2211yescharacteristic
49#63857C2211yescharacteristic
50C2×#3719C2211yescharacteristic, complemented
51C2×#3716C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×C3×AGL(1,ℤ/8)—31no—
64#5824—31no—
65#5806—31no—
66C2×#912—31no—
67C2×#912—31no—
68C2×#912—61no—
69C2×#911D311yescharacteristic, complemented
70#5555—31no—
71#5554—31no—
72C3×#442—31no—
73#5239—31no—
74#5218—31no—
75#5173—31no—
76#5171—31no—
77#5167—31no—
78#5162—31no—
79#5158—31no—
80#5153—31no—
81#5152D311yescharacteristic, complemented
82#5137—31no—
83#5127—31no—
84#5019—31no—
85#5016—31no—
86#4867—31no—
87#4864—31no—
88#4783—31no—
89#4783—31no—
90#4781—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100C22×C3⋊Dic3—21no—
101#3830—22no—
102#3830—22no—
103#3830—41no—
104#3830—41no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—41no—
115C3×D3×D4—22no—
116C3×D3×D4—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626D411yescharacteristic
122C32×D8D414yescomplemented
123C2×C32×C8C2311yescharacteristic
124#3754—22no—
125#3754—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3746—22no—
128C8×C3⋊D3—22no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#214—22no—
132C3×#213—22no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×ΓL(1,𝔽25)—22no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3719—41no—
155#3716—41no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237—31no—
162C2×#237—31no—
163C2×#237—61no—
164C2×#237—61no—
165C2×#237C2×D311yescharacteristic
166C2×D3×D4C2×D311yescharacteristic
167C3×AGL(1,ℤ/8)—64no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—21no—
171C2×C3×D8—31no—
172C2×C3×D8C2×D311yescharacteristic
173C2×C3×D8C2×D311yescharacteristic
174C2×C3×M16—31no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177#953—61no—
178C2×#217—61no—
179#946—31no—
180#944—31no—
181C2×#216—31no—
182#939—61no—
183#939—61no—
184#938—31no—
185#936—31no—
186#935—61no—
187#935—61no—
188D4×Dic3C2×D311yescharacteristic
189D4×Dic3C2×D311yescharacteristic, complemented
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—61no—
196C2×#214—61no—
197C2×#214C2×D311yescharacteristic
198C2×#213C2×D311yescharacteristic
199#930—61no—
200#930—61no—
201#929—61no—
202C4×#67—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×C4⋊Dic3—61no—
205#924—31no—
206#924—31no—
207C2×Dic3⋊C4—61no—
208#912—68no—
209#912—64no—
210#912—64no—
211#911—24no—
212C2×Dic12—31no—
213C2×Dic12—31no—
214C2×Dic12—31no—
215C2×Dic12—61no—
216C2×#204—31no—
217C2×#204C2×D311yescharacteristic
218C2×ΓL(1,𝔽25)C2×D311yescharacteristic
219C2×D3×C8—31no—
220C2×D3×C8—31no—
221C2×D3×C8—61no—
222#897—31no—
223#897—31no—
224#897—31no—
225#895—31no—
226#886—61no—
227#886—61no—
228#886—61no—
229#882—61no—
230#875—31no—
231C4×D12—31no—
232#869—31no—
233C3×#106—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#97—31no—
237#835—31no—
238#832—31no—
239#832C2×D311yescharacteristic
240#832C2×D311yescharacteristic, complemented
241#830—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245#817C2×D311yescharacteristic, complemented
246#816—31no—
247#816—31no—
248#815C2×D311yescharacteristic, complemented
249Dic3⋊C8—31no—
250#810—31no—
251#810—31no—
252#810—31no—
253#809—31no—
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C23×C32—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C32×D4C2×D412yes—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—42no—
273C2×C3⋊Dic3—42no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277#634—21no—
278#634—21no—
279#634—21no—
280#634—21no—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—41no—
299#626—81no—
300C32×C8C2×D412yes—
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—31no—
305C2×#135—91no—
306#547—91no—
307#546—91no—
308#497—91no—
309#470—91no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—91no—
316#449—91no—
317#442—31no—
318#435—91no—
319C24×C3—61no—
320C23×D3—21no—
321C3×#41—62no—
322C3×#41—121no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67—121no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—121no—
357C22×Dic3—121no—
358#237—22no—
359#237—41no—
360#237—64no—
361#237—64no—
362#237—62no—
363#237—62no—
364#237—62no—
365#237—62no—
366#237—121no—
367#237—121no—
368#237—121no—
369#237—121no—
370#237—122no—
371#237—122no—
372D3×D4—22no—
373D3×D4—41no—
374C2×D12—31no—
375C2×D12—61no—
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—31no—
378C2×C4×D3—31no—
379C2×C4×D3—61no—
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6—31no—
382C2×Dic6—31no—
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6—61no—
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—62no—
389C3×SD16—62no—
390C3×D8—24no—
391C3×D8—62no—
392C3×D8D1214yescomplemented
393C3×D8#6714yescomplemented
394C3×M16—62no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—31no—
405#217—21no—
406#217—21no—
407#217—31no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#216—121no—
414#214—22no—
415#214—64no—
416#214—64no—
417#214—62no—
418#214—62no—
419#214—62no—
420#214—62no—
421#214—121no—
422#213—22no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447C4×Dic3C22×D311yescharacteristic
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453Dic12—64no—
454Dic12—62no—
455Dic12—62no—
456Dic12—121no—
457#204—22no—
458#204—121no—
459ΓL(1,𝔽25)—22no—
460D3×C8—64no—
461D3×C8—62no—
462D3×C8—62no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—21no—
483C3⋊Dic3—41no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—91no—
493C2×#41—91no—
494C22×D4—31no—
495AGL(1,ℤ/8)—64no—
496#135—184no—
497C2×Q16—91no—
498C2×Q16—91no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—31no—
505C2×D8D3211yescharacteristic
506C2×M16—31no—
507C22×C8—91no—
508C4⋊Q8—91no—
509#124—91no—
510#123—181no—
511#123—181no—
512#123—181no—
513C22⋊Q8—91no—
514C22⋊Q8—91no—
515C22⋊Q8—91no—
516#121—91no—
517#121—181no—
518#121—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—181no—
525#106—31no—
526C4⋊C8—91no—
527#103—91no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—31no—
532#102—91no—
533C22⋊C8—91no—
534C22⋊C8—91no—
535#97—31no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—241no—
547C22×D3—21no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—61no—
553C22×D3—81no—
554C22×D3D3×D411yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4C2×D1212yes—
570C3×D4C2×D1212yes—
571C3×D4C2×#6712yes—
572C3×D4C2×#6712yes—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—122no—
583C2×C3×C4—122no—
584C2×C3×C4—241no—
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—42no—
588#67—42no—
589#67—121no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—124no—
595#67—124no—
596#67—241no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—42no—
603C2×Dic3—42no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—81no—
610C2×Dic3—121no—
611C2×Dic3—121no—
612C2×Dic3—122no—
613C2×Dic3—122no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—124no—
617C2×Dic3—124no—
618C2×Dic3D3×D411yescharacteristic
619C2×Dic3D3×D411yescharacteristic
620C2×Dic3D3×D411yescharacteristic
621D12—21no—
622D12—21no—
623D12—121no—
624D12—241no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—62no—
628C4×D3—62no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—61no—
632C4×D3—61no—
633Dic6—21no—
634Dic6—21no—
635Dic6—62no—
636Dic6—62no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—61no—
641Dic6—61no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—121no—
646Dic6—121no—
647C3×C8—22no—
648C3×C8—61no—
649C3×C8—61no—
650C3×C8C2×D1212yes—
651C3×C8C2×#6712yes—
652C3⋊C8—21no—
653C3⋊C8—21no—
654C3⋊C8—62no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C2×C32—42no—
658C2×C32—42no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57711yescharacteristic
662C3⋊D3—41no—
663C3×D3—41no—
664C3×D3—81no—
665C24—61no—
666#41—62no—
667#41—121no—
668#41—182no—
669#41—182no—
670#41—361no—
671#41—361no—
672C2×Q8—31no—
673C2×Q8—91no—
674C2×Q8—91no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—62no—
678C2×D4—61no—
679C2×D4—91no—
680C2×D4—121no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4C2×D3211yescharacteristic
685C2×D4C2×D3211yescharacteristic
686C22×C4—31no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—91no—
691C22×C4—181no—
692C22×C4—181no—
693Q16—182no—
694Q16—361no—
695SD16—62no—
696SD16—62no—
697SD16—182no—
698SD16—182no—
699SD16—361no—
700D8—62no—
701D8#62614yescomplemented
702M16—62no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—91no—
706C2×C8—182no—
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C4⋊C4—181no—
713C4⋊C4—181no—
714C4⋊C4—181no—
715C4⋊C4—181no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—91no—
719C22⋊C4—91no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—244no—
753C22×C3C2×D3×D411yescharacteristic
754C22×C3C2×D3×D411yescharacteristic
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—62no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—84no—
769C2×D3—121no—
770C2×D3—121no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4C22×D1211yescharacteristic
780C3×C4#100411yescharacteristic
781C3×C4#100911yescharacteristic
782C3×C4C22×#6711yescharacteristic
783Dic3—21no—
784Dic3—21no—
785Dic3—21no—
786Dic3—41no—
787Dic3—41no—
788Dic3—41no—
789Dic3—62no—
790Dic3—61no—
791Dic3—61no—
792Dic3—122no—
793Dic3—122no—
794Dic3—121no—
795Dic3—121no—
796Dic3—121no—
797Dic3—121no—
798C32#326711yescharacteristic, complemented, Sylow
799C23—21no—
800C23—21no—
801C23—31no—
802C23—61no—
803C23—91no—
804C23—122no—
805C23—122no—
806C23—241no—
807Q8—61no—
808Q8—61no—
809Q8—181no—
810Q8—181no—
811Q8—181no—
812Q8—181no—
813D4—21no—
814D4—21no—
815D4—61no—
816D4—61no—
817D4—122no—
818D4—122no—
819D4—361no—
820D4—362no—
821D4—362no—
822D4—721no—
823D4C2×#62612yes—
824D4C2×#62612yes—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—91no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—241no—
841C2×C4—362no—
842C2×C4—362no—
843C2×C4C22×D3211yescharacteristic
844C8—61no—
845C8—61no—
846C8—181no—
847C8C2×#62612yes—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—42no—
852C2×C3—42no—
853C2×C3—42no—
854C2×C3—42no—
855C2×C3—82no—
856C2×C3—82no—
857C2×C3—121no—
858C2×C3—241no—
859C2×C3D4×D1211yescharacteristic
860C2×C3#577311yescharacteristic
861C2×C3#577311yescharacteristic
862C2×C3#577511yescharacteristic
863C2×C3#577511yescharacteristic
864C2×C3D4×#6711yescharacteristic
865D3—41no—
866D3—81no—
867D3—122no—
868D3—121no—
869D3—121no—
870C22—22no—
871C22—22no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—181no—
883C22—181no—
884C22—181no—
885C22—244no—
886C22D32×D411yescharacteristic
887C4—61no—
888C4—61no—
889C4—61no—
890C4—121no—
891C4—121no—
892C4—121no—
893C4—181no—
894C4—361no—
895C4—361no—
896C4#6431411yescharacteristic
897C4C22×#62611yescharacteristic
898C3—21no—
899C3#7987911yescharacteristic, complemented
900C3#8395411yescharacteristic, complemented
901C2—42no—
902C2—42no—
903C2—121no—
904C2—241no—
905C2—361no—
906C2#1059472811yescharacteristic
907C2#1059473311yescharacteristic
908C2D4×#62611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64121C2semidirect
2. C2×C3×#911C2semidirect
3. #10595248C2semidirect
4. #10595246C2semidirect
5. C3×#5152C2semidirect
6. #10591489C2semidirect
7. #10591468C2semidirect
8. #10591466C2semidirect
9. #10591463C2semidirect
10. #10591459C2semidirect
11. #10591457C2semidirect
12. #10590897C2semidirect
13. #10590853C2semidirect
14. #10590843C2semidirect
15. #10590736C2semidirect
19. C2×#3830C22semidirect
24. C2×#3754C22semidirect
26. C2×#3746C22semidirect
27. C2×C8×C3⋊D3C22semidirect
29. C3×D4×Dic3C22semidirect
45. #63871C22semidirect
46. #63866C22semidirect
50. C2×#3719C22semidirect
53. C3×#832C22semidirect
54. C3×#817C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63565C22semidirect
61. #63557C22semidirect
69. C2×#911D3semidirect
81. #5152D3semidirect
122. C32×D8D4semidirect
189. D4×Dic3C2×D3semidirect
240. #832C2×D3semidirect
245. #817C2×D3semidirect
248. #815C2×D3semidirect
392. C3×D8D12semidirect
393. C3×D8#67semidirect
701. D8#626semidirect
798. C32#3267semidirect
899. C3#79879semidirect
900. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C2×#641212
C2×C3×#9112
#105952482
#105952462
C3×#51522
#105914892
#105914682
#105914662
#105914632
#105914592
#105914572
#105908972
#105908532
#105908432
#105907362
#839543
#798793