Finite Group Databasebeta

← #11884003

Subgroups — #11884003

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594621C211yesmaximal, characteristic, complemented
4#10594382C211yesmaximal, characteristic, complemented
5#10592585C211yesmaximal, characteristic, complemented
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4883C211yesmaximal, characteristic, complemented
8#10590883C211yesmaximal, characteristic, complemented
9#10590726C211yesmaximal, characteristic, complemented
10#10590617C211yesmaximal, characteristic, complemented
11#10590603C211yesmaximal, characteristic, complemented
12#10590597C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590549C211yesmaximal, characteristic, complemented
15#10590530C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#79794—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic, complemented
24C2×#3743C2211yescharacteristic, complemented
25#64106C2211yescharacteristic, complemented
26#64104C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic, complemented
32C3×#893C2211yescharacteristic
33C3×#887C2211yescharacteristic, complemented
34#63923—21no—
35#63922—21no—
36#63911C2211yescharacteristic
37#63906—21no—
38C4×#626C2211yescharacteristic
39#63893—21no—
40Dic3×D12—21no—
41#63886—21no—
42#63860C2211yescharacteristic, complemented
43#63852—21no—
44C2×#3717C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic
46C2×#3716C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50#63798—24no—
51D3×#204—24no—
52C32×#107C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×#911—31no—
66C22×#204—31no—
67#5609—31no—
68#5598—31no—
69#5576—31no—
70D4×D12—31no—
71C3×#466—31no—
72C3×#440—31no—
73#5154—31no—
74#5111—31no—
75#5040—31no—
76#5036—31no—
77#5027—31no—
78#5016—31no—
79#4889D311yescharacteristic, complemented
80#4886—31no—
81#4886—31no—
82#4886—61no—
83#4883D311yescharacteristic, complemented
84#4810—31no—
85#4806—31no—
86#4787—31no—
87#4781—31no—
88#4776—31no—
89#4776—31no—
90#4773—31no—
91#4762—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626D411yescharacteristic
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119D3×D12—22no—
120D3×D12—44no—
121D3×D12—41no—
122#3796—22no—
123#3796—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131C4⋊(C3⋊Dic3)—21no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3744—22no—
134#3743—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D24—22no—
144C3×#204D414yescomplemented
145C3×D3×C8—22no—
146Dic3⋊Dic3D411yescharacteristic
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3716—22no—
153#3716—41no—
154#3715—22no—
155#3714—41no—
156#3713—22no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C22×D12—31no—
166C22×D12—61no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C22×C3×C8—31no—
171C3×#121—31no—
172C3×#121—31no—
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175C2×#215—31no—
176C2×#215—31no—
177#940—31no—
178#939—61no—
179#937—61no—
180#936—31no—
181D4×Dic3—61no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188#930—61no—
189C4×#67—31no—
190#914—64no—
191D3×SD16—64no—
192#911—64no—
193C2×D24—31no—
194C2×D24C2×D311yescharacteristic, complemented
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—61no—
201C2×#204—64no—
202C2×#204C2×D311yescharacteristic
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—61no—
206C2×D3×C8C2×D311yescharacteristic, complemented
207#897—31no—
208#897—31no—
209#897—61no—
210#897—61no—
211#895—31no—
212#895—31no—
213#895—61no—
214#895—61no—
215#895C2×D311yescharacteristic
216#895C2×D311yescharacteristic, complemented
217#893C2×D311yescharacteristic
218#887C2×D311yescharacteristic, complemented
219#885—61no—
220#884—61no—
221#882—61no—
222#882—61no—
223#882—61no—
224#878—61no—
225#875—31no—
226#875—61no—
227#874—31no—
228C4×D12—31no—
229C4×D12—61no—
230C3×#107—21no—
231C3×#107C2×D311yescharacteristic, complemented
232C3×#107C2×D311yescharacteristic, complemented
233C3×#103—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#97—31no—
238#830—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#815C2×D311yescharacteristic, complemented
243Dic3⋊C8—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#810C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic
252#809C2×D311yescharacteristic, complemented
253#809C2×D311yescharacteristic, complemented
254C4⋊(C3⋊C8)—31no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—42no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277#634—21no—
278#634—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—42no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6C2×D412yescomplemented
296#627—42no—
297#626—22no—
298#626—42no—
299#626—42no—
300#626—42no—
301#626—81no—
302#625—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8C2×D412yescomplemented
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—31no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—31no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C2×#67—31no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345#239—62no—
346#239—121no—
347D3×Q8—62no—
348D3×Q8—121no—
349#237—62no—
350#237—121no—
351D3×D4—62no—
352D3×D4—62no—
353D3×D4—62no—
354D3×D4—121no—
355D3×D4—124no—
356D3×D4—121no—
357D3×D4—121no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—62no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12—121no—
373C2×D12—124no—
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—121no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—34no—
393C3×D8—62no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411C3×C42—61no—
412#217—31no—
413#217—61no—
414#217—61no—
415#215—62no—
416#215—62no—
417#214—62no—
418#214—62no—
419#214—121no—
420#213—62no—
421#213—62no—
422#213—121no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—121no—
436(C2×D3)⋊C4—121no—
437C4⋊Dic3—31no—
438C4⋊Dic3—61no—
439C4⋊Dic3—61no—
440C4⋊Dic3—121no—
441Dic3⋊C4—21no—
442Dic3⋊C4—31no—
443C4×Dic3—21no—
444C4×Dic3C22×D311yescharacteristic
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—22no—
451D24—121no—
452#204—62no—
453#204—62no—
454#204—62no—
455#204—62no—
456#204—122no—
457#204—121no—
458#204D1214yescomplemented
459ΓL(1,𝔽25)—62no—
460ΓL(1,𝔽25)—62no—
461ΓL(1,𝔽25)—122no—
462D3×C8—22no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3AGL(1,ℤ/8)12yescomplemented
482D32—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—91no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—31no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—31no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107D3211yescharacteristic, complemented
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—31no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—121no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3D3×D411yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—32no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—122no—
574C3×D4—122no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—62no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—241no—
598C2×Dic3—21no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—122no—
606C2×Dic3—122no—
607C2×Dic3D3×D411yescharacteristic
608C2×Dic3D3×D411yescharacteristic
609C2×Dic3D3×D411yescharacteristic
610D12—21no—
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—42no—
616D12—42no—
617D12—62no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—121no—
623D12—121no—
624D12—122no—
625D12—122no—
626D12—122no—
627D12—122no—
628D12—122no—
629D12—242no—
630D12—241no—
631D12C2×D1212yes—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—42no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—121no—
640C4×D3—121no—
641C4×D3—122no—
642C4×D3—122no—
643Dic6—21no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649Dic6—121no—
650Dic6—122no—
651Dic6—122no—
652Dic6C2×D1212yescomplemented
653C3×C8—22no—
654C3×C8—61no—
655C3×C8—61no—
656C3×C8C2×D1212yescomplemented
657C3×C8D3×D412yescomplemented
658C3⋊C8—21no—
659C3⋊C8—21no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C2×C32D4211yescharacteristic
664C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
665C2×C32#57711yescharacteristic
666C3⋊D3—41no—
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—181no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—91no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—182no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4—361no—
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—91no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—34no—
705SD16—182no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—62no—
711D8—182no—
712D8—361no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8—91no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—61no—
720C4⋊C4—91no—
721C4⋊C4—181no—
722C4⋊C4C2×D3211yescharacteristic
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—91no—
728C22⋊C4—91no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
734C42—61no—
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—62no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—22no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—244no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#91112yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—62no—
794C3×C4—81no—
795C3×C4—81no—
796C3×C4C22×D1211yescharacteristic
797C3×C4C2×D3×D411yescharacteristic
798C3×C4#100911yescharacteristic
799C3×C4#100911yescharacteristic
800Dic3—21no—
801Dic3—21no—
802Dic3—22no—
803Dic3—21no—
804Dic3—61no—
805Dic3—61no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—31no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—91no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—32no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—122no—
835D4—122no—
836D4—182no—
837D4—181no—
838D4—181no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—91no—
854C2×C4—122no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4C22×D3211yescharacteristic
861C8—61no—
862C8—61no—
863C8—181no—
864C8D3×D1212yescomplemented
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—122no—
870C2×C3—241no—
871C2×C3—241no—
872C2×C3D4×D1211yescharacteristic
873C2×C3#560911yescharacteristic
874C2×C3C2×#91111yescharacteristic
875C2×C3#577011yescharacteristic
876C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
877C2×C3#577811yescharacteristic
878D3—22no—
879D3—42no—
880D3—81no—
881D3—81no—
882D3—121no—
883D3—121no—
884D3—241no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—32no—
889C22—61no—
890C22—61no—
891C22—62no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—724no—
907C22—724no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—41no—
911C4—61no—
912C4—62no—
913C4—61no—
914C4—61no—
915C4—181no—
916C4—361no—
917C4C2×D3×D1211yescharacteristic
918C4#6432011yescharacteristic
919C3—21no—
920C3#7979411yescharacteristic, complemented
921C3#8072711yescharacteristic, complemented
922C2—62no—
923C2—122no—
924C2—241no—
925C2—241no—
926C2—361no—
927C2—721no—
928C2#1059462111yescharacteristic
929C2D3×#91111yescharacteristic
930C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63798C2semidirect
2. C2×D3×#204C2semidirect
3. #10594621C2semidirect
4. #10594382C2semidirect
5. #10592585C2semidirect
6. C3×#4889C2semidirect
7. C3×#4883C2semidirect
8. #10590883C2semidirect
9. #10590726C2semidirect
10. #10590617C2semidirect
11. #10590603C2semidirect
12. #10590597C2semidirect
13. #10590595C2semidirect
14. #10590549C2semidirect
15. #10590530C2semidirect
21. C2×#3796C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×#3744C22semidirect
24. C2×#3743C22semidirect
25. #64106C22semidirect
27. C2×C3×D24C22semidirect
29. C2×C3×D3×C8C22semidirect
31. C3×#895C22semidirect
33. C3×#887C22semidirect
42. #63860C22semidirect
44. C2×#3717C22semidirect
46. C2×#3716C22semidirect
47. C2×#3715C22semidirect
48. C2×#3714C22semidirect
52. C32×#107C22semidirect
53. #63637C22semidirect
54. #63636C22semidirect
55. C3×#815C22semidirect
56. C3×#810C22semidirect
58. C3×#809C22semidirect
59. C3×#809C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63557C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #4889D3semidirect
83. #4883D3semidirect
144. C3×#204D4semidirect
194. C2×D24C2×D3semidirect
206. C2×D3×C8C2×D3semidirect
216. #895C2×D3semidirect
218. #887C2×D3semidirect
231. C3×#107C2×D3semidirect
232. C3×#107C2×D3semidirect
242. #815C2×D3semidirect
247. #810C2×D3semidirect
252. #809C2×D3semidirect
253. #809C2×D3semidirect
295. C3×Dic6C2×D4semidirect
305. C32×C8C2×D4semidirect
458. #204D12semidirect
481. C2×C3×D3AGL(1,ℤ/8)semidirect
528. #107D32semidirect
652. Dic6C2×D12semidirect
656. C3×C8C2×D12semidirect
657. C3×C8D3×D4semidirect
783. C2×D3#911semidirect
810. C32#3265semidirect
864. C8D3×D12semidirect
920. C3#79794semidirect
921. C3#80727semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
C2×D3×#2042
#105946212
#105943822
#105925852
C3×#48892
C3×#48832
#105908832
#105907262
#105906172
#105906032
#105905972
#105905952
#105905492
#105905302
#807273
#797943