Finite Group Databasebeta

← #11867145

Subgroups — #11867145

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63794C211yesmaximal, characteristic, complemented
2C2×#63791C211yesmaximal, characteristic, complemented
3#10594627C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592582C211yesmaximal, characteristic, complemented
6C3×#4886C211yesmaximal, characteristic, complemented
7C3×#4881C211yesmaximal, characteristic, complemented
8#10590843C211yesmaximal, characteristic, complemented
9#10590835C211yesmaximal, characteristic, complemented
10#10590609C211yesmaximal, characteristic, complemented
11#10590592C211yesmaximal, characteristic, complemented
12#10590586C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14#10590523C211yesmaximal, characteristic, complemented
15#10590509C211yesmaximal, characteristic, complemented
16#80805—31nomaximal
17#79211—31nomaximal
18C2×D3×D12—21no—
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C2×#3745C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64104C2211yescharacteristic
25#64104C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#892C2211yescharacteristic
32C3×D3×C4⋊C4C2211yescharacteristic
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63910—21no—
37#63909C2211yescharacteristic
38#63909C2211yescharacteristic, complemented
39#63894—21no—
40#63890—21no—
41#63886—21no—
42#63880—21no—
43#63871C2211yescharacteristic, complemented
44C2×#3717C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46C2×#3711C2211yescharacteristic
47C2×#3711C2211yescharacteristic, complemented
48C2×#3710C2211yescharacteristic, complemented
49#63794—24no—
50#63791—24no—
51C32×#107C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#908—31no—
65C2×D3×M16—31no—
66C2×D3×M16—31no—
67#5627—31no—
68D3×#121—31no—
69#5524—31no—
70C2×#895—31no—
71C3×#468—31no—
72C3×#428—31no—
73#5171—31no—
74#5135—31no—
75#5049—31no—
76#5039—31no—
77#5001—31no—
78#4966—31no—
79#4886—31no—
80#4886D311yescharacteristic, complemented
81#4883—31no—
82#4883—31no—
83#4883—31no—
84#4883—61no—
85#4881D311yescharacteristic, complemented
86#4865—31no—
87#4865—31no—
88#4864—31no—
89#4864—31no—
90#4807—31no—
91#4803—31no—
92#4775—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32D411yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C2×#624D411yescharacteristic
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116D3×D12—22no—
117D3×D12—22no—
118D3×D12—44no—
119C4×D32—22no—
120C4×D32—22no—
121#3799—22no—
122#3799—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126#3752—21no—
127#3752—21no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129#3745—22no—
130C8×C3⋊D3—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×ΓL(1,𝔽25)D414yescomplemented
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149#3717—22no—
150#3714—22no—
151#3711—22no—
152#3711—22no—
153#3710—22no—
154#3055—91noSylow
155C2×#239—31no—
156C2×D3×D4—31no—
157C2×D3×D4—61no—
158C2×#235—31no—
159C22×D12—31no—
160C22×D12—61no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×SD16—31no—
164C2×C3×M16—31no—
165C2×C3×M16—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C3×#117—31no—
169C2×C3×C4⋊C4—31no—
170#946—31no—
171C2×#215—31no—
172#939—61no—
173#938—31no—
174C2×#213—31no—
175#930—31no—
176#930—31no—
177C2×(C2×D3)⋊C4—61no—
178C2×#208—31no—
179C2×#208—31no—
180#914—64no—
181#908—64no—
182D3×M16—64no—
183D3×M16—64no—
184C2×D24—31no—
185C2×D24—31no—
186C2×D24—31no—
187C2×D24—61no—
188C2×#204—31no—
189C2×#204C2×D311yescharacteristic, complemented
190C2×ΓL(1,𝔽25)—31no—
191C2×ΓL(1,𝔽25)—31no—
192C2×ΓL(1,𝔽25)C2×D311yescharacteristic
193C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
194C2×D3×C8—31no—
195C2×D3×C8—31no—
196C2×D3×C8—31no—
197C2×D3×C8—31no—
198C2×D3×C8—61no—
199#897—31no—
200#897C2×D311yescharacteristic, complemented
201#895—31no—
202#895—31no—
203#895—31no—
204#895—31no—
205#895—31no—
206#895—31no—
207#895—31no—
208#895—61no—
209#895—61no—
210#895—61no—
211#895—61no—
212#895C2×D311yescharacteristic
213#894—61no—
214#893—61no—
215#892C2×D311yescharacteristic
216D3×C4⋊C4C2×D311yescharacteristic
217#886—61no—
218#884—61no—
219#882—61no—
220#882—61no—
221#67⋊C4—61no—
222D3×C22⋊C4—61no—
223C4×D12—61no—
224C4×D12—61no—
225C3×#107—21no—
226C3×#107—31no—
227C3×#107C2×D311yescharacteristic, complemented
228C3×#107C2×D311yescharacteristic, complemented
229C3×#106—31no—
230C3×#106—31no—
231C3×#103—31no—
232C3×#102—31no—
233#835—31no—
234#832—31no—
235#821—31no—
236#821—31no—
237#817C2×D311yescharacteristic, complemented
238#810—31no—
239#810C2×D311yescharacteristic, complemented
240#809—31no—
241#809—31no—
242#809—31no—
243#809—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809—61no—
249#809C2×D311yescharacteristic, complemented
250#808C2×D311yescharacteristic, complemented
251#807C2×D311yescharacteristic, complemented
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—22no—
259C2×D32—22no—
260C2×D32—41no—
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—42no—
273C4⋊(C3⋊D3)—42no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#626—42no—
295#626—42no—
296#624—22no—
297#624—42no—
298D3×Dic3—22no—
299D3×Dic3—22no—
300C32×C8C2×D412yescomplemented
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—91no—
305C22×M16—91no—
306#525—91no—
307C2×#121—91no—
308#469—91no—
309#469—91no—
310#468—31no—
311#468—91no—
312#466—91no—
313#466—91no—
314#465—91no—
315#465—91no—
316#428—31no—
317#418—91no—
318#417—91no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336#239—62no—
337#239—62no—
338D3×D4—62no—
339D3×D4—62no—
340D3×D4—124no—
341#235—62no—
342#235—62no—
343C2×D12—21no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—62no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—121no—
362C2×D12—121no—
363C2×D12—124no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—61no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3C22×D311yescharacteristic
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—62no—
383C3×M16—34no—
384C3×M16—62no—
385C2×C3×C8—21no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—61no—
404#217—61no—
405#215—62no—
406#213—62no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3—21no—
424C4⋊Dic3—61no—
425C4⋊Dic3C22×D311yescharacteristic
426C4⋊Dic3C22×D311yescharacteristic
427Dic3⋊C4—21no—
428Dic3⋊C4—61no—
429C4×Dic3—21no—
430#208—62no—
431#208—62no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437D24—62no—
438D24—62no—
439D24—62no—
440D24—122no—
441#204—22no—
442#204—62no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—62no—
445ΓL(1,𝔽25)—62no—
446ΓL(1,𝔽25)D1214yescomplemented
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—62no—
451D3×C8—122no—
452C22×C32C22×D411yescharacteristic
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
462C2×C3×D3—21no—
463C2×C3×D3—21no—
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#12112yes—
471D32—44no—
472D32—84no—
473C32×C4—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4C2×#4111yescharacteristic
477C3⋊Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—91no—
484C22×D4—91no—
485C22×D4—181no—
486C23×C4—91no—
487AGL(1,ℤ/8)—184no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—91no—
495C2×M16—91no—
496C2×M16—184no—
497C22×C8—91no—
498C22×C8—91no—
499#123—181no—
500C22⋊Q8—31no—
501C22⋊Q8—91no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—181no—
509#121—181no—
510#120—181no—
511C4×D4—181no—
512C4×D4—181no—
513#117—31no—
514C2×C4⋊C4—31no—
515C2×C22⋊C4—181no—
516#107—31no—
517#107D3211yescharacteristic, complemented
518#106—31no—
519#106—31no—
520#103—31no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527#102—91no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—61no—
531C22×D3—21no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—61no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3D3×D411yescharacteristic
554C22×D3D3×D411yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—31no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—122no—
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—61no—
590C2×Dic3—62no—
591C2×Dic3—62no—
592C2×Dic3D3×D411yescharacteristic
593C2×Dic3D3×D411yescharacteristic
594D12—21no—
595D12—21no—
596D12—42no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12—121no—
607D12—121no—
608D12—121no—
609D12—122no—
610D12—122no—
611D12—122no—
612D12—122no—
613D12—122no—
614D12—122no—
615D12—122no—
616D12—122no—
617D12—122no—
618D12—242no—
619D12—242no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—42no—
623C4×D3—62no—
624C4×D3—62no—
625C4×D3—62no—
626C4×D3—61no—
627C4×D3—61no—
628C4×D3—61no—
629C4×D3—61no—
630C4×D3—62no—
631C4×D3—121no—
632C4×D3—121no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3C2×D1212yes—
636C4×D3#23912yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—22no—
640C3×C8—32no—
641C3×C8—61no—
642C3×C8C2×D1212yescomplemented
643C3×C8D3×D412yescomplemented
644C3⋊C8—21no—
645C3⋊C8—61no—
646C3⋊C8—61no—
647C3⋊C8—121no—
648C3⋊C8C2×D1212yescomplemented
649C2×C32C2×#12111yescharacteristic
650C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
651C2×C32#57511yescharacteristic
652C3⋊D3—22no—
653C3⋊D3—81no—
654C3⋊D3—81no—
655C3×D3—22no—
656C3×D3—41no—
657C3×D3—81no—
658C24—91no—
659C24—181no—
660#41—182no—
661#41—182no—
662C2×Q8—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—91no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—182no—
670C2×D4—182no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—364no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—182no—
685C22×C4—182no—
686C22×C4—181no—
687SD16—62no—
688SD16—182no—
689D8—182no—
690D8—182no—
691M16—34no—
692M16—62no—
693M16—182no—
694M16—182no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—91no—
698C2×C8—182no—
699C2×C8—182no—
700C2×C8C2×D3211yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4—181no—
706C4⋊C4C2×D3211yescharacteristic
707C4⋊C4C2×D3211yescharacteristic
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—61no—
718C22×C3—21no—
719C22×C3—32no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—32no—
736C2×D3—32no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—62no—
741C2×D3—61no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—124no—
748C2×D3—124no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—241no—
764C2×D3—241no—
765C2×D3—241no—
766C2×D3—241no—
767C2×D3—244no—
768C2×D3—244no—
769C2×D3#89512yes—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—32no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—61no—
778C3×C4—81no—
779C3×C4—81no—
780C3×C4—121no—
781C3×C4—121no—
782C3×C4—121no—
783C3×C4C22×D1211yescharacteristic
784C3×C4C2×D3×D411yescharacteristic
785C3×C4C2×#23911yescharacteristic
786C3×C4D3×#4111yescharacteristic
787Dic3—21no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791Dic3—61no—
792Dic3—61no—
793Dic3—121no—
794Dic3#89512yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—31no—
797C23—31no—
798C23—61no—
799C23—91no—
800C23—182no—
801C23—182no—
802C23—181no—
803C23—181no—
804C23—362no—
805C23—361no—
806C23—362no—
807C23—362no—
808Q8—61no—
809Q8—61no—
810D4—61no—
811D4—61no—
812D4—122no—
813D4—181no—
814D4—181no—
815D4—181no—
816D4—181no—
817D4—362no—
818D4—362no—
819D4—362no—
820D4—362no—
821D4—362no—
822D4—362no—
823D4—362no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—31no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—91no—
836C2×C4—122no—
837C2×C4—182no—
838C2×C4—182no—
839C2×C4—182no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—362no—
843C2×C4C22×D3211yescharacteristic
844C8—32no—
845C8—61no—
846C8—181no—
847C8D3×D1212yescomplemented
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—62no—
852C2×C3—121no—
853C2×C3—241no—
854C2×C3C2×#89511yescharacteristic
855C2×C3D3×#12111yescharacteristic
856C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
857C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
858C2×C3#577711yescharacteristic
859C2×C3#577711yescharacteristic
860D3—22no—
861D3—41no—
862D3—62no—
863D3—62no—
864D3—81no—
865D3—122no—
866D3—241no—
867D3—241no—
868D3—241no—
869D3—241no—
870D3—481no—
871D3—481no—
872C22—32no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—92no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—181no—
883C22—181no—
884C22—364no—
885C22—361no—
886C22—361no—
887C22—361no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22D32×D411yescharacteristic
893C4—32no—
894C4—41no—
895C4—41no—
896C4—61no—
897C4—121no—
898C4—121no—
899C4—121no—
900C4—181no—
901C4C2×D3×D1211yescharacteristic
902C4D3×#23911yescharacteristic
903C3—21no—
904C3#7921111yescharacteristic, complemented
905C3#8080511yescharacteristic, complemented
906C2—62no—
907C2—121no—
908C2—182no—
909C2—241no—
910C2—721no—
911C2—721no—
912C2D3×#89511yescharacteristic
913C2#1059472611yescharacteristic
914C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3055
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×#63794C2semidirect
2. C2×#63791C2semidirect
3. #10594627C2semidirect
4. D3×#895C2semidirect
5. #10592582C2semidirect
6. C3×#4886C2semidirect
7. C3×#4881C2semidirect
8. #10590843C2semidirect
9. #10590835C2semidirect
10. #10590609C2semidirect
11. #10590592C2semidirect
12. #10590586C2semidirect
13. #10590585C2semidirect
14. #10590523C2semidirect
15. #10590509C2semidirect
22. C2×#3745C22semidirect
23. C2×C8×C3⋊D3C22semidirect
25. #64104C22semidirect
26. C2×C3×#204C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C3×#897C22semidirect
38. #63909C22semidirect
43. #63871C22semidirect
44. C2×#3717C22semidirect
45. C2×#3714C22semidirect
47. C2×#3711C22semidirect
48. C2×#3710C22semidirect
51. C32×#107C22semidirect
52. #63636C22semidirect
53. #63636C22semidirect
54. C3×#817C22semidirect
55. C3×#810C22semidirect
56. C3×#809C22semidirect
57. C3×#808C22semidirect
58. C3×#807C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
80. #4886D3semidirect
85. #4881D3semidirect
143. C3×ΓL(1,𝔽25)D4semidirect
189. C2×#204C2×D3semidirect
193. C2×ΓL(1,𝔽25)C2×D3semidirect
200. #897C2×D3semidirect
227. C3×#107C2×D3semidirect
228. C3×#107C2×D3semidirect
237. #817C2×D3semidirect
239. #810C2×D3semidirect
249. #809C2×D3semidirect
250. #808C2×D3semidirect
251. #807C2×D3semidirect
300. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
446. ΓL(1,𝔽25)D12semidirect
461. C2×C3⋊D3AGL(1,ℤ/8)semidirect
517. #107D32semidirect
642. C3×C8C2×D12semidirect
643. C3×C8D3×D4semidirect
648. C3⋊C8C2×D12semidirect
795. C32#3055semidirect
847. C8D3×D12semidirect
904. C3#79211semidirect
905. C3#80805semidirect

Maximal subgroups

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

subgroupindex
C2×#637942
C2×#637912
#105946272
D3×#8952
#105925822
C3×#48862
C3×#48812
#105908432
#105908352
#105906092
#105905922
#105905862
#105905852
#105905232
#105905092
#808053
#792113