Finite Group Databasebeta

← #11866256

Subgroups — #11866256

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5724C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10593994C211yesmaximal, characteristic, complemented
5#10592782C211yesmaximal, characteristic, complemented
6C3×#5083C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591564C211yesmaximal, characteristic, complemented
11#10591557C211yesmaximal, characteristic, complemented
12#10591556C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#83405—31nomaximal
17#80430—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C3×#947C2211yescharacteristic, complemented
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#896—21no—
30C3×#896—21no—
31C3×#894—21no—
32C3×#894—21no—
33C3×#875C2211yescharacteristic, complemented
34C3×C4×D12C2211yescharacteristic
35C3×#872C2211yescharacteristic
36#63939—24no—
37D3×#215—24no—
38#63921—21no—
39D3×(C2×D3)⋊C4—21no—
40#63904—21no—
41#63894C2211yescharacteristic
42Dic3×D12C2211yescharacteristic
43#63881—21no—
44#63841C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#536—31no—
64C2×#949—31no—
65C22×#215—31no—
66C2×#914—31no—
67C2×D3×SD16—31no—
68#5724D311yescharacteristic, complemented
69#5545—31no—
70#5521—31no—
71C3×#461—31no—
72#5233—31no—
73#5225—31no—
74#5165—31no—
75#5162—31no—
76#5083—31no—
77#5083—31no—
78#5083—31no—
79#5083—31no—
80#5083—61no—
81#5083D311yescharacteristic, complemented
82#5057—31no—
83#5057—31no—
84#5057—31no—
85#5057—31no—
86#5016—31no—
87#4999—31no—
88#4844—31no—
89#4839—31no—
90#4819—31no—
91#4818—31no—
92#4804—31no—
93#4802—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C3×#239—22no—
100C3×#239—22no—
101C3×D3×Q8—22no—
102C3×D3×Q8—22no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#624—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12D414yes—
117C32×C4⋊C4—21no—
118C32×C4⋊C4—21no—
119C32×C42C2311yescharacteristic
120#3755—22no—
121#3755—22no—
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#215—22no—
127C3×#215—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32—21no—
147#3717—22no—
148#3715—22no—
149#3714—22no—
150#3713—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3042—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C3×C4⋊Q8—21no—
163C3×C4⋊Q8—31no—
164C3×C4⋊Q8C2×D311yescharacteristic, complemented
165C3×C4⋊Q8C2×D311yescharacteristic, complemented
166C3×#124—31no—
167C3×#124—31no—
168C3×#123—61no—
169C3×#123—61no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8—61no—
172C3×C4×D4—31no—
173C3×#117—31no—
174#949—64no—
175#947C2×D311yescharacteristic, complemented
176#944C2×D311yescharacteristic, complemented
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—61no—
184C2×#215—61no—
185C2×#215—64no—
186C2×#215C2×D311yescharacteristic
187C2×#215C2×D311yescharacteristic
188D4×Dic3—31no—
189C2×#214—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C4×#67—61no—
194C2×(C2×D3)⋊C4—61no—
195#926—31no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198#914—64no—
199D3×SD16—64no—
200C2×D24—31no—
201C2×#204—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8—31no—
204#896—21no—
205#896—21no—
206#894—21no—
207#894—21no—
208#893—31no—
209#893—61no—
210#893—61no—
211#892—31no—
212#67⋊C4—61no—
213D3×C22⋊C4—61no—
214D3×C22⋊C4—61no—
215D3×C22⋊C4—61no—
216#875C2×D311yescharacteristic, complemented
217C4×D12—31no—
218C4×D12—31no—
219C4×D12—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12C2×D311yescharacteristic
223#872C2×D311yescharacteristic
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#835—61no—
235#835C2×D311yescharacteristic, complemented
236#835C2×D311yescharacteristic, complemented
237#832—31no—
238#832—31no—
239#821—31no—
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243#810—31no—
244#809—31no—
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)C2×D412yes—
270C4×C3⋊D3—81no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—42no—
280C3×D12C2×D412yes—
281C3×C4×D3—42no—
282C3×C4×D3—42no—
283C3×C4×D3—81no—
284C3×C4×D3C2×D412yes—
285C3×C4×D3#4112yes—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—42no—
289#626—24no—
290#624—81no—
291D3×Dic3—81no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—31no—
299#518—91no—
300#463—91no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—21no—
317C2×C3×Q8—31no—
318C2×C3×Q8—61no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C2×#67—61no—
333C22×Dic3—61no—
334#239—22no—
335#239—22no—
336D3×Q8—22no—
337D3×Q8—22no—
338D3×D4—34no—
339D3×D4—62no—
340C2×D12—21no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—34no—
344C2×D12—61no—
345C2×D12—62no—
346C2×D12—61no—
347C2×D12C22×D311yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—121no—
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—21no—
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—62no—
362C3×SD16—62no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—41no—
373C3×C4⋊C4—41no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—21no—
384C3×C42—31no—
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387#217—61no—
388#217—61no—
389#215—22no—
390#215—22no—
391#215—62no—
392#215—62no—
393#215—62no—
394#215—62no—
395#215—62no—
396#215—62no—
397#215—122no—
398#215—122no—
399#214—62no—
400#213—62no—
401#213—62no—
402#213—62no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4#6711yescharacteristic
416(C2×D3)⋊C4#6711yescharacteristic
417C4⋊Dic3—31no—
418C4⋊Dic3—31no—
419C4⋊Dic3—61no—
420C4⋊Dic3C22×D311yescharacteristic
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4#6711yescharacteristic
424Dic3⋊C4#6711yescharacteristic
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3C22×D311yescharacteristic
428#208—62no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—62no—
439#204—62no—
440ΓL(1,𝔽25)—62no—
441D3×C8—62no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4—41no—
460C32×C4C22×D411yescharacteristic
461C32×C4C2×#4111yescharacteristic
462C3⋊Dic3—41no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—31no—
470C22×D4—91no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—91no—
480C2×D8—91no—
481C2×M16—91no—
482C22×C8—91no—
483C4⋊Q8—31no—
484C4⋊Q8D3211yescharacteristic, complemented
485#124—31no—
486#124—31no—
487#123—61no—
488#123—61no—
489C22⋊Q8—61no—
490C22⋊Q8—61no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—31no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—31no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—64no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—64no—
522C22×D3—121no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3C2×#6711yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—41no—
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—41no—
540C3×Q8—61no—
541C3×Q8—61no—
542C3×Q8—122no—
543C3×D4—32no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—122no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—122no—
565C2×C3×C4—122no—
566C2×C3×C4—241no—
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4C2×#6711yescharacteristic
570C2×C3×C4C2×#6711yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—64no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—121no—
579C2×Dic3—241no—
580C2×Dic3C2×#6711yescharacteristic
581C2×Dic3C2×#6711yescharacteristic
582C2×Dic3C2×#6711yescharacteristic
583D12—21no—
584D12—21no—
585D12—21no—
586D12—32no—
587D12—32no—
588D12—42no—
589D12—62no—
590D12—64no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12D3×D412yes—
595C4×D3—42no—
596C4×D3—42no—
597C4×D3—81no—
598C4×D3—241no—
599C4×D3—241no—
600C4×D3—241no—
601C4×D3—241no—
602C4×D3—241no—
603C4×D3—242no—
604C4×D3D3×D412yes—
605C4×D3#23712yes—
606Dic6—21no—
607Dic6—21no—
608Dic6—42no—
609C3×C8—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—121no—
618C3⋊C8—121no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3⋊D3—42no—
623C3×D3—22no—
624C3×D3—42no—
625C3×D3—81no—
626C24—181no—
627#41—62no—
628#41—62no—
629C2×Q8—31no—
630C2×Q8—61no—
631C2×Q8—62no—
632C2×Q8—62no—
633C2×Q8C2×D3211yescharacteristic
634C2×Q8C2×D3211yescharacteristic
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4—94no—
639C2×D4—91no—
640C2×D4—182no—
641C2×D4—181no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—62no—
650SD16—62no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—182no—
656D8—182no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—91no—
661C2×C8—91no—
662C2×C8—182no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—91no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—181no—
684C42C2×D3211yescharacteristic
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C22×#6711yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—122no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3#93812yes—
717C3×C4—22no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—61no—
731C3×C4—61no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4C2×D3×D411yescharacteristic
737C3×C4C2×D3×D411yescharacteristic
738C3×C4C2×#23711yescharacteristic
739C3×C4D3×#4111yescharacteristic
740Dic3—21no—
741Dic3—21no—
742Dic3—41no—
743Dic3—41no—
744Dic3—121no—
745Dic3—121no—
746Dic3—241no—
747Dic3#93812yes—
748C32#304211yescharacteristic, complemented, Sylow
749C23—31no—
750C23—61no—
751C23—61no—
752C23—184no—
753C23—181no—
754C23—721no—
755C23—721no—
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—21no—
760Q8—61no—
761Q8—61no—
762Q8—122no—
763D4—32no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—92no—
768D4—122no—
769D4—184no—
770D4—181no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—31no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—181no—
783C2×C4—241no—
784C2×C4—721no—
785C2×C4—721no—
786C2×C4—721no—
787C2×C4D3×#6711yescharacteristic
788C2×C4D3×#6711yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C8—61no—
791C8—61no—
792C8—181no—
793C8—181no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—62no—
798C2×C3—122no—
799C2×C3—241no—
800C2×C3D3×#12111yescharacteristic
801C2×C3#576211yescharacteristic
802C2×C3#577811yescharacteristic
803C2×C3C2×#93811yescharacteristic
804C2×C3#583711yescharacteristic
805C2×C3#583711yescharacteristic
806D3—22no—
807D3—42no—
808D3—81no—
809D3—122no—
810D3—122no—
811D3—242no—
812C22—32no—
813C22—61no—
814C22—61no—
815C22—62no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—182no—
822C22—361no—
823C22—361no—
824C22—724no—
825C22C2×D3×#6711yescharacteristic
826C4—21no—
827C4—21no—
828C4—32no—
829C4—41no—
830C4—41no—
831C4—61no—
832C4—61no—
833C4—121no—
834C4—121no—
835C4—361no—
836C4D32×D411yescharacteristic
837C4D3×#23711yescharacteristic
838C3—21no—
839C3#8043011yescharacteristic, complemented
840C3#8340511yescharacteristic, complemented
841C2—62no—
842C2—122no—
843C2—241no—
844C2—362no—
845C2D3×#93811yescharacteristic
846C2#1059531811yescharacteristic
847C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#63939C2
hypercenterC4⋊Q8D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5724C2semidirect
3. C2×D3×#215C2semidirect
4. #10593994C2semidirect
5. #10592782C2semidirect
6. C3×#5083C2semidirect
7. #10591568C2semidirect
8. #10591567C2semidirect
9. #10591565C2semidirect
10. #10591564C2semidirect
11. #10591557C2semidirect
12. #10591556C2semidirect
13. #10590356C2semidirect
14. #10590348C2semidirect
15. #10590324C2semidirect
21. C32×C4⋊Q8C22semidirect
25. C3×#947C22semidirect
26. C3×#944C22semidirect
33. C3×#875C22semidirect
51. #63662C22semidirect
52. #63662C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#835C22semidirect
55. C3×#835C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
68. #5724D3semidirect
81. #5083D3semidirect
164. C3×C4⋊Q8C2×D3semidirect
165. C3×C4⋊Q8C2×D3semidirect
175. #947C2×D3semidirect
176. #944C2×D3semidirect
216. #875C2×D3semidirect
235. #835C2×D3semidirect
236. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
484. C4⋊Q8D32semidirect
748. C32#3042semidirect
839. C3#80430semidirect
840. C3#83405semidirect

Maximal subgroups

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

subgroupindex
C3×#57242
C2×#639392
C2×D3×#2152
#105939942
#105927822
C3×#50832
#105915682
#105915672
#105915652
#105915642
#105915572
#105915562
#105903562
#105903482
#105903242
#834053
#804303