Finite Group Databasebeta

← C151×#17766 #50322691

Subgroups — C151×#17766 #50322691

Order 38656.

982 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3508×C151C211yesmaximal, characteristic
2#2989×C151C211yesmaximal, characteristic, complemented
3#2925×C151C211yesmaximal, characteristic, complemented
4#1560×C151C211yesmaximal, characteristic, complemented
5#1559×C151C211yesmaximal, characteristic, complemented
6#1557×C151C211yesmaximal, characteristic, complemented
7#1555×C151C211yesmaximal, characteristic, complemented
8#1554×C151C211yesmaximal, characteristic, complemented
9#1553×C151C211yesmaximal, characteristic, complemented
10#1551×C151C211yesmaximal, characteristic, complemented
11#1551×C151C211yesmaximal, characteristic, complemented
12#1547×C151C211yesmaximal, characteristic, complemented
13#1545×C151C211yesmaximal, characteristic, complemented
14#1543×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#559×C151—21no—
17#559×C151C412yes—
18#550×C151—21no—
19#550×C151C412yes—
20#546×C151—21no—
21#546×C151—21no—
22#546×C151C412yes—
23#546×C151C412yes—
24#540×C151—21no—
25#540×C151—21no—
26#535×C151—21no—
27#533×C151C2211yescharacteristic
28#532×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#532×C151C2211yescharacteristic
31#532×C151C2211yescharacteristic
32C2×#127×C151C2211yescharacteristic
33#518×C151—21no—
34C4×#41×C151C2211yescharacteristic
35#446×C151—21no—
36#436×C151—21no—
37#435×C151—21no—
38#435×C151—21no—
39#433×C151—21no—
40#433×C151—21no—
41#432×C151C2211yescharacteristic
42#432×C151C2211yescharacteristic
43#432×C151C2211yescharacteristic, complemented
44#432×C151C2211yescharacteristic, complemented
45#431×C151C2211yescharacteristic
46#431×C151C2211yescharacteristic, complemented
47#431×C151C2211yescharacteristic, complemented
48#423×C151C2211yescharacteristic
49#423×C151C2211yescharacteristic, complemented
50#423×C151C2211yescharacteristic, complemented
51C2×C4⋊C8×C151C2211yescharacteristic, complemented
52C2×C4⋊C8×C151C2211yescharacteristic, complemented
53#408×C151—21no—
54#405×C151—21no—
55#333×C151C2211yescharacteristic, complemented
56#333×C151C2211yescharacteristic, complemented
57#333×C151C2211yescharacteristic, complemented
58#333×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#332×C151C2211yescharacteristic, complemented
61#332×C151C2211yescharacteristic, complemented
62#332×C151C2211yescharacteristic, complemented
63#331×C151C2211yescharacteristic
64#331×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67#331×C151C2211yescharacteristic
68#331×C151C2211yescharacteristic
69#331×C151C2211yescharacteristic
70#331×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151C2×C412yes—
74C2×#41×C151C2×C412yes—
75C2×#41×C151D411yescharacteristic
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151C2×C412yes—
79C2×M16×C151—21no—
80C2×M16×C151—21no—
81C2×M16×C151—21no—
82C22×C8×C151—21no—
83C22×C8×C151—21no—
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151—22no—
87#127×C151—21no—
88#127×C151—21no—
89#127×C151C2×C412yes—
90#127×C151C2311yescharacteristic
91#127×C151C2311yescharacteristic
92#125×C151—21no—
93#124×C151—21no—
94#124×C151—21no—
95#124×C151—22no—
96#124×C151C2×C412yes—
97#124×C151C2×C412yes—
98#123×C151—22no—
99#123×C151—22no—
100#123×C151—22no—
101#123×C151—22no—
102C22⋊Q8×C151—21no—
103C22⋊Q8×C151C2×C412yes—
104#121×C151—21no—
105#121×C151—21no—
106#121×C151—21no—
107#121×C151—21no—
108#121×C151—21no—
109#121×C151—21no—
110#121×C151—22no—
111#121×C151—22no—
112#121×C151—22no—
113#121×C151—22no—
114#121×C151C2×C412yes—
115#121×C151C2×C412yes—
116#120×C151—22no—
117#120×C151—22no—
118C4×Q8×C151—21no—
119C4×Q8×C151C2×C411yescharacteristic
120C4×Q8×C151C2×C412yes—
121C4×Q8×C151D411yescharacteristic
122C4×D4×C151—22no—
123C4×D4×C151—22no—
124C4×D4×C151—21no—
125C4×D4×C151—21no—
126C4×D4×C151—21no—
127C4×D4×C151—21no—
128C4×D4×C151—21no—
129C4×D4×C151—21no—
130C4×D4×C151C2×C412yes—
131C4×D4×C151C2×C412yes—
132C4×D4×C151C2×C411yescharacteristic
133C4×D4×C151C2×C411yescharacteristic
134C4×D4×C151C2×C411yescharacteristic
135C4×D4×C151D411yescharacteristic
136C4×D4×C151D411yescharacteristic
137C4×D4×C151D411yescharacteristic
138#117×C151—21no—
139#117×C151D411yescharacteristic
140#117×C151D411yescharacteristic
141#117×C151D411yescharacteristic
142C2×C22⋊C4×C151—22no—
143C2×C22⋊C4×C151—22no—
144C2×C42×C151C2311yescharacteristic
145C2×C42×C151C2311yescharacteristic
146C2×C42×C151C2311yescharacteristic
147C4⋊C8×C151—21no—
148C4⋊C8×C151—21no—
149C4⋊C8×C151—21no—
150C4⋊C8×C151—21no—
151C4⋊C8×C151—21no—
152C4⋊C8×C151C2311yescharacteristic
153C4⋊C8×C151C2311yescharacteristic
154C4⋊C8×C151C2311yescharacteristic
155C4⋊C8×C151C2311yescharacteristic
156C4⋊C8×C151C2311yescharacteristic
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C22⋊C8×C151—21no—
161C22⋊C8×C151—21no—
162C22⋊C8×C151—21no—
163C22⋊C8×C151—21no—
164C22⋊C8×C151—21no—
165C22⋊C8×C151—21no—
166C22⋊C8×C151—21no—
167#97×C151—21no—
168#97×C151—21no—
169#97×C151—21no—
170#97×C151—21no—
171C4×C8×C151—21no—
172C4×C8×C151—21no—
173C4×C8×C151—21no—
174C24×C151—22no—
175#41×C151—41no—
176#41×C151—41no—
177#41×C151—81no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—82no—
182#41×C151—82no—
183C2×Q8×C151—21no—
184C2×Q8×C151C22⋊C411yescharacteristic
185C2×Q8×C151C22×C412yes—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—42no—
198C2×D4×C151—42no—
199C2×D4×C151—81no—
200C2×D4×C151—81no—
201C2×D4×C151—82no—
202C2×D4×C151C22⋊C411yescharacteristic
203C2×D4×C151C22⋊C411yescharacteristic
204C2×D4×C151C22⋊C411yescharacteristic
205C2×D4×C151C22×C412yes—
206C2×D4×C151C22×C412yes—
207C22×C4×C151—22no—
208C22×C4×C151—22no—
209C22×C4×C151—22no—
210C22×C4×C151—22no—
211C22×C4×C151C22×C411yescharacteristic
212C22×C4×C151C22×C411yescharacteristic
213C22×C4×C151C22×C411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220M16×C151—42no—
221M16×C151—81no—
222M16×C151—81no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—42no—
232C2×C8×C151—81no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—22no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151C22⋊C411yescharacteristic
239C4⋊C4×C151C22⋊C411yescharacteristic
240C4⋊C4×C151C22⋊C411yescharacteristic
241C4⋊C4×C151C22⋊C411yescharacteristic
242C4⋊C4×C151C22⋊C411yescharacteristic
243C4⋊C4×C151C22⋊C411yescharacteristic
244C4⋊C4×C151C22×C412yes—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151C22⋊C411yescharacteristic
255C22⋊C4×C151C22⋊C411yescharacteristic
256C22⋊C4×C151C22⋊C411yescharacteristic
257C22⋊C4×C151C22⋊C411yescharacteristic
258C22⋊C4×C151C22⋊C411yescharacteristic
259C22⋊C4×C151C22⋊C411yescharacteristic
260C42×C151—22no—
261C42×C151C22×C411yescharacteristic
262C42×C151C22×C411yescharacteristic
263C42×C151C22×C411yescharacteristic
264C42×C151C2×D411yescharacteristic
265C42×C151C2×D411yescharacteristic
266C42×C151C2×D411yescharacteristic
267C42×C151C2×D411yescharacteristic
268C42×C151C2×D411yescharacteristic
269C42×C151C2×D411yescharacteristic
270C42×C151C2411yescharacteristic
271C23×C151—22no—
272C23×C151—22no—
273C23×C151—44no—
274C23×C151—82no—
275C23×C151—82no—
276C23×C151C2×C22⋊C411yescharacteristic
277C23×C151C2×C22⋊C411yescharacteristic
278C23×C151C2×C22⋊C411yescharacteristic
279Q8×C151—41no—
280Q8×C151—42no—
281Q8×C151—41no—
282Q8×C151—41no—
283D4×C151—41no—
284D4×C151—41no—
285D4×C151—41no—
286D4×C151—42no—
287D4×C151—42no—
288D4×C151—44no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—82no—
298D4×C151—82no—
299D4×C151—82no—
300D4×C151—82no—
301D4×C151—82no—
302D4×C151—82no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—22no—
316C2×C4×C151—22no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—82no—
321C2×C4×C151—82no—
322C2×C4×C151—82no—
323C2×C4×C151—82no—
324C2×C4×C151C2×C22⋊C411yescharacteristic
325C2×C4×C151C2×C22⋊C411yescharacteristic
326C2×C4×C151C2×C22⋊C411yescharacteristic
327C2×C4×C151C2×C22⋊C411yescharacteristic
328C2×C4×C151C2×C22⋊C411yescharacteristic
329C2×C4×C151C2×C22⋊C411yescharacteristic
330C2×C4×C151C2×C22⋊C411yescharacteristic
331C2×C4×C151C2×C22⋊C411yescharacteristic
332C2×C4×C151C2×C22⋊C411yescharacteristic
333C2×C4×C151C23×C411yescharacteristic
334C2×C4×C151C22×D411yescharacteristic
335C2×C4×C151C22×D411yescharacteristic
336C8×C151—41no—
337C8×C151—41no—
338C8×C151—41no—
339C8×C151—41no—
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C22×C151—21no—
345C22×C151—21no—
346C22×C151—21no—
347C22×C151—21no—
348C22×C151—21no—
349C22×C151—21no—
350C22×C151—21no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—42no—
358C22×C151—42no—
359C22×C151—164no—
360C22×C151C22×C22⋊C411yescharacteristic
361C4×C151—21no—
362C4×C151—21no—
363C4×C151—21no—
364C4×C151—21no—
365C4×C151—21no—
366C4×C151—21no—
367C4×C151—21no—
368C4×C151—21no—
369C4×C151—21no—
370C4×C151—21no—
371C4×C151—42no—
372C4×C151—42no—
373C4×C151#57511yescharacteristic
374C4×C151#57511yescharacteristic
375C4×C151#57611yescharacteristic
376C4×C151#57711yescharacteristic
377C2×C151—41no—
378C2×C151—41no—
379C2×C151—41no—
380C2×C151—82no—
381C2×C151—82no—
382C2×C151#288811yescharacteristic
383C2×C151#289611yescharacteristic
384C2×C151#289711yescharacteristic
385#17766C15111yesmaximal, characteristic, direct product factor, Sylow
386C151#1776611yescharacteristic, direct product factor, Sylow
387#3508C2×C15111yescharacteristic
388#2989C2×C15111yescharacteristic, complemented
389#2925C2×C15111yescharacteristic, complemented
390#1560C2×C15111yescharacteristic, complemented
391#1559C2×C15111yescharacteristic, complemented
392#1557C2×C15111yescharacteristic, complemented
393#1555C2×C15111yescharacteristic, complemented
394#1554C2×C15111yescharacteristic, complemented
395#1553C2×C15111yescharacteristic, complemented
396#1551C2×C15111yescharacteristic, complemented
397#1551C2×C15111yescharacteristic, complemented
398#1547C2×C15111yescharacteristic, complemented
399#1545C2×C15111yescharacteristic, complemented
400#1543C2×C15111yescharacteristic, complemented
401#1540C2×C15111yescharacteristic, complemented
402#559—21no—
403#559C4×C15112yes—
404#550—21no—
405#550C4×C15112yes—
406#546—21no—
407#546—21no—
408#546C4×C15112yes—
409#546C4×C15112yes—
410#540—21no—
411#540—21no—
412#535—21no—
413#533C22×C15111yescharacteristic
414#532C22×C15111yescharacteristic
415#532C22×C15111yescharacteristic
416#532C22×C15111yescharacteristic
417#532C22×C15111yescharacteristic
418C2×#127C22×C15111yescharacteristic
419#518—21no—
420C4×#41C22×C15111yescharacteristic
421#446—21no—
422#436—21no—
423#435—21no—
424#435—21no—
425#433—21no—
426#433—21no—
427#432C22×C15111yescharacteristic
428#432C22×C15111yescharacteristic
429#432C22×C15111yescharacteristic, complemented
430#432C22×C15111yescharacteristic, complemented
431#431C22×C15111yescharacteristic
432#431C22×C15111yescharacteristic, complemented
433#431C22×C15111yescharacteristic, complemented
434#423C22×C15111yescharacteristic
435#423C22×C15111yescharacteristic, complemented
436#423C22×C15111yescharacteristic, complemented
437C2×C4⋊C8C22×C15111yescharacteristic, complemented
438C2×C4⋊C8C22×C15111yescharacteristic, complemented
439#408—21no—
440#405—21no—
441#333C22×C15111yescharacteristic, complemented
442#333C22×C15111yescharacteristic, complemented
443#333C22×C15111yescharacteristic, complemented
444#333C22×C15111yescharacteristic, complemented
445#332C22×C15111yescharacteristic, complemented
446#332C22×C15111yescharacteristic, complemented
447#332C22×C15111yescharacteristic, complemented
448#332C22×C15111yescharacteristic, complemented
449#331C22×C15111yescharacteristic
450#331C22×C15111yescharacteristic
451#331C22×C15111yescharacteristic
452#331C22×C15111yescharacteristic
453#331C22×C15111yescharacteristic
454#331C22×C15111yescharacteristic
455#331C22×C15111yescharacteristic
456#331C22×C15111yescharacteristic
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×C4×C15112yes—
460C2×#41C2×C4×C15112yes—
461C2×#41D4×C15111yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C2×C4×C15112yes—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C22×C8—21no—
469C22×C8—21no—
470C4⋊Q8C23×C15111yescharacteristic
471C4⋊Q8C23×C15111yescharacteristic
472#127—22no—
473#127—21no—
474#127—21no—
475#127C2×C4×C15112yes—
476#127C23×C15111yescharacteristic
477#127C23×C15111yescharacteristic
478#125—21no—
479#124—22no—
480#124—21no—
481#124—21no—
482#124C2×C4×C15112yes—
483#124C2×C4×C15112yes—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488C22⋊Q8—21no—
489C22⋊Q8C2×C4×C15112yes—
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121C2×C4×C15112yes—
501#121C2×C4×C15112yes—
502#120—22no—
503#120—22no—
504C4×Q8—21no—
505C4×Q8C2×C4×C15112yes—
506C4×Q8C2×C4×C15111yescharacteristic
507C4×Q8D4×C15111yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4C2×C4×C15112yes—
517C4×D4C2×C4×C15112yes—
518C4×D4C2×C4×C15111yescharacteristic
519C4×D4C2×C4×C15111yescharacteristic
520C4×D4C2×C4×C15111yescharacteristic
521C4×D4D4×C15111yescharacteristic
522C4×D4D4×C15111yescharacteristic
523C4×D4D4×C15111yescharacteristic
524#117—21no—
525#117D4×C15111yescharacteristic
526#117D4×C15111yescharacteristic
527#117D4×C15111yescharacteristic
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C42C23×C15111yescharacteristic
531C2×C42C23×C15111yescharacteristic
532C2×C42C23×C15111yescharacteristic
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8—21no—
536C4⋊C8—21no—
537C4⋊C8—21no—
538C4⋊C8C23×C15111yescharacteristic
539C4⋊C8C23×C15111yescharacteristic
540C4⋊C8C23×C15111yescharacteristic
541C4⋊C8C23×C15111yescharacteristic
542C4⋊C8C23×C15111yescharacteristic
543C4⋊C8C23×C15111yescharacteristic
544C4⋊C8C23×C15111yescharacteristic
545C4⋊C8C23×C15111yescharacteristic
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C22⋊C8—21no—
552C22⋊C8—21no—
553#97—21no—
554#97—21no—
555#97—21no—
556#97—21no—
557C4×C8—21no—
558C4×C8—21no—
559C4×C8—21no—
560C24—22no—
561#41—41no—
562#41—41no—
563#41—81no—
564#41—81no—
565#41—81no—
566#41—81no—
567#41—82no—
568#41—82no—
569C2×Q8—21no—
570C2×Q8C22⋊C4×C15111yescharacteristic
571C2×Q8C22×C4×C15112yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—82no—
588C2×D4C22⋊C4×C15111yescharacteristic
589C2×D4C22⋊C4×C15111yescharacteristic
590C2×D4C22⋊C4×C15111yescharacteristic
591C2×D4C22×C4×C15112yes—
592C2×D4C22×C4×C15112yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4C22×C4×C15111yescharacteristic
598C22×C4C22×C4×C15111yescharacteristic
599C22×C4C22×C4×C15111yescharacteristic
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4C2×D4×C15111yescharacteristic
602C22×C4C2×D4×C15111yescharacteristic
603C22×C4C2×D4×C15111yescharacteristic
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606M16—42no—
607M16—81no—
608M16—81no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—42no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4C22⋊C4×C15111yescharacteristic
625C4⋊C4C22⋊C4×C15111yescharacteristic
626C4⋊C4C22⋊C4×C15111yescharacteristic
627C4⋊C4C22⋊C4×C15111yescharacteristic
628C4⋊C4C22⋊C4×C15111yescharacteristic
629C4⋊C4C22⋊C4×C15111yescharacteristic
630C4⋊C4C22×C4×C15112yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4C22⋊C4×C15111yescharacteristic
641C22⋊C4C22⋊C4×C15111yescharacteristic
642C22⋊C4C22⋊C4×C15111yescharacteristic
643C22⋊C4C22⋊C4×C15111yescharacteristic
644C22⋊C4C22⋊C4×C15111yescharacteristic
645C22⋊C4C22⋊C4×C15111yescharacteristic
646C42—22no—
647C42C22×C4×C15111yescharacteristic
648C42C22×C4×C15111yescharacteristic
649C42C22×C4×C15111yescharacteristic
650C42C2×D4×C15111yescharacteristic
651C42C2×D4×C15111yescharacteristic
652C42C2×D4×C15111yescharacteristic
653C42C2×D4×C15111yescharacteristic
654C42C2×D4×C15111yescharacteristic
655C42C2×D4×C15111yescharacteristic
656C42C24×C15111yescharacteristic
657C23—22no—
658C23—22no—
659C23—44no—
660C23—82no—
661C23—82no—
662C23C2×C22⋊C4×C15111yescharacteristic
663C23C2×C22⋊C4×C15111yescharacteristic
664C23C2×C22⋊C4×C15111yescharacteristic
665Q8—41no—
666Q8—42no—
667Q8—41no—
668Q8—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—42no—
673D4—42no—
674D4—44no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—82no—
684D4—82no—
685D4—82no—
686D4—82no—
687D4—82no—
688D4—82no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4C2×C22⋊C4×C15111yescharacteristic
711C2×C4C2×C22⋊C4×C15111yescharacteristic
712C2×C4C2×C22⋊C4×C15111yescharacteristic
713C2×C4C2×C22⋊C4×C15111yescharacteristic
714C2×C4C2×C22⋊C4×C15111yescharacteristic
715C2×C4C2×C22⋊C4×C15111yescharacteristic
716C2×C4C2×C22⋊C4×C15111yescharacteristic
717C2×C4C2×C22⋊C4×C15111yescharacteristic
718C2×C4C2×C22⋊C4×C15111yescharacteristic
719C2×C4C23×C4×C15111yescharacteristic
720C2×C4C22×D4×C15111yescharacteristic
721C2×C4C22×D4×C15111yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—164no—
746C22C22×C22⋊C4×C15111yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—42no—
759C4#575×C15111yescharacteristic
760C4#575×C15111yescharacteristic
761C4#576×C15111yescharacteristic
762C4#577×C15111yescharacteristic
763C2—41no—
764C2—41no—
765C2—41no—
766C2—82no—
767C2—82no—
768C2#2888×C15111yescharacteristic
769C2#2896×C15111yescharacteristic
770C2#2897×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radical#3508×C151C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C4×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2989×C151C2semidirect
3. #2925×C151C2semidirect
4. #1560×C151C2semidirect
5. #1559×C151C2semidirect
6. #1557×C151C2semidirect
7. #1555×C151C2semidirect
8. #1554×C151C2semidirect
9. #1553×C151C2semidirect
10. #1551×C151C2semidirect
11. #1551×C151C2semidirect
12. #1547×C151C2semidirect
13. #1545×C151C2semidirect
14. #1543×C151C2semidirect
15. #1540×C151C2semidirect
43. #432×C151C22semidirect
44. #432×C151C22semidirect
46. #431×C151C22semidirect
47. #431×C151C22semidirect
49. #423×C151C22semidirect
50. #423×C151C22semidirect
51. C2×C4⋊C8×C151C22semidirect
52. C2×C4⋊C8×C151C22semidirect
55. #333×C151C22semidirect
56. #333×C151C22semidirect
57. #333×C151C22semidirect
58. #333×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
61. #332×C151C22semidirect
62. #332×C151C22semidirect
385. #17766C151direct (N × H)
386. C151#17766direct (N × H)
388. #2989C2×C151semidirect
389. #2925C2×C151semidirect
390. #1560C2×C151semidirect
391. #1559C2×C151semidirect
392. #1557C2×C151semidirect
393. #1555C2×C151semidirect
394. #1554C2×C151semidirect
395. #1553C2×C151semidirect
396. #1551C2×C151semidirect
397. #1551C2×C151semidirect
398. #1547C2×C151semidirect
399. #1545C2×C151semidirect
400. #1543C2×C151semidirect
401. #1540C2×C151semidirect
429. #432C22×C151semidirect
430. #432C22×C151semidirect
432. #431C22×C151semidirect
433. #431C22×C151semidirect
435. #423C22×C151semidirect
436. #423C22×C151semidirect
437. C2×C4⋊C8C22×C151semidirect
438. C2×C4⋊C8C22×C151semidirect
441. #333C22×C151semidirect
442. #333C22×C151semidirect
443. #333C22×C151semidirect
444. #333C22×C151semidirect
445. #332C22×C151semidirect
446. #332C22×C151semidirect
447. #332C22×C151semidirect
448. #332C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3508×C1512
#2989×C1512
#2925×C1512
#1560×C1512
#1559×C1512
#1557×C1512
#1555×C1512
#1554×C1512
#1553×C1512
#1551×C1512
#1547×C1512
#1545×C1512
#1543×C1512
#1540×C1512
#17766151