Finite Group Databasebeta

← C151×#17768 #50322693

Subgroups — C151×#17768 #50322693

Order 38656.

918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic
2#2989×C151C211yesmaximal, characteristic, complemented
3#2925×C151C211yesmaximal, characteristic, complemented
4#1560×C151C211yesmaximal, characteristic, complemented
5#1559×C151C211yesmaximal, characteristic, complemented
6#1558×C151C211yesmaximal, characteristic, complemented
7#1557×C151C211yesmaximal, characteristic, complemented
8#1554×C151C211yesmaximal, characteristic, complemented
9#1553×C151C211yesmaximal, characteristic, complemented
10#1551×C151C211yesmaximal, characteristic, complemented
11#1551×C151C211yesmaximal, characteristic, complemented
12#1550×C151C211yesmaximal, characteristic, complemented
13#1548×C151C211yesmaximal, characteristic, complemented
14#1543×C151C211yesmaximal, characteristic, complemented
15#1542×C151C211yesmaximal, characteristic, complemented
16#556×C151C412yes—
17#555×C151—21no—
18#554×C151—21no—
19#553×C151—21no—
20#553×C151—21no—
21#548×C151C412yes—
22#548×C151C412yes—
23#547×C151C412yes—
24#542×C151—21no—
25#542×C151—21no—
26#537×C151—21no—
27#533×C151C2211yescharacteristic
28#533×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#532×C151C2211yescharacteristic
31#532×C151C2211yescharacteristic
32C2×C4⋊Q8×C151C2211yescharacteristic
33#520×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
44#432×C151C2211yescharacteristic
45#431×C151C2211yescharacteristic
46#431×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#423×C151C2211yescharacteristic
49#423×C151C2211yescharacteristic
50#423×C151C2211yescharacteristic
51C2×C4⋊C8×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#408×C151—21no—
54#405×C151—21no—
55#333×C151C2211yescharacteristic
56#333×C151C2211yescharacteristic
57#333×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#333×C151C2211yescharacteristic
62#333×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#332×C151C2211yescharacteristic
66#332×C151C2211yescharacteristic
67#331×C151C2211yescharacteristic
68#331×C151C2211yescharacteristic
69#331×C151C2211yescharacteristic
70#331×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151C2×C412yes—
73C2×#41×C151C2×C412yes—
74C2×#41×C151D411yescharacteristic
75C22×Q8×C151C2×C412yes—
76C2×M16×C151—21no—
77C2×M16×C151—21no—
78C2×M16×C151—21no—
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151—21no—
83C4⋊Q8×C151C2×C412yes—
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151C2311yescharacteristic
88#126×C151—22no—
89#126×C151—22no—
90#125×C151—21no—
91#125×C151—21no—
92#124×C151—22no—
93#124×C151—22no—
94#124×C151—21no—
95#124×C151C2×C412yes—
96#124×C151C2×C412yes—
97#123×C151—22no—
98#123×C151—22no—
99C22⋊Q8×C151—21no—
100C22⋊Q8×C151—21no—
101C22⋊Q8×C151—22no—
102C22⋊Q8×C151—22no—
103C22⋊Q8×C151—22no—
104C22⋊Q8×C151C2×C412yes—
105C22⋊Q8×C151C2×C412yes—
106#121×C151—22no—
107#121×C151—22no—
108#121×C151—22no—
109#121×C151—21no—
110#121×C151—21no—
111#121×C151—21no—
112#121×C151—21no—
113#121×C151—21no—
114#121×C151C2×C412yes—
115C4×Q8×C151—21no—
116C4×Q8×C151—21no—
117C4×Q8×C151C2×C411yescharacteristic
118C4×Q8×C151C2×C412yes—
119C4×Q8×C151C2×C412yes—
120C4×Q8×C151D411yescharacteristic
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125C4×D4×C151—21no—
126C4×D4×C151—21no—
127C4×D4×C151—21no—
128C4×D4×C151C2×C412yes—
129C4×D4×C151C2×C411yescharacteristic
130C4×D4×C151C2×C411yescharacteristic
131C4×D4×C151C2×C411yescharacteristic
132C4×D4×C151D411yescharacteristic
133C4×D4×C151D411yescharacteristic
134C4×D4×C151D411yescharacteristic
135#117×C151—21no—
136#117×C151—21no—
137#117×C151—22no—
138#117×C151D411yescharacteristic
139#117×C151D411yescharacteristic
140#117×C151D411yescharacteristic
141C2×C4⋊C4×C151—21no—
142C2×C4⋊C4×C151—21no—
143C2×C4⋊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—
174#41×C151—41no—
175#41×C151—41no—
176#41×C151—42no—
177#41×C151—42no—
178#41×C151—82no—
179#41×C151—82no—
180C2×Q8×C151—22no—
181C2×Q8×C151—21no—
182C2×Q8×C151—82no—
183C2×Q8×C151C22⋊C411yescharacteristic
184C2×Q8×C151C22×C412yes—
185C2×Q8×C151C22×C412yes—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151C22⋊C411yescharacteristic
192C2×D4×C151C22⋊C411yescharacteristic
193C2×D4×C151C22⋊C411yescharacteristic
194C2×D4×C151C22×C412yes—
195C22×C4×C151—22no—
196C22×C4×C151—22no—
197C22×C4×C151—22no—
198C22×C4×C151—22no—
199C22×C4×C151C22×C411yescharacteristic
200C22×C4×C151C22×C411yescharacteristic
201C22×C4×C151C22×C411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208M16×C151—42no—
209M16×C151—81no—
210M16×C151—81no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—42no—
220C2×C8×C151—81no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151C22⋊C411yescharacteristic
233C4⋊C4×C151C22⋊C411yescharacteristic
234C4⋊C4×C151C22⋊C411yescharacteristic
235C4⋊C4×C151C22⋊C411yescharacteristic
236C4⋊C4×C151C22⋊C411yescharacteristic
237C4⋊C4×C151C22⋊C411yescharacteristic
238C4⋊C4×C151C22×C412yes—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—22no—
241C22⋊C4×C151—22no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151C22⋊C411yescharacteristic
248C22⋊C4×C151C22⋊C411yescharacteristic
249C22⋊C4×C151C22⋊C411yescharacteristic
250C22⋊C4×C151C22⋊C411yescharacteristic
251C22⋊C4×C151C22⋊C411yescharacteristic
252C22⋊C4×C151C22⋊C411yescharacteristic
253C42×C151—22no—
254C42×C151—22no—
255C42×C151C22×C411yescharacteristic
256C42×C151C22×C411yescharacteristic
257C42×C151C22×C411yescharacteristic
258C42×C151C2×D411yescharacteristic
259C42×C151C2×D411yescharacteristic
260C42×C151C2×D411yescharacteristic
261C42×C151C2×D411yescharacteristic
262C42×C151C2×D411yescharacteristic
263C42×C151C2×D411yescharacteristic
264C42×C151C2411yescharacteristic
265C23×C151—22no—
266C23×C151C2×C22⋊C411yescharacteristic
267C23×C151C2×C22⋊C411yescharacteristic
268C23×C151C2×C22⋊C411yescharacteristic
269Q8×C151—41no—
270Q8×C151—42no—
271Q8×C151—42no—
272Q8×C151—41no—
273Q8×C151—41no—
274Q8×C151—82no—
275D4×C151—41no—
276D4×C151—41no—
277D4×C151—41no—
278D4×C151—42no—
279D4×C151—44no—
280D4×C151—41no—
281D4×C151—41no—
282D4×C151—41no—
283D4×C151—41no—
284D4×C151—82no—
285D4×C151—82no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—44no—
305C2×C4×C151—82no—
306C2×C4×C151—82no—
307C2×C4×C151—82no—
308C2×C4×C151C2×C22⋊C411yescharacteristic
309C2×C4×C151C2×C22⋊C411yescharacteristic
310C2×C4×C151C2×C22⋊C411yescharacteristic
311C2×C4×C151C2×C22⋊C411yescharacteristic
312C2×C4×C151C2×C22⋊C411yescharacteristic
313C2×C4×C151C2×C22⋊C411yescharacteristic
314C2×C4×C151C2×C22⋊C411yescharacteristic
315C2×C4×C151C2×C22⋊C411yescharacteristic
316C2×C4×C151C2×C22⋊C411yescharacteristic
317C2×C4×C151C23×C411yescharacteristic
318C2×C4×C151C22×D411yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C8×C151—41no—
321C8×C151—41no—
322C8×C151—41no—
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C22×C151—21no—
329C22×C151—21no—
330C22×C151—21no—
331C22×C151—21no—
332C22×C151—21no—
333C22×C151—21no—
334C22×C151—21no—
335C22×C151—21no—
336C22×C151—21no—
337C22×C151—42no—
338C22×C151—42no—
339C22×C151—42no—
340C22×C151C22×C22⋊C411yescharacteristic
341C4×C151—21no—
342C4×C151—21no—
343C4×C151—21no—
344C4×C151—21no—
345C4×C151—21no—
346C4×C151—21no—
347C4×C151—21no—
348C4×C151—21no—
349C4×C151—21no—
350C4×C151—21no—
351C4×C151—42no—
352C4×C151—42no—
353C4×C151—42no—
354C4×C151#57511yescharacteristic
355C4×C151#57511yescharacteristic
356C4×C151#57711yescharacteristic
357C4×C151#57811yescharacteristic
358C2×C151—41no—
359C2×C151—41no—
360C2×C151—41no—
361C2×C151—82no—
362C2×C151#288811yescharacteristic
363C2×C151#289611yescharacteristic
364C2×C151#289811yescharacteristic
365#17768C15111yesmaximal, characteristic, direct product factor, Sylow
366C151#1776811yescharacteristic, direct product factor, Sylow
367#3511C2×C15111yescharacteristic
368#2989C2×C15111yescharacteristic, complemented
369#2925C2×C15111yescharacteristic, complemented
370#1560C2×C15111yescharacteristic, complemented
371#1559C2×C15111yescharacteristic, complemented
372#1558C2×C15111yescharacteristic, complemented
373#1557C2×C15111yescharacteristic, complemented
374#1554C2×C15111yescharacteristic, complemented
375#1553C2×C15111yescharacteristic, complemented
376#1551C2×C15111yescharacteristic, complemented
377#1551C2×C15111yescharacteristic, complemented
378#1550C2×C15111yescharacteristic, complemented
379#1548C2×C15111yescharacteristic, complemented
380#1543C2×C15111yescharacteristic, complemented
381#1542C2×C15111yescharacteristic, complemented
382#556C4×C15112yes—
383#555—21no—
384#554—21no—
385#553—21no—
386#553—21no—
387#548C4×C15112yes—
388#548C4×C15112yes—
389#547C4×C15112yes—
390#542—21no—
391#542—21no—
392#537—21no—
393#533C22×C15111yescharacteristic
394#533C22×C15111yescharacteristic
395#532C22×C15111yescharacteristic
396#532C22×C15111yescharacteristic
397#532C22×C15111yescharacteristic
398C2×C4⋊Q8C22×C15111yescharacteristic
399#520—21no—
400C4×#41C22×C15111yescharacteristic
401#446—21no—
402#436—21no—
403#435—21no—
404#435—21no—
405#433—21no—
406#433—21no—
407#432C22×C15111yescharacteristic
408#432C22×C15111yescharacteristic
409#432C22×C15111yescharacteristic
410#432C22×C15111yescharacteristic
411#431C22×C15111yescharacteristic
412#431C22×C15111yescharacteristic
413#431C22×C15111yescharacteristic
414#423C22×C15111yescharacteristic
415#423C22×C15111yescharacteristic
416#423C22×C15111yescharacteristic
417C2×C4⋊C8C22×C15111yescharacteristic
418C2×C4⋊C8C22×C15111yescharacteristic
419#408—21no—
420#405—21no—
421#333C22×C15111yescharacteristic
422#333C22×C15111yescharacteristic
423#333C22×C15111yescharacteristic
424#333C22×C15111yescharacteristic
425#333C22×C15111yescharacteristic
426#333C22×C15111yescharacteristic
427#333C22×C15111yescharacteristic
428#333C22×C15111yescharacteristic
429#332C22×C15111yescharacteristic
430#332C22×C15111yescharacteristic
431#332C22×C15111yescharacteristic
432#332C22×C15111yescharacteristic
433#331C22×C15111yescharacteristic
434#331C22×C15111yescharacteristic
435#331C22×C15111yescharacteristic
436#331C22×C15111yescharacteristic
437C2×#41—21no—
438C2×#41C2×C4×C15112yes—
439C2×#41C2×C4×C15112yes—
440C2×#41D4×C15111yescharacteristic
441C22×Q8C2×C4×C15112yes—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C22×C8—21no—
446C22×C8—21no—
447C4⋊Q8—21no—
448C4⋊Q8—21no—
449C4⋊Q8C2×C4×C15112yes—
450C4⋊Q8C23×C15111yescharacteristic
451C4⋊Q8C23×C15111yescharacteristic
452C4⋊Q8C23×C15111yescharacteristic
453#127C23×C15111yescharacteristic
454#126—22no—
455#126—22no—
456#125—21no—
457#125—21no—
458#124—22no—
459#124—22no—
460#124—21no—
461#124C2×C4×C15112yes—
462#124C2×C4×C15112yes—
463#123—22no—
464#123—22no—
465C22⋊Q8—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8C2×C4×C15112yes—
471C22⋊Q8C2×C4×C15112yes—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121C2×C4×C15112yes—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8C2×C4×C15112yes—
484C4×Q8C2×C4×C15112yes—
485C4×Q8C2×C4×C15111yescharacteristic
486C4×Q8D4×C15111yescharacteristic
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×C4×C15112yes—
495C4×D4C2×C4×C15111yescharacteristic
496C4×D4C2×C4×C15111yescharacteristic
497C4×D4C2×C4×C15111yescharacteristic
498C4×D4D4×C15111yescharacteristic
499C4×D4D4×C15111yescharacteristic
500C4×D4D4×C15111yescharacteristic
501#117—21no—
502#117—21no—
503#117—22no—
504#117D4×C15111yescharacteristic
505#117D4×C15111yescharacteristic
506#117D4×C15111yescharacteristic
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—22no—
510C2×C42C23×C15111yescharacteristic
511C2×C42C23×C15111yescharacteristic
512C2×C42C23×C15111yescharacteristic
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518C4⋊C8C23×C15111yescharacteristic
519C4⋊C8C23×C15111yescharacteristic
520C4⋊C8C23×C15111yescharacteristic
521C4⋊C8C23×C15111yescharacteristic
522C4⋊C8C23×C15111yescharacteristic
523C4⋊C8C23×C15111yescharacteristic
524C4⋊C8C23×C15111yescharacteristic
525C4⋊C8C23×C15111yescharacteristic
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530C22⋊C8—21no—
531C22⋊C8—21no—
532C22⋊C8—21no—
533#97—21no—
534#97—21no—
535#97—21no—
536#97—21no—
537C4×C8—21no—
538C4×C8—21no—
539C4×C8—21no—
540#41—41no—
541#41—41no—
542#41—42no—
543#41—42no—
544#41—82no—
545#41—82no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—82no—
549C2×Q8C22⋊C4×C15111yescharacteristic
550C2×Q8C22×C4×C15112yes—
551C2×Q8C22×C4×C15112yes—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4C22⋊C4×C15111yescharacteristic
558C2×D4C22⋊C4×C15111yescharacteristic
559C2×D4C22⋊C4×C15111yescharacteristic
560C2×D4C22×C4×C15112yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4C22×C4×C15111yescharacteristic
566C22×C4C22×C4×C15111yescharacteristic
567C22×C4C22×C4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4C2×D4×C15111yescharacteristic
572C22×C4C2×D4×C15111yescharacteristic
573C22×C4C2×D4×C15111yescharacteristic
574M16—42no—
575M16—81no—
576M16—81no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—42no—
586C2×C8—81no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4C22⋊C4×C15111yescharacteristic
599C4⋊C4C22⋊C4×C15111yescharacteristic
600C4⋊C4C22⋊C4×C15111yescharacteristic
601C4⋊C4C22⋊C4×C15111yescharacteristic
602C4⋊C4C22⋊C4×C15111yescharacteristic
603C4⋊C4C22⋊C4×C15111yescharacteristic
604C4⋊C4C22×C4×C15112yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4C22⋊C4×C15111yescharacteristic
614C22⋊C4C22⋊C4×C15111yescharacteristic
615C22⋊C4C22⋊C4×C15111yescharacteristic
616C22⋊C4C22⋊C4×C15111yescharacteristic
617C22⋊C4C22⋊C4×C15111yescharacteristic
618C22⋊C4C22⋊C4×C15111yescharacteristic
619C42—22no—
620C42—22no—
621C42C22×C4×C15111yescharacteristic
622C42C22×C4×C15111yescharacteristic
623C42C22×C4×C15111yescharacteristic
624C42C2×D4×C15111yescharacteristic
625C42C2×D4×C15111yescharacteristic
626C42C2×D4×C15111yescharacteristic
627C42C2×D4×C15111yescharacteristic
628C42C2×D4×C15111yescharacteristic
629C42C2×D4×C15111yescharacteristic
630C42C24×C15111yescharacteristic
631C23—22no—
632C23C2×C22⋊C4×C15111yescharacteristic
633C23C2×C22⋊C4×C15111yescharacteristic
634C23C2×C22⋊C4×C15111yescharacteristic
635Q8—41no—
636Q8—42no—
637Q8—42no—
638Q8—41no—
639Q8—41no—
640Q8—82no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—42no—
645D4—44no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—82no—
651D4—82no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—44no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4C2×C22⋊C4×C15111yescharacteristic
675C2×C4C2×C22⋊C4×C15111yescharacteristic
676C2×C4C2×C22⋊C4×C15111yescharacteristic
677C2×C4C2×C22⋊C4×C15111yescharacteristic
678C2×C4C2×C22⋊C4×C15111yescharacteristic
679C2×C4C2×C22⋊C4×C15111yescharacteristic
680C2×C4C2×C22⋊C4×C15111yescharacteristic
681C2×C4C2×C22⋊C4×C15111yescharacteristic
682C2×C4C2×C22⋊C4×C15111yescharacteristic
683C2×C4C23×C4×C15111yescharacteristic
684C2×C4C22×D4×C15111yescharacteristic
685C2×C4C22×D4×C15111yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C8—41no—
693C8—41no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22C22×C22⋊C4×C15111yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4#575×C15111yescharacteristic
721C4#575×C15111yescharacteristic
722C4#577×C15111yescharacteristic
723C4#578×C15111yescharacteristic
724C2—41no—
725C2—41no—
726C2—41no—
727C2—82no—
728C2#2888×C15111yescharacteristic
729C2#2896×C15111yescharacteristic
730C2#2898×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radical#3511×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. #1558×C151C2semidirect
7. #1557×C151C2semidirect
8. #1554×C151C2semidirect
9. #1553×C151C2semidirect
10. #1551×C151C2semidirect
11. #1551×C151C2semidirect
12. #1550×C151C2semidirect
13. #1548×C151C2semidirect
14. #1543×C151C2semidirect
15. #1542×C151C2semidirect
365. #17768C151direct (N × H)
366. C151#17768direct (N × H)
368. #2989C2×C151semidirect
369. #2925C2×C151semidirect
370. #1560C2×C151semidirect
371. #1559C2×C151semidirect
372. #1558C2×C151semidirect
373. #1557C2×C151semidirect
374. #1554C2×C151semidirect
375. #1553C2×C151semidirect
376. #1551C2×C151semidirect
377. #1551C2×C151semidirect
378. #1550C2×C151semidirect
379. #1548C2×C151semidirect
380. #1543C2×C151semidirect
381. #1542C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#2989×C1512
#2925×C1512
#1560×C1512
#1559×C1512
#1558×C1512
#1557×C1512
#1554×C1512
#1553×C1512
#1551×C1512
#1550×C1512
#1548×C1512
#1543×C1512
#1542×C1512
#17768151