Finite Group Databasebeta

← C151×#24666 #50329591

Subgroups — C151×#24666 #50329591

Order 38656.

870 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic, complemented
2C2×#433×C151C211yesmaximal, characteristic, complemented
3#2621×C151C211yesmaximal, characteristic, complemented
4#2324×C151C211yesmaximal, characteristic
5#2036×C151C211yesmaximal, characteristic, complemented
6#2035×C151C211yesmaximal, characteristic, complemented
7#2000×C151C211yesmaximal, characteristic
8#2000×C151C211yesmaximal, characteristic
9#1981×C151C211yesmaximal, characteristic, complemented
10#1973×C151C211yesmaximal, characteristic, complemented
11#1968×C151C211yesmaximal, characteristic, complemented
12#1949×C151C211yesmaximal, characteristic, complemented
13#1935×C151C211yesmaximal, characteristic, complemented
14#1933×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#461×C151—24no—
25#433×C151—24no—
26C2×#107×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic
42#398×C151—21no—
43#398×C151—21no—
44#397×C151—21no—
45#397×C151—21no—
46#391×C151C2211yescharacteristic
47#391×C151C2211yescharacteristic
48#390×C151—21no—
49#390×C151C2211yescharacteristic
50#389×C151C2211yescharacteristic
51#388×C151—21no—
52#386×C151—21no—
53#385×C151—21no—
54#382×C151C2211yescharacteristic
55#380×C151C2211yescharacteristic
56C4×C4⋊C4×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151C2311yescharacteristic
67C2×SD16×C151—22no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151—41no—
72C2×SD16×C151—41no—
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C4⋊Q8×C151—22no—
78C4⋊Q8×C151—22no—
79C22⋊Q8×C151—41no—
80C22⋊Q8×C151—41no—
81C22⋊Q8×C151—41no—
82C22⋊Q8×C151—41no—
83#121×C151—22no—
84#121×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87#117×C151—22no—
88#117×C151—22no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C4⋊C4×C151D411yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C22⋊C4×C151D411yescharacteristic
110C2×C42×C151—21no—
111C2×C42×C151C2311yescharacteristic
112C2×C42×C151C2311yescharacteristic
113#107×C151—41no—
114#106×C151—41no—
115C4⋊C8×C151—22no—
116C4⋊C8×C151D414yescomplemented
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#103×C151—22no—
121#103×C151—41no—
122#103×C151—41no—
123#102×C151—41no—
124#102×C151—41no—
125C22⋊C8×C151—22no—
126C22⋊C8×C151—22no—
127#97×C151—22no—
128C4×C8×C151—22no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138C24×C151—21no—
139C24×C151C2×D411yescharacteristic
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×D4×C151—24no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—81no—
159C2×D4×C151—81no—
160C2×D4×C151#4112yes—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—42no—
175C22×C4×C151—81no—
176C22×C4×C151—81no—
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2411yescharacteristic
183SD16×C151—44no—
184SD16×C151—44no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151C2×D412yes—
196C2×C8×C151C2×D412yes—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—42no—
209C4⋊C4×C151—42no—
210C4⋊C4×C151—42no—
211C4⋊C4×C151—42no—
212C4⋊C4×C151—81no—
213C4⋊C4×C151#4112yes—
214C22⋊C4×C151—24no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—81no—
221C22⋊C4×C151—81no—
222C22⋊C4×C151—81no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—81no—
226C42×C151C2×D412yes—
227C42×C151#4112yes—
228C23×C151—21no—
229C23×C151—22no—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151C22×D411yescharacteristic
243Q8×C151—41no—
244Q8×C151—41no—
245Q8×C151—41no—
246Q8×C151—41no—
247Q8×C151—41no—
248Q8×C151—41no—
249Q8×C151—41no—
250Q8×C151—41no—
251D4×C151—22no—
252D4×C151—22no—
253D4×C151—41no—
254D4×C151—41no—
255D4×C151—84no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—84no—
295C2×C4×C151#12112yes—
296C2×C4×C151#12112yes—
297C2×C4×C151C22×D411yescharacteristic
298C2×C4×C151C2×#4111yescharacteristic
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C151C2×#4111yescharacteristic
301C2×C4×C151H(5,𝔽2)11yescharacteristic
302C2×C4×C151H(5,𝔽2)11yescharacteristic
303C8×C151—22no—
304C8×C151—22no—
305C8×C151—41no—
306C8×C151—41no—
307C22×C151—41no—
308C22×C151—42no—
309C22×C151—41no—
310C22×C151—42no—
311C22×C151—41no—
312C22×C151—42no—
313C22×C151—41no—
314C22×C151—41no—
315C22×C151—41no—
316C22×C151—41no—
317C22×C151—81no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151C2×#12111yescharacteristic
322C22×C151#52511yescharacteristic
323C22×C151#53511yescharacteristic
324C22×C151#57711yescharacteristic
325C22×C151#57711yescharacteristic
326C22×C151#57711yescharacteristic
327C22×C151#57811yescharacteristic
328C4×C151—22no—
329C4×C151—22no—
330C4×C151—42no—
331C4×C151—41no—
332C4×C151—41no—
333C4×C151—41no—
334C4×C151—81no—
335C4×C151—81no—
336C4×C151—81no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151#54611yescharacteristic
341C4×C151#55011yescharacteristic
342C4×C151#55311yescharacteristic
343C4×C151#55511yescharacteristic
344C2×C151—81no—
345C2×C151—82no—
346C2×C151#241411yescharacteristic
347C2×C151#305711yescharacteristic
348C2×C151#306311yescharacteristic
349C2×C151#312011yescharacteristic
350C2×C151#312311yescharacteristic
351C2×C151#322111yescharacteristic
352C2×C151#322511yescharacteristic
353#24666C15111yesmaximal, characteristic, direct product factor, Sylow
354C151#2466611yescharacteristic, direct product factor, Sylow
355C2×#461C2×C15111yescharacteristic, complemented
356C2×#433C2×C15111yescharacteristic, complemented
357#2621C2×C15111yescharacteristic, complemented
358#2324C2×C15111yescharacteristic
359#2036C2×C15111yescharacteristic, complemented
360#2035C2×C15111yescharacteristic, complemented
361#2000C2×C15111yescharacteristic
362#2000C2×C15111yescharacteristic
363#1981C2×C15111yescharacteristic, complemented
364#1973C2×C15111yescharacteristic, complemented
365#1968C2×C15111yescharacteristic, complemented
366#1949C2×C15111yescharacteristic, complemented
367#1935C2×C15111yescharacteristic, complemented
368#1933C2×C15111yescharacteristic, complemented
369#1804C2×C15111yescharacteristic, complemented
370C22×SD16C22×C15111yescharacteristic
371C22×SD16C22×C15111yescharacteristic
372C2×C4⋊Q8C22×C15111yescharacteristic
373C2×C22⋊Q8C22×C15111yescharacteristic
374C2×C22⋊Q8C22×C15111yescharacteristic
375C2×#121C22×C15111yescharacteristic
376C2×C4×D4C22×C15111yescharacteristic
377C2×#117C22×C15111yescharacteristic
378#461—24no—
379#433—24no—
380C2×#107C22×C15111yescharacteristic
381C2×#106C22×C15111yescharacteristic
382C2×C4⋊C8C22×C15111yescharacteristic
383C2×C4⋊C8C22×C15111yescharacteristic
384C2×#103C22×C15111yescharacteristic
385C2×#103C22×C15111yescharacteristic
386C2×#103C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#103C22×C15111yescharacteristic
390C2×#102C22×C15111yescharacteristic
391C2×#102C22×C15111yescharacteristic
392C2×C22⋊C8C22×C15111yescharacteristic
393C2×C22⋊C8C22×C15111yescharacteristic
394C2×#97C22×C15111yescharacteristic
395C2×C4×C8C22×C15111yescharacteristic
396#398—21no—
397#398—21no—
398#397—21no—
399#397—21no—
400#391C22×C15111yescharacteristic
401#391C22×C15111yescharacteristic
402#390—21no—
403#390C22×C15111yescharacteristic
404#389C22×C15111yescharacteristic
405#388—21no—
406#386—21no—
407#385—21no—
408#382C22×C15111yescharacteristic
409#380C22×C15111yescharacteristic
410C4×C4⋊C4C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#340C22×C15111yescharacteristic
415C22×Q8C23×C15111yescharacteristic
416C22×Q8C23×C15111yescharacteristic
417C22×D4—21no—
418C22×D4C23×C15111yescharacteristic
419C23×C4—21no—
420C23×C4C23×C15111yescharacteristic
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—41no—
426C2×SD16—41no—
427C22×C8C23×C15111yescharacteristic
428C22×C8C23×C15111yescharacteristic
429C22×C8C23×C15111yescharacteristic
430C22×C8C23×C15111yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—22no—
433C22⋊Q8—41no—
434C22⋊Q8—41no—
435C22⋊Q8—41no—
436C22⋊Q8—41no—
437#121—22no—
438#121—22no—
439C4×D4—22no—
440C4×D4—22no—
441#117—22no—
442#117—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4D4×C15111yescharacteristic
449C2×C4⋊C4D4×C15111yescharacteristic
450C2×C4⋊C4C23×C15111yescharacteristic
451C2×C4⋊C4C23×C15111yescharacteristic
452C2×C4⋊C4C23×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C4⋊C4C23×C15111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C15111yescharacteristic
463C2×C22⋊C4D4×C15111yescharacteristic
464C2×C42—21no—
465C2×C42C23×C15111yescharacteristic
466C2×C42C23×C15111yescharacteristic
467#107—41no—
468#106—41no—
469C4⋊C8—22no—
470C4⋊C8D4×C15114yescomplemented
471#103—22no—
472#103—22no—
473#103—22no—
474#103—22no—
475#103—41no—
476#103—41no—
477#102—41no—
478#102—41no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481#97—22no—
482C4×C8—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492C24—21no—
493C24C2×D4×C15111yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4#41×C15112yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×D4×C15111yescharacteristic
532C22×C4C2×D4×C15111yescharacteristic
533C22×C4C2×D4×C15111yescharacteristic
534C22×C4C2×D4×C15111yescharacteristic
535C22×C4C2×D4×C15111yescharacteristic
536C22×C4C24×C15111yescharacteristic
537SD16—44no—
538SD16—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8C2×D4×C15112yes—
550C2×C8C2×D4×C15112yes—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—81no—
567C4⋊C4#41×C15112yes—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—81no—
580C42C2×D4×C15112yes—
581C42#41×C15112yes—
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23C22×D4×C15111yescharacteristic
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605D4—22no—
606D4—22no—
607D4—41no—
608D4—41no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4#121×C15112yes—
650C2×C4#121×C15112yes—
651C2×C4C22×D4×C15111yescharacteristic
652C2×C4C2×#41×C15111yescharacteristic
653C2×C4C2×#41×C15111yescharacteristic
654C2×C4C2×#41×C15111yescharacteristic
655C2×C4H(5,𝔽2)×C15111yescharacteristic
656C2×C4H(5,𝔽2)×C15111yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×#121×C15111yescharacteristic
676C22#525×C15111yescharacteristic
677C22#535×C15111yescharacteristic
678C22#577×C15111yescharacteristic
679C22#577×C15111yescharacteristic
680C22#577×C15111yescharacteristic
681C22#578×C15111yescharacteristic
682C4—22no—
683C4—22no—
684C4—42no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4#546×C15111yescharacteristic
695C4#550×C15111yescharacteristic
696C4#553×C15111yescharacteristic
697C4#555×C15111yescharacteristic
698C2—81no—
699C2—82no—
700C2#2414×C15111yescharacteristic
701C2#3057×C15111yescharacteristic
702C2#3063×C15111yescharacteristic
703C2#3120×C15111yescharacteristic
704C2#3123×C15111yescharacteristic
705C2#3221×C15111yescharacteristic
706C2#3225×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#461×C151C2semidirect
2. C2×#433×C151C2semidirect
3. #2621×C151C2semidirect
5. #2036×C151C2semidirect
6. #2035×C151C2semidirect
9. #1981×C151C2semidirect
10. #1973×C151C2semidirect
11. #1968×C151C2semidirect
12. #1949×C151C2semidirect
13. #1935×C151C2semidirect
14. #1933×C151C2semidirect
15. #1804×C151C2semidirect
116. C4⋊C8×C151D4semidirect
353. #24666C151direct (N × H)
354. C151#24666direct (N × H)
355. C2×#461C2×C151semidirect
356. C2×#433C2×C151semidirect
357. #2621C2×C151semidirect
359. #2036C2×C151semidirect
360. #2035C2×C151semidirect
363. #1981C2×C151semidirect
364. #1973C2×C151semidirect
365. #1968C2×C151semidirect
366. #1949C2×C151semidirect
367. #1935C2×C151semidirect
368. #1933C2×C151semidirect
369. #1804C2×C151semidirect
470. C4⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
C2×#433×C1512
#2621×C1512
#2324×C1512
#2036×C1512
#2035×C1512
#2000×C1512
#1981×C1512
#1973×C1512
#1968×C1512
#1949×C1512
#1935×C1512
#1933×C1512
#1804×C1512
#24666151