Finite Group Databasebeta

← C151×#24562 #50329487

Subgroups — C151×#24562 #50329487

Order 38656.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C151C211yesmaximal, characteristic, complemented
2C2×#408×C151C211yesmaximal, characteristic, complemented
3#2615×C151C211yesmaximal, characteristic
4#2311×C151C211yesmaximal, characteristic, complemented
5#2076×C151C211yesmaximal, characteristic, complemented
6#2075×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1893×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1854×C151C211yesmaximal, characteristic, complemented
13#1824×C151C211yesmaximal, characteristic, complemented
14#1809×C151C211yesmaximal, characteristic, complemented
15#1808×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24#480×C151—24no—
25C2×#107×C151C2211yescharacteristic
26C2×#107×C151C2211yescharacteristic
27C2×#107×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29C2×#102×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33#408×C151—24no—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38#393×C151—21no—
39#392×C151—21no—
40#392×C151—21no—
41#392×C151—21no—
42#391×C151—21no—
43#390×C151—21no—
44#386×C151—21no—
45#386×C151—21no—
46#380×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48#380×C151C2211yescharacteristic
49#380×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151D411yescharacteristic
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—21no—
71C22×D4×C151D411yescharacteristic
72C22×D4×C151D411yescharacteristic
73C22×D4×C151D411yescharacteristic
74C22×D4×C151C2311yescharacteristic
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C23×C4×C151C2311yescharacteristic
79C2×M16×C151—22no—
80C2×M16×C151—22no—
81C2×M16×C151—41no—
82C22×C8×C151—22no—
83C22×C8×C151—22no—
84C22×C8×C151—41no—
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89#121×C151—22no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—41no—
94#121×C151—41no—
95#117×C151—41no—
96#117×C151—41no—
97C2×C4⋊C4×C151—22no—
98C2×C4⋊C4×C151—22no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C42×C151—21no—
119#107×C151—22no—
120#107×C151—22no—
121#107×C151—41no—
122#106×C151—41no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151—41no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151D414yescomplemented
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
140C24×C151C2×D411yescharacteristic
141C24×C151C2×D411yescharacteristic
142#41×C151—44no—
143#41×C151—44no—
144#41×C151—44no—
145#41×C151—44no—
146C2×Q8×C151—22no—
147C2×Q8×C151—22no—
148C2×Q8×C151—41no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—41no—
162C2×D4×C151—41no—
163C2×D4×C151—41no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—81no—
168C2×D4×C151—81no—
169C2×D4×C151—81no—
170C2×D4×C151—81no—
171C2×D4×C151—81no—
172C2×D4×C151—81no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—42no—
195C22×C4×C151—81no—
196C22×C4×C151—81no—
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D412yes—
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151#4112yes—
202C22×C4×C151#4112yes—
203C22×C4×C151#4112yes—
204C22×C4×C151C2411yescharacteristic
205M16×C151—44no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—44no—
217C2×C8×C151C2×D412yes—
218C2×C8×C151C2×D412yes—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—81no—
239C22⋊C4×C151—81no—
240C22⋊C4×C151—81no—
241C22⋊C4×C151—81no—
242C22⋊C4×C151—81no—
243C22⋊C4×C151—81no—
244C22⋊C4×C151—81no—
245C42×C151—42no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151#12112yes—
273C23×C151#12312yes—
274C23×C151C22×D411yescharacteristic
275Q8×C151—44no—
276D4×C151—44no—
277D4×C151—44no—
278D4×C151—44no—
279D4×C151—41no—
280D4×C151—41no—
281D4×C151—41no—
282D4×C151—41no—
283D4×C151—84no—
284D4×C151—84no—
285D4×C151—84no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—22no—
293C2×C4×C151—22no—
294C2×C4×C151—22no—
295C2×C4×C151—22no—
296C2×C4×C151—22no—
297C2×C4×C151—22no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—84no—
327C2×C4×C151#12112yes—
328C2×C4×C151#12312yes—
329C2×C4×C151C22×D411yescharacteristic
330C2×C4×C151C2×#4111yescharacteristic
331C2×C4×C151C2×#4111yescharacteristic
332C2×C4×C151C2×#4111yescharacteristic
333C2×C4×C151H(5,𝔽2)11yescharacteristic
334C2×C4×C151H(5,𝔽2)11yescharacteristic
335C8×C151—22no—
336C8×C151—22no—
337C8×C151—41no—
338C8×C151—41no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—22no—
342C22×C151—22no—
343C22×C151—22no—
344C22×C151—22no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—41no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—41no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—81no—
361C22×C151—81no—
362C22×C151—81no—
363C22×C151—81no—
364C22×C151—81no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151C2×#12111yescharacteristic
368C22×C151C2×#12311yescharacteristic
369C22×C151#53411yescharacteristic
370C22×C151#57611yescharacteristic
371C22×C151#57611yescharacteristic
372C22×C151#57711yescharacteristic
373C22×C151#57811yescharacteristic
374C4×C151—22no—
375C4×C151—22no—
376C4×C151—41no—
377C4×C151—81no—
378C4×C151—81no—
379C4×C151—81no—
380C4×C151—81no—
381C4×C151—81no—
382C4×C151—81no—
383C4×C151—81no—
384C4×C151#54611yescharacteristic
385C4×C151#54611yescharacteristic
386C4×C151#55111yescharacteristic
387C4×C151#55111yescharacteristic
388C2×C151—42no—
389C2×C151—42no—
390C2×C151—81no—
391C2×C151—161no—
392C2×C151#241211yescharacteristic
393C2×C151#305811yescharacteristic
394C2×C151#306311yescharacteristic
395C2×C151#309611yescharacteristic
396C2×C151#309811yescharacteristic
397C2×C151#319811yescharacteristic
398C2×C151#320311yescharacteristic
399#24562C15111yesmaximal, characteristic, direct product factor, Sylow
400C151#2456211yescharacteristic, direct product factor, Sylow
401C2×#480C2×C15111yescharacteristic, complemented
402C2×#408C2×C15111yescharacteristic, complemented
403#2615C2×C15111yescharacteristic
404#2311C2×C15111yescharacteristic, complemented
405#2076C2×C15111yescharacteristic, complemented
406#2075C2×C15111yescharacteristic, complemented
407#2034C2×C15111yescharacteristic, complemented
408#2033C2×C15111yescharacteristic, complemented
409#1895C2×C15111yescharacteristic, complemented
410#1893C2×C15111yescharacteristic, complemented
411#1875C2×C15111yescharacteristic, complemented
412#1854C2×C15111yescharacteristic, complemented
413#1824C2×C15111yescharacteristic, complemented
414#1809C2×C15111yescharacteristic, complemented
415#1808C2×C15111yescharacteristic, complemented
416C22×#41C22×C15111yescharacteristic
417C22×M16C22×C15111yescharacteristic
418C23×C8C22×C15111yescharacteristic
419C2×#121C22×C15111yescharacteristic
420C2×#121C22×C15111yescharacteristic
421C2×#121C22×C15111yescharacteristic
422C2×#117C22×C15111yescharacteristic
423C22×C4⋊C4C22×C15111yescharacteristic
424#480—24no—
425C2×#107C22×C15111yescharacteristic
426C2×#107C22×C15111yescharacteristic
427C2×#107C22×C15111yescharacteristic
428C2×#106C22×C15111yescharacteristic
429C2×#102C22×C15111yescharacteristic
430C2×#102C22×C15111yescharacteristic
431C2×#102C22×C15111yescharacteristic
432C2×#102C22×C15111yescharacteristic
433#408—24no—
434C2×C22⋊C8C22×C15111yescharacteristic
435C2×C22⋊C8C22×C15111yescharacteristic
436C2×C22⋊C8C22×C15111yescharacteristic
437C2×C22⋊C8C22×C15111yescharacteristic
438#393—21no—
439#392—21no—
440#392—21no—
441#392—21no—
442#391—21no—
443#390—21no—
444#386—21no—
445#386—21no—
446#380C22×C15111yescharacteristic
447#380C22×C15111yescharacteristic
448#380C22×C15111yescharacteristic
449#380C22×C15111yescharacteristic
450#380C22×C15111yescharacteristic
451#380C22×C15111yescharacteristic
452#380C22×C15111yescharacteristic
453#340C22×C15111yescharacteristic
454#340C22×C15111yescharacteristic
455#340C22×C15111yescharacteristic
456#340C22×C15111yescharacteristic
457#340C22×C15111yescharacteristic
458#340C22×C15111yescharacteristic
459#340C22×C15111yescharacteristic
460#340C22×C15111yescharacteristic
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8D4×C15111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C15111yescharacteristic
472C22×D4D4×C15111yescharacteristic
473C22×D4D4×C15111yescharacteristic
474C22×D4C23×C15111yescharacteristic
475C23×C4—21no—
476C23×C4C23×C15111yescharacteristic
477C23×C4C23×C15111yescharacteristic
478C23×C4C23×C15111yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C15111yescharacteristic
486C22×C8C23×C15111yescharacteristic
487C22×C8C23×C15111yescharacteristic
488C22×C8C23×C15111yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#117—41no—
496#117—41no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4C23×C15111yescharacteristic
501C2×C4⋊C4C23×C15111yescharacteristic
502C2×C4⋊C4C23×C15111yescharacteristic
503C2×C4⋊C4C23×C15111yescharacteristic
504C2×C4⋊C4C23×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#107—22no—
520#107—22no—
521#107—41no—
522#106—41no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8D4×C15114yescomplemented
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×D4×C15111yescharacteristic
540C24C2×D4×C15111yescharacteristic
541C24C2×D4×C15111yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C15111yescharacteristic
598C22×C4C2×D4×C15111yescharacteristic
599C22×C4C2×D4×C15112yes—
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4#41×C15112yes—
602C22×C4#41×C15112yes—
603C22×C4#41×C15112yes—
604C22×C4C24×C15111yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C15112yes—
618C2×C8C2×D4×C15112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23#121×C15112yes—
673C23#123×C15112yes—
674C23C22×D4×C15111yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—84no—
727C2×C4#121×C15112yes—
728C2×C4#123×C15112yes—
729C2×C4C22×D4×C15111yescharacteristic
730C2×C4C2×#41×C15111yescharacteristic
731C2×C4C2×#41×C15111yescharacteristic
732C2×C4C2×#41×C15111yescharacteristic
733C2×C4H(5,𝔽2)×C15111yescharacteristic
734C2×C4H(5,𝔽2)×C15111yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C15111yescharacteristic
768C22C2×#123×C15111yescharacteristic
769C22#534×C15111yescharacteristic
770C22#576×C15111yescharacteristic
771C22#576×C15111yescharacteristic
772C22#577×C15111yescharacteristic
773C22#578×C15111yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#546×C15111yescharacteristic
785C4#546×C15111yescharacteristic
786C4#551×C15111yescharacteristic
787C4#551×C15111yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2#2412×C15111yescharacteristic
793C2#3058×C15111yescharacteristic
794C2#3063×C15111yescharacteristic
795C2#3096×C15111yescharacteristic
796C2#3098×C15111yescharacteristic
797C2#3198×C15111yescharacteristic
798C2#3203×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2615×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#480×C151C2semidirect
2. C2×#408×C151C2semidirect
4. #2311×C151C2semidirect
5. #2076×C151C2semidirect
6. #2075×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1895×C151C2semidirect
10. #1893×C151C2semidirect
11. #1875×C151C2semidirect
12. #1854×C151C2semidirect
13. #1824×C151C2semidirect
14. #1809×C151C2semidirect
15. #1808×C151C2semidirect
130. C22⋊C8×C151D4semidirect
399. #24562C151direct (N × H)
400. C151#24562direct (N × H)
401. C2×#480C2×C151semidirect
402. C2×#408C2×C151semidirect
404. #2311C2×C151semidirect
405. #2076C2×C151semidirect
406. #2075C2×C151semidirect
407. #2034C2×C151semidirect
408. #2033C2×C151semidirect
409. #1895C2×C151semidirect
410. #1893C2×C151semidirect
411. #1875C2×C151semidirect
412. #1854C2×C151semidirect
413. #1824C2×C151semidirect
414. #1809C2×C151semidirect
415. #1808C2×C151semidirect
530. C22⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1512
C2×#408×C1512
#2615×C1512
#2311×C1512
#2076×C1512
#2075×C1512
#2034×C1512
#2033×C1512
#1895×C1512
#1893×C1512
#1875×C1512
#1854×C1512
#1824×C1512
#1809×C1512
#1808×C1512
#24562151