Finite Group Databasebeta

← C151×#24518 #50329443

Subgroups — C151×#24518 #50329443

Order 38656.

938 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#448×C151C211yesmaximal, characteristic
2C2×#433×C151C211yesmaximal, characteristic, complemented
3#2624×C151C211yesmaximal, characteristic
4#2310×C151C211yesmaximal, characteristic, complemented
5#2068×C151C211yesmaximal, characteristic, complemented
6#2066×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2055×C151C211yesmaximal, characteristic, complemented
9#1973×C151C211yesmaximal, characteristic, complemented
10#1968×C151C211yesmaximal, characteristic, complemented
11#1935×C151C211yesmaximal, characteristic, complemented
12#1933×C151C211yesmaximal, characteristic, complemented
13#1875×C151C211yesmaximal, characteristic
14#1854×C151C211yesmaximal, characteristic, complemented
15#1787×C151C211yesmaximal, characteristic, complemented
16C23×Q8×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#448×C151—24no—
23#433×C151—24no—
24C2×#107×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic
39C2×C4×C8×C151C2211yescharacteristic
40#399×C151—21no—
41#397×C151—21no—
42#394×C151—21no—
43#394×C151—21no—
44#391×C151—21no—
45#391×C151—21no—
46#391×C151C2211yescharacteristic
47#391×C151C2211yescharacteristic
48#391×C151C2211yescharacteristic
49#391×C151C2211yescharacteristic
50#390×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
52#389×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#381×C151—21no—
55#381×C151—21no—
56#380×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C22×Q8×C151—21no—
62C22×Q8×C151—22no—
63C22×Q8×C151—22no—
64C22×Q8×C151—22no—
65C22×Q8×C151—22no—
66C22×Q8×C151—41no—
67C22×Q8×C151—41no—
68C22×Q8×C151C2311yescharacteristic
69C22×Q8×C151C2311yescharacteristic
70C22×D4×C151—21no—
71C22×D4×C151C2311yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151C2311yescharacteristic
74C2×SD16×C151—22no—
75C2×SD16×C151—22no—
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—41no—
79C2×SD16×C151—41no—
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84#121×C151—22no—
85#121×C151—22no—
86#117×C151—22no—
87#117×C151—22no—
88#117×C151—41no—
89#117×C151—41no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
107C2×C22⋊C4×C151D411yescharacteristic
108C2×C42×C151—21no—
109C2×C42×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111#107×C151—41no—
112#106×C151—41no—
113C4⋊C8×C151—22no—
114C4⋊C8×C151—22no—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—41no—
120#103×C151—41no—
121#102×C151—41no—
122#102×C151—41no—
123C22⋊C8×C151—22no—
124C22⋊C8×C151D414yes—
125#97×C151—22no—
126C4×C8×C151—22no—
127#95×C151—21no—
128#95×C151—21no—
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—24no—
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—44no—
152C2×Q8×C151—44no—
153C2×Q8×C151—44no—
154C2×Q8×C151—44no—
155C2×Q8×C151—42no—
156C2×Q8×C151—42no—
157C2×Q8×C151#4112yes—
158C2×Q8×C151#4112yes—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—42no—
166C2×D4×C151—81no—
167C2×D4×C151—81no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—24no—
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—42no—
181C22×C4×C151—42no—
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D412yes—
188C22×C4×C151#4112yes—
189C22×C4×C151C2411yescharacteristic
190SD16×C151—44no—
191SD16×C151—44no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151C2×D412yes—
203C2×C8×C151C2×D412yes—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—22no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—81no—
217C4⋊C4×C151—81no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—81no—
223C22⋊C4×C151—81no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
226C22⋊C4×C151—81no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—42no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151#12112yes—
246C23×C151C22×D411yescharacteristic
247Q8×C151—22no—
248Q8×C151—22no—
249Q8×C151—22no—
250Q8×C151—22no—
251Q8×C151—48no—
252Q8×C151—41no—
253Q8×C151—41no—
254Q8×C151—41no—
255Q8×C151—41no—
256D4×C151—41no—
257D4×C151—41no—
258D4×C151—41no—
259D4×C151—41no—
260D4×C151—84no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—48no—
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—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151#12112yes—
302C2×C4×C151C22×D411yescharacteristic
303C2×C4×C151C2×#4111yescharacteristic
304C2×C4×C151C2×#4111yescharacteristic
305C2×C4×C151C2×#4111yescharacteristic
306C2×C4×C151H(5,𝔽2)11yescharacteristic
307C2×C4×C151H(5,𝔽2)11yescharacteristic
308C8×C151—22no—
309C8×C151—22no—
310C8×C151—41no—
311C8×C151—41no—
312C22×C151—22no—
313C22×C151—22no—
314C22×C151—22no—
315C22×C151—41no—
316C22×C151—41no—
317C22×C151—41no—
318C22×C151—41no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151—81no—
323C22×C151—81no—
324C22×C151—81no—
325C22×C151—81no—
326C22×C151C2×#12111yescharacteristic
327C22×C151#52511yescharacteristic
328C22×C151#53511yescharacteristic
329C22×C151#57711yescharacteristic
330C22×C151#57711yescharacteristic
331C22×C151#57711yescharacteristic
332C22×C151#57811yescharacteristic
333C4×C151—22no—
334C4×C151—42no—
335C4×C151—42no—
336C4×C151—41no—
337C4×C151—41no—
338C4×C151—41no—
339C4×C151—41no—
340C4×C151—81no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151#54611yescharacteristic
346C4×C151#54611yescharacteristic
347C4×C151#55111yescharacteristic
348C4×C151#55111yescharacteristic
349C2×C151—42no—
350C2×C151—161no—
351C2×C151#241111yescharacteristic
352C2×C151#305711yescharacteristic
353C2×C151#306311yescharacteristic
354C2×C151#312111yescharacteristic
355C2×C151#312611yescharacteristic
356C2×C151#322111yescharacteristic
357C2×C151#322511yescharacteristic
358#24518C15111yesmaximal, characteristic, direct product factor, Sylow
359C151#2451811yescharacteristic, direct product factor, Sylow
360C2×#448C2×C15111yescharacteristic
361C2×#433C2×C15111yescharacteristic, complemented
362#2624C2×C15111yescharacteristic
363#2310C2×C15111yescharacteristic, complemented
364#2068C2×C15111yescharacteristic, complemented
365#2066C2×C15111yescharacteristic, complemented
366#2055C2×C15111yescharacteristic, complemented
367#2055C2×C15111yescharacteristic, complemented
368#1973C2×C15111yescharacteristic, complemented
369#1968C2×C15111yescharacteristic, complemented
370#1935C2×C15111yescharacteristic, complemented
371#1933C2×C15111yescharacteristic, complemented
372#1875C2×C15111yescharacteristic
373#1854C2×C15111yescharacteristic, complemented
374#1787C2×C15111yescharacteristic, complemented
375C23×Q8C22×C15111yescharacteristic
376C22×SD16C22×C15111yescharacteristic
377C22×SD16C22×C15111yescharacteristic
378C2×#121C22×C15111yescharacteristic
379C2×#117C22×C15111yescharacteristic
380C2×#117C22×C15111yescharacteristic
381#448—24no—
382#433—24no—
383C2×#107C22×C15111yescharacteristic
384C2×#106C22×C15111yescharacteristic
385C2×C4⋊C8C22×C15111yescharacteristic
386C2×C4⋊C8C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#103C22×C15111yescharacteristic
389C2×#103C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×C22⋊C8C22×C15111yescharacteristic
396C2×C22⋊C8C22×C15111yescharacteristic
397C2×#97C22×C15111yescharacteristic
398C2×C4×C8C22×C15111yescharacteristic
399#399—21no—
400#397—21no—
401#394—21no—
402#394—21no—
403#391—21no—
404#391—21no—
405#391C22×C15111yescharacteristic
406#391C22×C15111yescharacteristic
407#391C22×C15111yescharacteristic
408#391C22×C15111yescharacteristic
409#390C22×C15111yescharacteristic
410#390C22×C15111yescharacteristic
411#389C22×C15111yescharacteristic
412#389C22×C15111yescharacteristic
413#381—21no—
414#381—21no—
415#380C22×C15111yescharacteristic
416#340C22×C15111yescharacteristic
417#340C22×C15111yescharacteristic
418#340C22×C15111yescharacteristic
419#340C22×C15111yescharacteristic
420C22×Q8—22no—
421C22×Q8—22no—
422C22×Q8—21no—
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—41no—
426C22×Q8—41no—
427C22×Q8C23×C15111yescharacteristic
428C22×Q8C23×C15111yescharacteristic
429C22×D4—21no—
430C22×D4C23×C15111yescharacteristic
431C23×C4—21no—
432C23×C4C23×C15111yescharacteristic
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—41no—
438C2×SD16—41no—
439C22×C8C23×C15111yescharacteristic
440C22×C8C23×C15111yescharacteristic
441C22×C8C23×C15111yescharacteristic
442C22×C8C23×C15111yescharacteristic
443#121—22no—
444#121—22no—
445#117—22no—
446#117—22no—
447#117—41no—
448#117—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C15111yescharacteristic
452C2×C4⋊C4D4×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C4⋊C4C23×C15111yescharacteristic
455C2×C4⋊C4C23×C15111yescharacteristic
456C2×C4⋊C4C23×C15111yescharacteristic
457C2×C4⋊C4C23×C15111yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C15111yescharacteristic
466C2×C22⋊C4D4×C15111yescharacteristic
467C2×C42—21no—
468C2×C42C23×C15111yescharacteristic
469C2×C42C23×C15111yescharacteristic
470#107—41no—
471#106—41no—
472C4⋊C8—22no—
473C4⋊C8—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—41no—
479#103—41no—
480#102—41no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8D4×C15114yes—
484#97—22no—
485C4×C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C15111yescharacteristic
499C2×Q8—24no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8#41×C15112yes—
517C2×Q8#41×C15112yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—81no—
526C2×D4—81no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4C2×D4×C15111yescharacteristic
542C22×C4C2×D4×C15111yescharacteristic
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15112yes—
547C22×C4#41×C15112yes—
548C22×C4C24×C15111yescharacteristic
549SD16—44no—
550SD16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8C2×D4×C15112yes—
562C2×C8C2×D4×C15112yes—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—42no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23#121×C15112yes—
605C23C22×D4×C15111yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—48no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4#121×C15112yes—
661C2×C4C22×D4×C15111yescharacteristic
662C2×C4C2×#41×C15111yescharacteristic
663C2×C4C2×#41×C15111yescharacteristic
664C2×C4C2×#41×C15111yescharacteristic
665C2×C4H(5,𝔽2)×C15111yescharacteristic
666C2×C4H(5,𝔽2)×C15111yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#121×C15111yescharacteristic
686C22#525×C15111yescharacteristic
687C22#535×C15111yescharacteristic
688C22#577×C15111yescharacteristic
689C22#577×C15111yescharacteristic
690C22#577×C15111yescharacteristic
691C22#578×C15111yescharacteristic
692C4—22no—
693C4—42no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4#546×C15111yescharacteristic
705C4#546×C15111yescharacteristic
706C4#551×C15111yescharacteristic
707C4#551×C15111yescharacteristic
708C2—42no—
709C2—161no—
710C2#2411×C15111yescharacteristic
711C2#3057×C15111yescharacteristic
712C2#3063×C15111yescharacteristic
713C2#3121×C15111yescharacteristic
714C2#3126×C15111yescharacteristic
715C2#3221×C15111yescharacteristic
716C2#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
2. C2×#433×C151C2semidirect
4. #2310×C151C2semidirect
5. #2068×C151C2semidirect
6. #2066×C151C2semidirect
7. #2055×C151C2semidirect
8. #2055×C151C2semidirect
9. #1973×C151C2semidirect
10. #1968×C151C2semidirect
11. #1935×C151C2semidirect
12. #1933×C151C2semidirect
14. #1854×C151C2semidirect
15. #1787×C151C2semidirect
358. #24518C151direct (N × H)
359. C151#24518direct (N × H)
361. C2×#433C2×C151semidirect
363. #2310C2×C151semidirect
364. #2068C2×C151semidirect
365. #2066C2×C151semidirect
366. #2055C2×C151semidirect
367. #2055C2×C151semidirect
368. #1973C2×C151semidirect
369. #1968C2×C151semidirect
370. #1935C2×C151semidirect
371. #1933C2×C151semidirect
373. #1854C2×C151semidirect
374. #1787C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#448×C1512
C2×#433×C1512
#2624×C1512
#2310×C1512
#2068×C1512
#2066×C1512
#2055×C1512
#1973×C1512
#1968×C1512
#1935×C1512
#1933×C1512
#1875×C1512
#1854×C1512
#1787×C1512
#24518151