Finite Group Databasebeta

← C151×#24512 #50329437

Subgroups — C151×#24512 #50329437

Order 38656.

1098 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×#447×C151C211yesmaximal, characteristic
2C2×#433×C151C211yesmaximal, characteristic, complemented
3#2624×C151C211yesmaximal, characteristic, complemented
4#2309×C151C211yesmaximal, characteristic, complemented
5#2067×C151C211yesmaximal, characteristic, complemented
6#2065×C151C211yesmaximal, characteristic, complemented
7#2054×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#1972×C151C211yesmaximal, characteristic, complemented
10#1970×C151C211yesmaximal, characteristic, complemented
11#1936×C151C211yesmaximal, characteristic, complemented
12#1934×C151C211yesmaximal, characteristic, complemented
13#1875×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#447×C151—24no—
23#433×C151—24no—
24C2×#107×C151C2211yescharacteristic, complemented
25C2×#106×C151C2211yescharacteristic, complemented
26C2×C4⋊C8×C151C2211yescharacteristic, complemented
27C2×C4⋊C8×C151C2211yescharacteristic, complemented
28C2×#102×C151C2211yescharacteristic
29C2×#102×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic, complemented
35C2×#102×C151C2211yescharacteristic, complemented
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic, complemented
39C2×C4×C8×C151C2211yescharacteristic, complemented
40#399×C151—21no—
41#397×C151—21no—
42#394×C151—21no—
43#394×C151—21no—
44#390×C151—21no—
45#390×C151—21no—
46#390×C151C2211yescharacteristic
47#390×C151C2211yescharacteristic
48#390×C151C2211yescharacteristic
49#390×C151C2211yescharacteristic
50#390×C151C2211yescharacteristic, complemented
51#390×C151C2211yescharacteristic, complemented
52#389×C151C2211yescharacteristic, complemented
53#389×C151C2211yescharacteristic, complemented
54#380×C151C2211yescharacteristic
55#379×C151—21no—
56#379×C151—21no—
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61C25×C151—21no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151C2311yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C2×D8×C151—22no—
75C2×D8×C151—22no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—41no—
79C2×D8×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×C151—21no—
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×C151D411yescharacteristic
115C2×C22⋊C4×C151D411yescharacteristic
116C2×C42×C151—21no—
117C2×C42×C151C2311yescharacteristic
118C2×C42×C151C2311yescharacteristic
119#107×C151—41no—
120#106×C151—41no—
121C4⋊C8×C151—22no—
122C4⋊C8×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—41no—
128#102×C151—41no—
129#102×C151—41no—
130#102×C151—41no—
131C22⋊C8×C151—22no—
132C22⋊C8×C151D414yes—
133#97×C151—22no—
134C4×C8×C151—22no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138C24×C151—24no—
139C24×C151—21no—
140C24×C151—21no—
141C24×C151—21no—
142C24×C151—42no—
143C24×C151—42no—
144C24×C151—81no—
145C24×C151—81no—
146C24×C151—81no—
147C24×C151—81no—
148C24×C151C2×D411yescharacteristic
149C2×D4×C151—24no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
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—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—44no—
167C2×D4×C151—44no—
168C2×D4×C151—44no—
169C2×D4×C151—44no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—81no—
174C2×D4×C151—81no—
175C2×D4×C151#4112yes—
176C2×D4×C151#4112yes—
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×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D412yes—
192C22×C4×C151#4112yes—
193C22×C4×C151C2411yescharacteristic
194D8×C151—44no—
195D8×C151—44no—
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×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151C2×D412yes—
207C2×C8×C151C2×D412yes—
208C4⋊C4×C151—22no—
209C4⋊C4×C151—22no—
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—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—81no—
221C4⋊C4×C151—81no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—81no—
227C22⋊C4×C151—81no—
228C22⋊C4×C151—81no—
229C22⋊C4×C151—81no—
230C22⋊C4×C151—81no—
231C22⋊C4×C151—81no—
232C22⋊C4×C151—81no—
233C22⋊C4×C151—81no—
234C22⋊C4×C151—81no—
235C22⋊C4×C151—81no—
236C22⋊C4×C151—81no—
237C22⋊C4×C151—81no—
238C22⋊C4×C151—81no—
239C42×C151—21no—
240C42×C151—21no—
241C42×C151—21no—
242C42×C151—21no—
243C42×C151—42no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—22no—
251C23×C151—22no—
252C23×C151—48no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—41no—
260C23×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—84no—
273C23×C151—84no—
274C23×C151—84no—
275C23×C151—84no—
276C23×C151—84no—
277C23×C151—84no—
278C23×C151#12112yes—
279C23×C151C22×D411yescharacteristic
280D4×C151—22no—
281D4×C151—22no—
282D4×C151—22no—
283D4×C151—22no—
284D4×C151—48no—
285D4×C151—41no—
286D4×C151—41no—
287D4×C151—41no—
288D4×C151—41no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—84no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—22no—
297C2×C4×C151—22no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
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—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—41no—
327C2×C4×C151#12112yes—
328C2×C4×C151C22×D411yescharacteristic
329C2×C4×C151C2×#4111yescharacteristic
330C2×C4×C151C2×#4111yescharacteristic
331C2×C4×C151C2×#4111yescharacteristic
332C2×C4×C151H(5,𝔽2)11yescharacteristic
333C2×C4×C151H(5,𝔽2)11yescharacteristic
334C8×C151—22no—
335C8×C151—22no—
336C8×C151—41no—
337C8×C151—41no—
338C22×C151—22no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—42no—
346C22×C151—42no—
347C22×C151—42no—
348C22×C151—42no—
349C22×C151—42no—
350C22×C151—42no—
351C22×C151—816no—
352C22×C151—81no—
353C22×C151—81no—
354C22×C151—81no—
355C22×C151—81no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151—81no—
359C22×C151—81no—
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×C151#52511yescharacteristic
369C22×C151#53511yescharacteristic
370C22×C151#57611yescharacteristic
371C22×C151#57611yescharacteristic
372C22×C151#57611yescharacteristic
373C22×C151#57711yescharacteristic
374C4×C151—22no—
375C4×C151—41no—
376C4×C151—41no—
377C4×C151—41no—
378C4×C151—41no—
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—82no—
390C2×C151—82no—
391C2×C151—161no—
392C2×C151#241111yescharacteristic
393C2×C151#305811yescharacteristic
394C2×C151#306211yescharacteristic
395C2×C151#311811yescharacteristic
396C2×C151#312211yescharacteristic
397C2×C151#322011yescharacteristic
398C2×C151#322411yescharacteristic
399#24512C15111yesmaximal, characteristic, direct product factor, Sylow
400C151#2451211yescharacteristic, direct product factor, Sylow
401C2×#447C2×C15111yescharacteristic
402C2×#433C2×C15111yescharacteristic, complemented
403#2624C2×C15111yescharacteristic, complemented
404#2309C2×C15111yescharacteristic, complemented
405#2067C2×C15111yescharacteristic, complemented
406#2065C2×C15111yescharacteristic, complemented
407#2054C2×C15111yescharacteristic, complemented
408#2054C2×C15111yescharacteristic, complemented
409#1972C2×C15111yescharacteristic, complemented
410#1970C2×C15111yescharacteristic, complemented
411#1936C2×C15111yescharacteristic, complemented
412#1934C2×C15111yescharacteristic, complemented
413#1875C2×C15111yescharacteristic, complemented
414#1854C2×C15111yescharacteristic, complemented
415#1786C2×C15111yescharacteristic, complemented
416C23×D4C22×C15111yescharacteristic
417C22×D8C22×C15111yescharacteristic
418C22×D8C22×C15111yescharacteristic
419C2×#121C22×C15111yescharacteristic
420C2×#117C22×C15111yescharacteristic
421C2×#117C22×C15111yescharacteristic
422#447—24no—
423#433—24no—
424C2×#107C22×C15111yescharacteristic, complemented
425C2×#106C22×C15111yescharacteristic, complemented
426C2×C4⋊C8C22×C15111yescharacteristic, complemented
427C2×C4⋊C8C22×C15111yescharacteristic, complemented
428C2×#102C22×C15111yescharacteristic
429C2×#102C22×C15111yescharacteristic
430C2×#102C22×C15111yescharacteristic
431C2×#102C22×C15111yescharacteristic
432C2×#102C22×C15111yescharacteristic
433C2×#102C22×C15111yescharacteristic
434C2×#102C22×C15111yescharacteristic, complemented
435C2×#102C22×C15111yescharacteristic, complemented
436C2×C22⋊C8C22×C15111yescharacteristic
437C2×C22⋊C8C22×C15111yescharacteristic
438C2×#97C22×C15111yescharacteristic, complemented
439C2×C4×C8C22×C15111yescharacteristic, complemented
440#399—21no—
441#397—21no—
442#394—21no—
443#394—21no—
444#390—21no—
445#390—21no—
446#390C22×C15111yescharacteristic
447#390C22×C15111yescharacteristic
448#390C22×C15111yescharacteristic
449#390C22×C15111yescharacteristic
450#390C22×C15111yescharacteristic, complemented
451#390C22×C15111yescharacteristic, complemented
452#389C22×C15111yescharacteristic, complemented
453#389C22×C15111yescharacteristic, complemented
454#380C22×C15111yescharacteristic
455#379—21no—
456#379—21no—
457#340C22×C15111yescharacteristic, complemented
458#340C22×C15111yescharacteristic, complemented
459#340C22×C15111yescharacteristic, complemented
460#340C22×C15111yescharacteristic, complemented
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—21no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C23×C15111yescharacteristic
471C22×D4C23×C15111yescharacteristic
472C22×D4C23×C15111yescharacteristic
473C23×C4C23×C15111yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8C23×C15111yescharacteristic
481C22×C8C23×C15111yescharacteristic
482C22×C8C23×C15111yescharacteristic
483C22×C8C23×C15111yescharacteristic
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C15111yescharacteristic
493C2×C4⋊C4D4×C15111yescharacteristic
494C2×C4⋊C4C23×C15111yescharacteristic
495C2×C4⋊C4C23×C15111yescharacteristic
496C2×C4⋊C4C23×C15111yescharacteristic
497C2×C4⋊C4C23×C15111yescharacteristic
498C2×C4⋊C4C23×C15111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
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⋊C4D4×C15111yescharacteristic
515C2×C22⋊C4D4×C15111yescharacteristic
516C2×C42—21no—
517C2×C42C23×C15111yescharacteristic
518C2×C42C23×C15111yescharacteristic
519#107—41no—
520#106—41no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—22no—
532C22⋊C8D4×C15114yes—
533#97—22no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C15111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C15112yes—
576C2×D4#41×C15112yes—
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×C4C2×D4×C15111yescharacteristic
587C22×C4C2×D4×C15111yescharacteristic
588C22×C4C2×D4×C15111yescharacteristic
589C22×C4C2×D4×C15111yescharacteristic
590C22×C4C2×D4×C15111yescharacteristic
591C22×C4C2×D4×C15112yes—
592C22×C4#41×C15112yes—
593C22×C4C24×C15111yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8C2×D4×C15112yes—
607C2×C8C2×D4×C15112yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#121×C15112yes—
679C23C22×D4×C15111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
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—41no—
727C2×C4#121×C15112yes—
728C2×C4C22×D4×C15111yescharacteristic
729C2×C4C2×#41×C15111yescharacteristic
730C2×C4C2×#41×C15111yescharacteristic
731C2×C4C2×#41×C15111yescharacteristic
732C2×C4H(5,𝔽2)×C15111yescharacteristic
733C2×C4H(5,𝔽2)×C15111yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C15111yescharacteristic
768C22#525×C15111yescharacteristic
769C22#535×C15111yescharacteristic
770C22#576×C15111yescharacteristic
771C22#576×C15111yescharacteristic
772C22#576×C15111yescharacteristic
773C22#577×C15111yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
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—82no—
790C2—82no—
791C2—161no—
792C2#2411×C15111yescharacteristic
793C2#3058×C15111yescharacteristic
794C2#3062×C15111yescharacteristic
795C2#3118×C15111yescharacteristic
796C2#3122×C15111yescharacteristic
797C2#3220×C15111yescharacteristic
798C2#3224×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
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
3. #2624×C151C2semidirect
4. #2309×C151C2semidirect
5. #2067×C151C2semidirect
6. #2065×C151C2semidirect
7. #2054×C151C2semidirect
8. #2054×C151C2semidirect
9. #1972×C151C2semidirect
10. #1970×C151C2semidirect
11. #1936×C151C2semidirect
12. #1934×C151C2semidirect
13. #1875×C151C2semidirect
14. #1854×C151C2semidirect
15. #1786×C151C2semidirect
24. C2×#107×C151C22semidirect
25. C2×#106×C151C22semidirect
26. C2×C4⋊C8×C151C22semidirect
27. C2×C4⋊C8×C151C22semidirect
34. C2×#102×C151C22semidirect
35. C2×#102×C151C22semidirect
38. C2×#97×C151C22semidirect
39. C2×C4×C8×C151C22semidirect
50. #390×C151C22semidirect
51. #390×C151C22semidirect
52. #389×C151C22semidirect
53. #389×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
399. #24512C151direct (N × H)
400. C151#24512direct (N × H)
402. C2×#433C2×C151semidirect
403. #2624C2×C151semidirect
404. #2309C2×C151semidirect
405. #2067C2×C151semidirect
406. #2065C2×C151semidirect
407. #2054C2×C151semidirect
408. #2054C2×C151semidirect
409. #1972C2×C151semidirect
410. #1970C2×C151semidirect
411. #1936C2×C151semidirect
412. #1934C2×C151semidirect
413. #1875C2×C151semidirect
414. #1854C2×C151semidirect
415. #1786C2×C151semidirect
424. C2×#107C22×C151semidirect
425. C2×#106C22×C151semidirect
426. C2×C4⋊C8C22×C151semidirect
427. C2×C4⋊C8C22×C151semidirect
434. C2×#102C22×C151semidirect
435. C2×#102C22×C151semidirect
438. C2×#97C22×C151semidirect
439. C2×C4×C8C22×C151semidirect
450. #390C22×C151semidirect
451. #390C22×C151semidirect
452. #389C22×C151semidirect
453. #389C22×C151semidirect
457. #340C22×C151semidirect
458. #340C22×C151semidirect
459. #340C22×C151semidirect
460. #340C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C2×#433×C1512
#2624×C1512
#2309×C1512
#2067×C1512
#2065×C1512
#2054×C1512
#1972×C1512
#1970×C1512
#1936×C1512
#1934×C1512
#1875×C1512
#1854×C1512
#1786×C1512
#24512151