Finite Group Databasebeta

← C151×#24516 #50329441

Subgroups — C151×#24516 #50329441

Order 38656.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C151C211yesmaximal, characteristic
2C2×#433×C151C211yesmaximal, characteristic, complemented
3#2625×C151C211yesmaximal, characteristic, complemented
4#2309×C151C211yesmaximal, characteristic
5#2067×C151C211yesmaximal, characteristic, complemented
6#2065×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2055×C151C211yesmaximal, characteristic, complemented
9#1973×C151C211yesmaximal, characteristic, complemented
10#1968×C151C211yesmaximal, characteristic, complemented
11#1936×C151C211yesmaximal, characteristic, complemented
12#1934×C151C211yesmaximal, characteristic, complemented
13#1873×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic
16C23×D4×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#450×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×#103×C151C2211yescharacteristic, complemented
29C2×#103×C151C2211yescharacteristic, complemented
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic, complemented
39C2×C4×C8×C151C2211yescharacteristic, complemented
40#400×C151—21no—
41#398×C151—21no—
42#397×C151—21no—
43#397×C151—21no—
44#391×C151C2211yescharacteristic, complemented
45#391×C151C2211yescharacteristic, complemented
46#390×C151—21no—
47#390×C151—21no—
48#390×C151C2211yescharacteristic
49#390×C151C2211yescharacteristic
50#390×C151C2211yescharacteristic
51#390×C151C2211yescharacteristic
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×Q8×C151C2311yescharacteristic
63C22×D4×C151—22no—
64C22×D4×C151—22no—
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
72C23×C4×C151C2311yescharacteristic
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—22no—
76C2×SD16×C151—22no—
77C2×SD16×C151—41no—
78C2×SD16×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85#117×C151—22no—
86#117×C151—22no—
87#117×C151—41no—
88#117×C151—41no—
89C2×C4⋊C4×C151—21no—
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×C151D411yescharacteristic
111C2×C22⋊C4×C151D411yescharacteristic
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114C2×C42×C151C2311yescharacteristic
115#107×C151—41no—
116#106×C151—41no—
117C4⋊C8×C151—22no—
118C4⋊C8×C151—22no—
119#103×C151—41no—
120#103×C151—41no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151—41no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151D414yes—
129#97×C151—22no—
130C4×C8×C151—22no—
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—24no—
139C24×C151—21no—
140C24×C151—21no—
141C24×C151—42no—
142C24×C151—42no—
143C24×C151—81no—
144C24×C151—81no—
145C24×C151—81no—
146C24×C151—81no—
147C24×C151C2×D411yescharacteristic
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×D4×C151—24no—
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—44no—
166C2×D4×C151—44no—
167C2×D4×C151—44no—
168C2×D4×C151—44no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151#4112yes—
172C2×D4×C151#4112yes—
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×C151C2×D411yescharacteristic
184C22×C4×C151C2×D411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D412yes—
189C22×C4×C151#4112yes—
190C22×C4×C151C2411yescharacteristic
191SD16×C151—44no—
192SD16×C151—44no—
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×C151—21no—
203C2×C8×C151C2×D412yes—
204C2×C8×C151C2×D412yes—
205C4⋊C4×C151—22no—
206C4⋊C4×C151—22no—
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—21no—
217C4⋊C4×C151—42no—
218C4⋊C4×C151—81no—
219C4⋊C4×C151—81no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
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—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—42no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—22no—
245C23×C151—22no—
246C23×C151—48no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—84no—
260C23×C151—84no—
261C23×C151—84no—
262C23×C151—84no—
263C23×C151—84no—
264C23×C151—84no—
265C23×C151#12112yes—
266C23×C151C22×D411yescharacteristic
267Q8×C151—41no—
268Q8×C151—41no—
269Q8×C151—41no—
270Q8×C151—41no—
271D4×C151—22no—
272D4×C151—22no—
273D4×C151—22no—
274D4×C151—22no—
275D4×C151—48no—
276D4×C151—41no—
277D4×C151—41no—
278D4×C151—41no—
279D4×C151—41no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
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—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
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#12112yes—
317C2×C4×C151C22×D411yescharacteristic
318C2×C4×C151C2×#4111yescharacteristic
319C2×C4×C151C2×#4111yescharacteristic
320C2×C4×C151C2×#4111yescharacteristic
321C2×C4×C151H(5,𝔽2)11yescharacteristic
322C2×C4×C151H(5,𝔽2)11yescharacteristic
323C8×C151—22no—
324C8×C151—22no—
325C8×C151—41no—
326C8×C151—41no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—42no—
335C22×C151—42no—
336C22×C151—42no—
337C22×C151—42no—
338C22×C151—42no—
339C22×C151—42no—
340C22×C151—816no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151—81no—
345C22×C151—81no—
346C22×C151—81no—
347C22×C151—81no—
348C22×C151—81no—
349C22×C151C2×#12111yescharacteristic
350C22×C151#52511yescharacteristic
351C22×C151#53511yescharacteristic
352C22×C151#57611yescharacteristic
353C22×C151#57711yescharacteristic
354C22×C151#57711yescharacteristic
355C22×C151#57711yescharacteristic
356C4×C151—22no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—81no—
362C4×C151—81no—
363C4×C151—81no—
364C4×C151—81no—
365C4×C151—81no—
366C4×C151—81no—
367C4×C151#54611yescharacteristic
368C4×C151#54611yescharacteristic
369C4×C151#55111yescharacteristic
370C4×C151#55111yescharacteristic
371C2×C151—42no—
372C2×C151—82no—
373C2×C151—82no—
374C2×C151#241111yescharacteristic
375C2×C151#305711yescharacteristic
376C2×C151#306211yescharacteristic
377C2×C151#311811yescharacteristic
378C2×C151#312311yescharacteristic
379C2×C151#322211yescharacteristic
380C2×C151#322411yescharacteristic
381#24516C15111yesmaximal, characteristic, direct product factor, Sylow
382C151#2451611yescharacteristic, direct product factor, Sylow
383C2×#450C2×C15111yescharacteristic
384C2×#433C2×C15111yescharacteristic, complemented
385#2625C2×C15111yescharacteristic, complemented
386#2309C2×C15111yescharacteristic
387#2067C2×C15111yescharacteristic, complemented
388#2065C2×C15111yescharacteristic, complemented
389#2055C2×C15111yescharacteristic, complemented
390#2055C2×C15111yescharacteristic, complemented
391#1973C2×C15111yescharacteristic, complemented
392#1968C2×C15111yescharacteristic, complemented
393#1936C2×C15111yescharacteristic, complemented
394#1934C2×C15111yescharacteristic, complemented
395#1873C2×C15111yescharacteristic, complemented
396#1854C2×C15111yescharacteristic, complemented
397#1786C2×C15111yescharacteristic
398C23×D4C22×C15111yescharacteristic
399C22×SD16C22×C15111yescharacteristic
400C22×SD16C22×C15111yescharacteristic
401C2×C22⋊Q8C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403C2×#117C22×C15111yescharacteristic
404#450—24no—
405#433—24no—
406C2×#107C22×C15111yescharacteristic, complemented
407C2×#106C22×C15111yescharacteristic, complemented
408C2×C4⋊C8C22×C15111yescharacteristic, complemented
409C2×C4⋊C8C22×C15111yescharacteristic, complemented
410C2×#103C22×C15111yescharacteristic, complemented
411C2×#103C22×C15111yescharacteristic, complemented
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×#102C22×C15111yescharacteristic
418C2×C22⋊C8C22×C15111yescharacteristic
419C2×C22⋊C8C22×C15111yescharacteristic
420C2×#97C22×C15111yescharacteristic, complemented
421C2×C4×C8C22×C15111yescharacteristic, complemented
422#400—21no—
423#398—21no—
424#397—21no—
425#397—21no—
426#391C22×C15111yescharacteristic, complemented
427#391C22×C15111yescharacteristic, complemented
428#390—21no—
429#390—21no—
430#390C22×C15111yescharacteristic
431#390C22×C15111yescharacteristic
432#390C22×C15111yescharacteristic
433#390C22×C15111yescharacteristic
434#389C22×C15111yescharacteristic, complemented
435#389C22×C15111yescharacteristic, complemented
436#380C22×C15111yescharacteristic
437#379—21no—
438#379—21no—
439#340C22×C15111yescharacteristic, complemented
440#340C22×C15111yescharacteristic, complemented
441#340C22×C15111yescharacteristic, complemented
442#340C22×C15111yescharacteristic, complemented
443C25—21no—
444C22×Q8C23×C15111yescharacteristic
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4—41no—
451C22×D4—41no—
452C22×D4C23×C15111yescharacteristic
453C22×D4C23×C15111yescharacteristic
454C23×C4C23×C15111yescharacteristic
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—22no—
459C2×SD16—41no—
460C2×SD16—41no—
461C22×C8C23×C15111yescharacteristic
462C22×C8C23×C15111yescharacteristic
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467#117—22no—
468#117—22no—
469#117—41no—
470#117—41no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4D4×C15111yescharacteristic
475C2×C4⋊C4D4×C15111yescharacteristic
476C2×C4⋊C4C23×C15111yescharacteristic
477C2×C4⋊C4C23×C15111yescharacteristic
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C4⋊C4C23×C15111yescharacteristic
480C2×C4⋊C4C23×C15111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C15111yescharacteristic
493C2×C22⋊C4D4×C15111yescharacteristic
494C2×C42—21no—
495C2×C42C23×C15111yescharacteristic
496C2×C42C23×C15111yescharacteristic
497#107—41no—
498#106—41no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501#103—41no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—41no—
508#102—41no—
509C22⋊C8—22no—
510C22⋊C8D4×C15114yes—
511#97—22no—
512C4×C8—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C24—24no—
521C24—21no—
522C24—21no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24C2×D4×C15111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4#41×C15112yes—
554C2×D4#41×C15112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4C2×D4×C15111yescharacteristic
566C22×C4C2×D4×C15111yescharacteristic
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15112yes—
571C22×C4#41×C15112yes—
572C22×C4C24×C15111yescharacteristic
573SD16—44no—
574SD16—44no—
575C2×C8—21no—
576C2×C8—21no—
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×C8C2×D4×C15112yes—
586C2×C8C2×D4×C15112yes—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23#121×C15112yes—
648C23C22×D4×C15111yescharacteristic
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4#121×C15112yes—
699C2×C4C22×D4×C15111yescharacteristic
700C2×C4C2×#41×C15111yescharacteristic
701C2×C4C2×#41×C15111yescharacteristic
702C2×C4C2×#41×C15111yescharacteristic
703C2×C4H(5,𝔽2)×C15111yescharacteristic
704C2×C4H(5,𝔽2)×C15111yescharacteristic
705C8—22no—
706C8—22no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—816no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#121×C15111yescharacteristic
732C22#525×C15111yescharacteristic
733C22#535×C15111yescharacteristic
734C22#576×C15111yescharacteristic
735C22#577×C15111yescharacteristic
736C22#577×C15111yescharacteristic
737C22#577×C15111yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4#546×C15111yescharacteristic
750C4#546×C15111yescharacteristic
751C4#551×C15111yescharacteristic
752C4#551×C15111yescharacteristic
753C2—42no—
754C2—82no—
755C2—82no—
756C2#2411×C15111yescharacteristic
757C2#3057×C15111yescharacteristic
758C2#3062×C15111yescharacteristic
759C2#3118×C15111yescharacteristic
760C2#3123×C15111yescharacteristic
761C2#3222×C15111yescharacteristic
762C2#3224×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC23×D4×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
3. #2625×C151C2semidirect
5. #2067×C151C2semidirect
6. #2065×C151C2semidirect
7. #2055×C151C2semidirect
8. #2055×C151C2semidirect
9. #1973×C151C2semidirect
10. #1968×C151C2semidirect
11. #1936×C151C2semidirect
12. #1934×C151C2semidirect
13. #1873×C151C2semidirect
14. #1854×C151C2semidirect
24. C2×#107×C151C22semidirect
25. C2×#106×C151C22semidirect
26. C2×C4⋊C8×C151C22semidirect
27. C2×C4⋊C8×C151C22semidirect
28. C2×#103×C151C22semidirect
29. C2×#103×C151C22semidirect
38. C2×#97×C151C22semidirect
39. C2×C4×C8×C151C22semidirect
44. #391×C151C22semidirect
45. #391×C151C22semidirect
52. #389×C151C22semidirect
53. #389×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
381. #24516C151direct (N × H)
382. C151#24516direct (N × H)
384. C2×#433C2×C151semidirect
385. #2625C2×C151semidirect
387. #2067C2×C151semidirect
388. #2065C2×C151semidirect
389. #2055C2×C151semidirect
390. #2055C2×C151semidirect
391. #1973C2×C151semidirect
392. #1968C2×C151semidirect
393. #1936C2×C151semidirect
394. #1934C2×C151semidirect
395. #1873C2×C151semidirect
396. #1854C2×C151semidirect
406. C2×#107C22×C151semidirect
407. C2×#106C22×C151semidirect
408. C2×C4⋊C8C22×C151semidirect
409. C2×C4⋊C8C22×C151semidirect
410. C2×#103C22×C151semidirect
411. C2×#103C22×C151semidirect
420. C2×#97C22×C151semidirect
421. C2×C4×C8C22×C151semidirect
426. #391C22×C151semidirect
427. #391C22×C151semidirect
434. #389C22×C151semidirect
435. #389C22×C151semidirect
439. #340C22×C151semidirect
440. #340C22×C151semidirect
441. #340C22×C151semidirect
442. #340C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1512
C2×#433×C1512
#2625×C1512
#2309×C1512
#2067×C1512
#2065×C1512
#2055×C1512
#1973×C1512
#1968×C1512
#1936×C1512
#1934×C1512
#1873×C1512
#1854×C1512
#1786×C1512
#24516151