Finite Group Databasebeta

← C151×#22588 #50327513

Subgroups — C151×#22588 #50327513

Order 38656.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2924×C151C211yesmaximal, characteristic, complemented
2#2896×C151C211yesmaximal, characteristic
3#2880×C151C211yesmaximal, characteristic
4#1938×C151C211yesmaximal, characteristic, complemented
5#1937×C151C211yesmaximal, characteristic, complemented
6#1929×C151C211yesmaximal, characteristic, complemented
7#1929×C151C211yesmaximal, characteristic, complemented
8#1866×C151C211yesmaximal, characteristic, complemented
9#1866×C151C211yesmaximal, characteristic, complemented
10#1826×C151C211yesmaximal, characteristic, complemented
11#1811×C151C211yesmaximal, characteristic, complemented
12#1789×C151C211yesmaximal, characteristic
13#1765×C151C211yesmaximal, characteristic, complemented
14#1764×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C2×#131×C151C2211yescharacteristic
18C2×#131×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21#433×C151—21no—
22#433×C151—21no—
23#432×C151—21no—
24#431×C151—21no—
25C2×#108×C151C2211yescharacteristic, complemented
26C2×#108×C151C2211yescharacteristic, complemented
27#424×C151C2211yescharacteristic, complemented
28#424×C151C2211yescharacteristic, complemented
29C2×#104×C151C2211yescharacteristic
30C2×#104×C151C2211yescharacteristic
31C2×#104×C151C2211yescharacteristic
32C2×#104×C151C2211yescharacteristic
33#419×C151C411yescharacteristic, complemented
34#419×C151C411yescharacteristic, complemented
35#418×C151C411yescharacteristic, complemented
36#418×C151C411yescharacteristic, complemented
37#417×C151C411yescharacteristic, complemented
38#417×C151C411yescharacteristic, complemented
39#417×C151C411yescharacteristic, complemented
40#417×C151C411yescharacteristic, complemented
41#416×C151C2211yescharacteristic
42#416×C151C2211yescharacteristic
43#416×C151C2211yescharacteristic
44#416×C151C2211yescharacteristic
45#408×C151—21no—
46#408×C151—21no—
47#408×C151C2211yescharacteristic
48#408×C151C2211yescharacteristic
49#407×C151—21no—
50#407×C151C2211yescharacteristic
51#407×C151C2211yescharacteristic
52C2×C22⋊C8×C151—21no—
53C2×C22⋊C8×C151C2211yescharacteristic
54#405×C151C2211yescharacteristic, complemented
55#405×C151C2211yescharacteristic, complemented
56C2×#97×C151C2211yescharacteristic, complemented
57C2×C4×C8×C151C2211yescharacteristic, complemented
58C4×C22⋊C4×C151C2211yescharacteristic
59#341×C151C2211yescharacteristic, complemented
60#341×C151C2211yescharacteristic, complemented
61#339×C151C2211yescharacteristic, complemented
62#339×C151C2211yescharacteristic, complemented
63#339×C151C2211yescharacteristic, complemented
64#339×C151C2211yescharacteristic, complemented
65#336×C151C2211yescharacteristic, complemented
66#336×C151C2211yescharacteristic, complemented
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—21no—
70C2×#41×C151—21no—
71C2×#41×C151—41no—
72C2×#41×C151—41no—
73C2×#41×C151C2×C411yescharacteristic
74C2×#41×C151C2×C411yescharacteristic
75C2×#41×C151C2311yescharacteristic
76C2×#41×C151C2311yescharacteristic
77C22×Q8×C151C2×C411yescharacteristic
78C22×D4×C151—21no—
79C22×D4×C151C2×C411yescharacteristic
80C23×C4×C151—21no—
81C23×C4×C151C2311yescharacteristic
82#131×C151—22no—
83#131×C151—22no—
84#131×C151—41no—
85#131×C151—41no—
86C2×M16×C151—21no—
87C2×M16×C151—21no—
88C2×M16×C151—41no—
89C2×M16×C151—41no—
90C2×M16×C151C2×C411yescharacteristic
91C2×M16×C151C2×C411yescharacteristic
92C2×M16×C151C2×C411yescharacteristic
93C2×M16×C151C2×C411yescharacteristic
94C2×M16×C151C2311yescharacteristic
95C2×M16×C151C2311yescharacteristic
96C2×M16×C151C2311yescharacteristic
97C2×M16×C151C2311yescharacteristic
98C22×C8×C151—21no—
99C22×C8×C151—21no—
100C22×C8×C151C2311yescharacteristic
101C22×C8×C151C2311yescharacteristic
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104#117×C151—21no—
105#117×C151—21no—
106#117×C151C2×C411yescharacteristic
107#117×C151C2×C411yescharacteristic
108#117×C151C2311yescharacteristic
109#117×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2×C411yescharacteristic
111C2×C4⋊C4×C151C2×C411yescharacteristic
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C42×C151—21no—
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117#108×C151—41no—
118#108×C151—41no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151—21no—
123#104×C151—22no—
124#104×C151—22no—
125#104×C151—41no—
126#104×C151—41no—
127#103×C151C2×C411yescharacteristic
128#103×C151C2×C411yescharacteristic
129#103×C151C2×C411yescharacteristic
130#103×C151C2×C411yescharacteristic
131#103×C151C2×C411yescharacteristic
132#103×C151C2×C411yescharacteristic
133#103×C151C2×C411yescharacteristic
134#103×C151C2×C411yescharacteristic
135#102×C151C2×C411yescharacteristic
136#102×C151C2×C411yescharacteristic
137#102×C151C2×C411yescharacteristic
138#102×C151C2×C411yescharacteristic
139#102×C151C2×C411yescharacteristic
140#102×C151C2×C411yescharacteristic
141#102×C151C2×C411yescharacteristic
142#102×C151C2×C411yescharacteristic
143C22⋊C8×C151—21no—
144C22⋊C8×C151—21no—
145C22⋊C8×C151—21no—
146C22⋊C8×C151—21no—
147C22⋊C8×C151—21no—
148C22⋊C8×C151—21no—
149C22⋊C8×C151—21no—
150C22⋊C8×C151—21no—
151C22⋊C8×C151D411yescharacteristic
152C22⋊C8×C151D411yescharacteristic
153C22⋊C8×C151D411yescharacteristic
154C22⋊C8×C151D411yescharacteristic
155#97×C151—21no—
156#97×C151—21no—
157#97×C151—41no—
158C4×C8×C151—21no—
159C4×C8×C151—21no—
160C4×C8×C151—41no—
161#95×C151—21no—
162C24×C151—21no—
163C24×C151#4111yescharacteristic
164#41×C151—21no—
165#41×C151—21no—
166#41×C151—22no—
167#41×C151—22no—
168#41×C151—21no—
169#41×C151—21no—
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—42no—
173#41×C151—42no—
174#41×C151—41no—
175#41×C151—41no—
176#41×C151—42no—
177#41×C151—42no—
178#41×C151#4112yes—
179#41×C151#4112yes—
180C2×Q8×C151—21no—
181C2×Q8×C151—22no—
182C2×Q8×C151—41no—
183C2×Q8×C151C22×C411yescharacteristic
184C2×Q8×C151C22×C411yescharacteristic
185C2×D4×C151—21no—
186C2×D4×C151—22no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—41no—
192C2×D4×C151—42no—
193C2×D4×C151—42no—
194C2×D4×C151C22×C411yescharacteristic
195C2×D4×C151C22×C411yescharacteristic
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—42no—
210C22×C4×C151—42no—
211C22×C4×C151C22×C411yescharacteristic
212C22×C4×C151C22×C411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151#4111yescharacteristic
216C22×C4×C151C2411yescharacteristic
217M16×C151—21no—
218M16×C151—21no—
219M16×C151—21no—
220M16×C151—21no—
221M16×C151—21no—
222M16×C151—21no—
223M16×C151—21no—
224M16×C151—21no—
225M16×C151—41no—
226M16×C151—41no—
227M16×C151—41no—
228M16×C151—41no—
229M16×C151—42no—
230M16×C151—42no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—42no—
244C2×C8×C151—42no—
245C2×C8×C151C22×C411yescharacteristic
246C2×C8×C151C22×C411yescharacteristic
247C2×C8×C151C22×C411yescharacteristic
248C2×C8×C151C22×C411yescharacteristic
249C2×C8×C151C2×D411yescharacteristic
250C2×C8×C151C2×D411yescharacteristic
251C2×C8×C151C2×D411yescharacteristic
252C2×C8×C151C2×D411yescharacteristic
253C4⋊C4×C151—21no—
254C4⋊C4×C151—21no—
255C4⋊C4×C151C22×C411yescharacteristic
256C4⋊C4×C151C22×C411yescharacteristic
257C4⋊C4×C151C22×C411yescharacteristic
258C4⋊C4×C151C22×C411yescharacteristic
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—42no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151—21no—
267C42×C151—21no—
268C42×C151—21no—
269C42×C151—21no—
270C42×C151—21no—
271C42×C151—21no—
272C23×C151—21no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—41no—
277C23×C151—41no—
278C23×C151—42no—
279C23×C151—42no—
280C23×C151—81no—
281C23×C151C4×D411yescharacteristic
282C23×C151C4×D411yescharacteristic
283C23×C151C2×#4111yescharacteristic
284Q8×C151—21no—
285Q8×C151—21no—
286Q8×C151—21no—
287Q8×C151—42no—
288Q8×C151#11712yes—
289D4×C151—22no—
290D4×C151—22no—
291D4×C151—21no—
292D4×C151—21no—
293D4×C151—21no—
294D4×C151—42no—
295D4×C151—42no—
296D4×C151—42no—
297D4×C151—41no—
298D4×C151—41no—
299D4×C151#11712yes—
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—22no—
308C2×C4×C151—22no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—22no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—41no—
323C2×C4×C151—42no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—81no—
331C2×C4×C151C4×D411yescharacteristic
332C2×C4×C151C4×D411yescharacteristic
333C2×C4×C151C23×C411yescharacteristic
334C2×C4×C151C22×D411yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151C2×#4111yescharacteristic
337C2×C4×C151H(5,𝔽2)11yescharacteristic
338C2×C4×C151H(5,𝔽2)11yescharacteristic
339C8×C151—21no—
340C8×C151—21no—
341C8×C151—21no—
342C8×C151—21no—
343C8×C151—21no—
344C8×C151—21no—
345C8×C151—21no—
346C8×C151—21no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C8×C151—41no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—21no—
355C22×C151—22no—
356C22×C151—21no—
357C22×C151—21no—
358C22×C151—21no—
359C22×C151—21no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151—84no—
368C22×C151C2×C4×D411yescharacteristic
369C22×C151#55111yescharacteristic
370C22×C151#55111yescharacteristic
371C4×C151—21no—
372C4×C151—21no—
373C4×C151—22no—
374C4×C151—42no—
375C4×C151—41no—
376C4×C151—41no—
377C4×C151—41no—
378C4×C151—41no—
379C4×C151—41no—
380C4×C151—81no—
381C4×C151C2×#11711yescharacteristic
382C4×C151#51811yescharacteristic
383C4×C151#54611yescharacteristic
384C4×C151#54611yescharacteristic
385C2×C151—21no—
386C2×C151—21no—
387C2×C151—41no—
388C2×C151—41no—
389C2×C151—42no—
390C2×C151—81no—
391C2×C151#234211yescharacteristic
392C2×C151#295511yescharacteristic
393C2×C151#295611yescharacteristic
394#22588C15111yesmaximal, characteristic, direct product factor, Sylow
395C151#2258811yescharacteristic, direct product factor, Sylow
396#2924C2×C15111yescharacteristic, complemented
397#2896C2×C15111yescharacteristic
398#2880C2×C15111yescharacteristic
399#1938C2×C15111yescharacteristic, complemented
400#1937C2×C15111yescharacteristic, complemented
401#1929C2×C15111yescharacteristic, complemented
402#1929C2×C15111yescharacteristic, complemented
403#1866C2×C15111yescharacteristic, complemented
404#1866C2×C15111yescharacteristic, complemented
405#1826C2×C15111yescharacteristic, complemented
406#1811C2×C15111yescharacteristic, complemented
407#1789C2×C15111yescharacteristic
408#1765C2×C15111yescharacteristic, complemented
409#1764C2×C15111yescharacteristic, complemented
410#1753C2×C15111yescharacteristic, complemented
411C22×#41C22×C15111yescharacteristic
412C2×#131C22×C15111yescharacteristic
413C2×#131C22×C15111yescharacteristic
414C22×M16C22×C15111yescharacteristic
415C2×#117C22×C15111yescharacteristic
416#433—21no—
417#433—21no—
418#432—21no—
419#431—21no—
420C2×#108C22×C15111yescharacteristic, complemented
421C2×#108C22×C15111yescharacteristic, complemented
422#424C22×C15111yescharacteristic, complemented
423#424C22×C15111yescharacteristic, complemented
424C2×#104C22×C15111yescharacteristic
425C2×#104C22×C15111yescharacteristic
426C2×#104C22×C15111yescharacteristic
427C2×#104C22×C15111yescharacteristic
428#419C4×C15111yescharacteristic, complemented
429#419C4×C15111yescharacteristic, complemented
430#418C4×C15111yescharacteristic, complemented
431#418C4×C15111yescharacteristic, complemented
432#417C4×C15111yescharacteristic, complemented
433#417C4×C15111yescharacteristic, complemented
434#417C4×C15111yescharacteristic, complemented
435#417C4×C15111yescharacteristic, complemented
436#416C22×C15111yescharacteristic
437#416C22×C15111yescharacteristic
438#416C22×C15111yescharacteristic
439#416C22×C15111yescharacteristic
440#408—21no—
441#408—21no—
442#408C22×C15111yescharacteristic
443#408C22×C15111yescharacteristic
444#407—21no—
445#407C22×C15111yescharacteristic
446#407C22×C15111yescharacteristic
447C2×C22⋊C8—21no—
448C2×C22⋊C8C22×C15111yescharacteristic
449#405C22×C15111yescharacteristic, complemented
450#405C22×C15111yescharacteristic, complemented
451C2×#97C22×C15111yescharacteristic, complemented
452C2×C4×C8C22×C15111yescharacteristic, complemented
453C4×C22⋊C4C22×C15111yescharacteristic
454#341C22×C15111yescharacteristic, complemented
455#341C22×C15111yescharacteristic, complemented
456#339C22×C15111yescharacteristic, complemented
457#339C22×C15111yescharacteristic, complemented
458#339C22×C15111yescharacteristic, complemented
459#339C22×C15111yescharacteristic, complemented
460#336C22×C15111yescharacteristic, complemented
461#336C22×C15111yescharacteristic, complemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×C4×C15111yescharacteristic
469C2×#41C2×C4×C15111yescharacteristic
470C2×#41C23×C15111yescharacteristic
471C2×#41C23×C15111yescharacteristic
472C22×Q8C2×C4×C15111yescharacteristic
473C22×D4—21no—
474C22×D4C2×C4×C15111yescharacteristic
475C23×C4—21no—
476C23×C4C23×C15111yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—41no—
484C2×M16—41no—
485C2×M16C2×C4×C15111yescharacteristic
486C2×M16C2×C4×C15111yescharacteristic
487C2×M16C2×C4×C15111yescharacteristic
488C2×M16C2×C4×C15111yescharacteristic
489C2×M16C23×C15111yescharacteristic
490C2×M16C23×C15111yescharacteristic
491C2×M16C23×C15111yescharacteristic
492C2×M16C23×C15111yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8C23×C15111yescharacteristic
496C22×C8C23×C15111yescharacteristic
497C22×C8C23×C15111yescharacteristic
498C22×C8C23×C15111yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×C4×C15111yescharacteristic
502#117C2×C4×C15111yescharacteristic
503#117C23×C15111yescharacteristic
504#117C23×C15111yescharacteristic
505C2×C4⋊C4C2×C4×C15111yescharacteristic
506C2×C4⋊C4C2×C4×C15111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C15111yescharacteristic
511C2×C42C23×C15111yescharacteristic
512#108—41no—
513#108—41no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103C2×C4×C15111yescharacteristic
523#103C2×C4×C15111yescharacteristic
524#103C2×C4×C15111yescharacteristic
525#103C2×C4×C15111yescharacteristic
526#103C2×C4×C15111yescharacteristic
527#103C2×C4×C15111yescharacteristic
528#103C2×C4×C15111yescharacteristic
529#103C2×C4×C15111yescharacteristic
530#102C2×C4×C15111yescharacteristic
531#102C2×C4×C15111yescharacteristic
532#102C2×C4×C15111yescharacteristic
533#102C2×C4×C15111yescharacteristic
534#102C2×C4×C15111yescharacteristic
535#102C2×C4×C15111yescharacteristic
536#102C2×C4×C15111yescharacteristic
537#102C2×C4×C15111yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8D4×C15111yescharacteristic
547C22⋊C8D4×C15111yescharacteristic
548C22⋊C8D4×C15111yescharacteristic
549C22⋊C8D4×C15111yescharacteristic
550#97—21no—
551#97—21no—
552#97—41no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—41no—
556#95—21no—
557C24—21no—
558C24#41×C15111yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C15112yes—
574#41#41×C15112yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C15111yescharacteristic
579C2×Q8C22×C4×C15111yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C15111yescharacteristic
590C2×D4C22×C4×C15111yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C15111yescharacteristic
607C22×C4C22×C4×C15111yescharacteristic
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15111yescharacteristic
610C22×C4#41×C15111yescharacteristic
611C22×C4C24×C15111yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C15111yescharacteristic
641C2×C8C22×C4×C15111yescharacteristic
642C2×C8C22×C4×C15111yescharacteristic
643C2×C8C22×C4×C15111yescharacteristic
644C2×C8C2×D4×C15111yescharacteristic
645C2×C8C2×D4×C15111yescharacteristic
646C2×C8C2×D4×C15111yescharacteristic
647C2×C8C2×D4×C15111yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C15111yescharacteristic
651C4⋊C4C22×C4×C15111yescharacteristic
652C4⋊C4C22×C4×C15111yescharacteristic
653C4⋊C4C22×C4×C15111yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C15111yescharacteristic
677C23C4×D4×C15111yescharacteristic
678C23C2×#41×C15111yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#117×C15112yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#117×C15112yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C15111yescharacteristic
727C2×C4C4×D4×C15111yescharacteristic
728C2×C4C23×C4×C15111yescharacteristic
729C2×C4C22×D4×C15111yescharacteristic
730C2×C4C2×#41×C15111yescharacteristic
731C2×C4C2×#41×C15111yescharacteristic
732C2×C4H(5,𝔽2)×C15111yescharacteristic
733C2×C4H(5,𝔽2)×C15111yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C15111yescharacteristic
764C22#551×C15111yescharacteristic
765C22#551×C15111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×#117×C15111yescharacteristic
777C4#518×C15111yescharacteristic
778C4#546×C15111yescharacteristic
779C4#546×C15111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2342×C15111yescharacteristic
787C2#2955×C15111yescharacteristic
788C2#2956×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C2×C4×D4
prime radicalC22×#41×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C22⋊C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2924×C151C2semidirect
4. #1938×C151C2semidirect
5. #1937×C151C2semidirect
6. #1929×C151C2semidirect
7. #1929×C151C2semidirect
8. #1866×C151C2semidirect
9. #1866×C151C2semidirect
10. #1826×C151C2semidirect
11. #1811×C151C2semidirect
13. #1765×C151C2semidirect
14. #1764×C151C2semidirect
15. #1753×C151C2semidirect
25. C2×#108×C151C22semidirect
26. C2×#108×C151C22semidirect
27. #424×C151C22semidirect
28. #424×C151C22semidirect
33. #419×C151C4semidirect
34. #419×C151C4semidirect
35. #418×C151C4semidirect
36. #418×C151C4semidirect
37. #417×C151C4semidirect
38. #417×C151C4semidirect
39. #417×C151C4semidirect
40. #417×C151C4semidirect
54. #405×C151C22semidirect
55. #405×C151C22semidirect
56. C2×#97×C151C22semidirect
57. C2×C4×C8×C151C22semidirect
59. #341×C151C22semidirect
60. #341×C151C22semidirect
61. #339×C151C22semidirect
62. #339×C151C22semidirect
63. #339×C151C22semidirect
64. #339×C151C22semidirect
65. #336×C151C22semidirect
66. #336×C151C22semidirect
394. #22588C151direct (N × H)
395. C151#22588direct (N × H)
396. #2924C2×C151semidirect
399. #1938C2×C151semidirect
400. #1937C2×C151semidirect
401. #1929C2×C151semidirect
402. #1929C2×C151semidirect
403. #1866C2×C151semidirect
404. #1866C2×C151semidirect
405. #1826C2×C151semidirect
406. #1811C2×C151semidirect
408. #1765C2×C151semidirect
409. #1764C2×C151semidirect
410. #1753C2×C151semidirect
420. C2×#108C22×C151semidirect
421. C2×#108C22×C151semidirect
422. #424C22×C151semidirect
423. #424C22×C151semidirect
428. #419C4×C151semidirect
429. #419C4×C151semidirect
430. #418C4×C151semidirect
431. #418C4×C151semidirect
432. #417C4×C151semidirect
433. #417C4×C151semidirect
434. #417C4×C151semidirect
435. #417C4×C151semidirect
449. #405C22×C151semidirect
450. #405C22×C151semidirect
451. C2×#97C22×C151semidirect
452. C2×C4×C8C22×C151semidirect
454. #341C22×C151semidirect
455. #341C22×C151semidirect
456. #339C22×C151semidirect
457. #339C22×C151semidirect
458. #339C22×C151semidirect
459. #339C22×C151semidirect
460. #336C22×C151semidirect
461. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
#2924×C1512
#2896×C1512
#2880×C1512
#1938×C1512
#1937×C1512
#1929×C1512
#1866×C1512
#1826×C1512
#1811×C1512
#1789×C1512
#1765×C1512
#1764×C1512
#1753×C1512
#22588151