Finite Group Databasebeta

← C151×#23017 #50327942

Subgroups — C151×#23017 #50327942

Order 38656.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3035×C151C211yesmaximal, characteristic
2C2×#444×C151C211yesmaximal, characteristic, complemented
3C2×#443×C151C211yesmaximal, characteristic, complemented
4#2935×C151C211yesmaximal, characteristic, complemented
5#2906×C151C211yesmaximal, characteristic, complemented
6#1963×C151C211yesmaximal, characteristic, complemented
7#1950×C151C211yesmaximal, characteristic, complemented
8#1938×C151C211yesmaximal, characteristic, complemented
9#1937×C151C211yesmaximal, characteristic, complemented
10#1876×C151C211yesmaximal, characteristic, complemented
11#1876×C151C211yesmaximal, characteristic, complemented
12#1866×C151C211yesmaximal, characteristic, complemented
13#1866×C151C211yesmaximal, characteristic, complemented
14#1768×C151C211yesmaximal, characteristic, complemented
15#1759×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151C2211yescharacteristic
17C2×#135×C151C2211yescharacteristic
18C2×#131×C151C2211yescharacteristic
19C2×#131×C151C2211yescharacteristic
20C2×#131×C151C2211yescharacteristic
21C2×#131×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C4×#41×C151C2211yescharacteristic
24#464×C151C411yescharacteristic, complemented
25#464×C151C411yescharacteristic, complemented
26#463×C151C411yescharacteristic, complemented
27#463×C151C411yescharacteristic, complemented
28#462×C151C411yescharacteristic, complemented
29#461×C151C411yescharacteristic, complemented
30#460×C151C411yescharacteristic, complemented
31#459×C151C411yescharacteristic, complemented
32#444×C151—24no—
33#443×C151—24no—
34#436×C151—21no—
35#435×C151—21no—
36#435×C151—21no—
37C8×D4×C151—21no—
38C2×#108×C151C2211yescharacteristic
39C2×#108×C151C2211yescharacteristic
40#424×C151—21no—
41#424×C151—21no—
42#424×C151C2211yescharacteristic
43#424×C151C2211yescharacteristic
44#423×C151—21no—
45#423×C151C2211yescharacteristic
46C2×C4⋊C8×C151—21no—
47C2×C4⋊C8×C151C2211yescharacteristic
48C2×C4⋊C8×C151C2211yescharacteristic
49C2×#104×C151C2211yescharacteristic
50C2×#104×C151C2211yescharacteristic
51C2×#104×C151C2211yescharacteristic
52C2×#104×C151C2211yescharacteristic
53C2×#104×C151C2211yescharacteristic
54C2×#104×C151C2211yescharacteristic
55#416×C151C2211yescharacteristic
56#416×C151C2211yescharacteristic
57#408×C151C2211yescharacteristic
58#408×C151C2211yescharacteristic
59C4×M16×C151C2211yescharacteristic
60C2×#97×C151C2211yescharacteristic
61C2×C4×C8×C151C2211yescharacteristic
62#376×C151C2211yescharacteristic
63#341×C151C2211yescharacteristic
64#341×C151C2211yescharacteristic
65#339×C151C2211yescharacteristic
66#339×C151C2211yescharacteristic
67#336×C151C2211yescharacteristic
68#336×C151C2211yescharacteristic
69C2×#41×C151C2311yescharacteristic
70C2×#41×C151C2311yescharacteristic
71C2×#41×C151C2311yescharacteristic
72#135×C151—22no—
73#135×C151—22no—
74#135×C151—22no—
75#135×C151—22no—
76C2×Q16×C151C2×C411yescharacteristic
77C2×Q16×C151C2×C411yescharacteristic
78C2×SD16×C151C2×C411yescharacteristic
79C2×SD16×C151C2×C411yescharacteristic
80C2×SD16×C151C2×C411yescharacteristic
81C2×SD16×C151C2×C411yescharacteristic
82C2×D8×C151C2×C411yescharacteristic
83C2×D8×C151C2×C411yescharacteristic
84#131×C151—22no—
85#131×C151—22no—
86#131×C151—22no—
87#131×C151—22no—
88#131×C151—41no—
89#131×C151—41no—
90#131×C151—41no—
91#131×C151—41no—
92C2×M16×C151—21no—
93C2×M16×C151—21no—
94C2×M16×C151—21no—
95C2×M16×C151—21no—
96C2×M16×C151C2311yescharacteristic
97C2×M16×C151C2311yescharacteristic
98C2×M16×C151C2311yescharacteristic
99C2×M16×C151C2311yescharacteristic
100C22×C8×C151—21no—
101C22×C8×C151—21no—
102C22×C8×C151—21no—
103C22×C8×C151—21no—
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108C4⋊Q8×C151C2×C411yescharacteristic
109#127×C151C2×C411yescharacteristic
110#124×C151C2×C411yescharacteristic
111#124×C151C2×C411yescharacteristic
112#121×C151—21no—
113#121×C151—21no—
114C4×Q8×C151C2×C411yescharacteristic
115C4×Q8×C151C2×C411yescharacteristic
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151C2×C411yescharacteristic
121C4×D4×C151C2×C411yescharacteristic
122#117×C151—21no—
123#117×C151C2311yescharacteristic
124C2×C42×C151—21no—
125C2×C42×C151C2311yescharacteristic
126C2×C42×C151C2311yescharacteristic
127C2×C42×C151C2311yescharacteristic
128#108×C151—22no—
129#108×C151—22no—
130C4⋊C8×C151—21no—
131C4⋊C8×C151—21no—
132C4⋊C8×C151—21no—
133C4⋊C8×C151—21no—
134C4⋊C8×C151—21no—
135C4⋊C8×C151—21no—
136C4⋊C8×C151C2×C411yescharacteristic
137C4⋊C8×C151C2×C411yescharacteristic
138C4⋊C8×C151C2×C411yescharacteristic
139C4⋊C8×C151C2×C411yescharacteristic
140C4⋊C8×C151D411yescharacteristic
141C4⋊C8×C151D411yescharacteristic
142C4⋊C8×C151D411yescharacteristic
143C4⋊C8×C151D411yescharacteristic
144#104×C151—22no—
145#104×C151—22no—
146#104×C151—22no—
147#104×C151—41no—
148#104×C151—41no—
149#104×C151D414yescomplemented
150#103×C151C2×C411yescharacteristic
151#103×C151C2×C411yescharacteristic
152#103×C151C2×C411yescharacteristic
153#103×C151C2×C411yescharacteristic
154#102×C151C2×C411yescharacteristic
155#102×C151C2×C411yescharacteristic
156#102×C151C2×C411yescharacteristic
157#102×C151C2×C411yescharacteristic
158C22⋊C8×C151—21no—
159C22⋊C8×C151—21no—
160C22⋊C8×C151—21no—
161C22⋊C8×C151—21no—
162#97×C151—22no—
163#97×C151—21no—
164C4×C8×C151—22no—
165C4×C8×C151—21no—
166#95×C151—21no—
167#95×C151—21no—
168#41×C151—21no—
169#41×C151—21no—
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—21no—
173#41×C151—21no—
174#41×C151—21no—
175#41×C151—21no—
176#41×C151—21no—
177#41×C151—21no—
178#41×C151C2×D412yes—
179#41×C151#4112yes—
180C2×Q8×C151C22×C411yescharacteristic
181C2×Q8×C151C22×C411yescharacteristic
182C2×Q8×C151C22×C411yescharacteristic
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151C22×C411yescharacteristic
189C2×D4×C151C22×C411yescharacteristic
190C2×D4×C151C22×C411yescharacteristic
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151#4111yescharacteristic
199C22×C4×C151#4111yescharacteristic
200C22×C4×C151C2411yescharacteristic
201Q16×C151—22no—
202Q16×C151—22no—
203SD16×C151—22no—
204SD16×C151—22no—
205SD16×C151—22no—
206SD16×C151—22no—
207D8×C151—22no—
208D8×C151—22no—
209M16×C151—21no—
210M16×C151—21no—
211M16×C151—21no—
212M16×C151—21no—
213M16×C151—21no—
214M16×C151—21no—
215M16×C151—21no—
216M16×C151—42no—
217M16×C151—42no—
218M16×C151—42no—
219M16×C151—42no—
220M16×C151C2×D412yes—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×C151—42no—
234C2×C8×C151—42no—
235C2×C8×C151—42no—
236C2×C8×C151—42no—
237C2×C8×C151C22×C411yescharacteristic
238C2×C8×C151C22×C411yescharacteristic
239C2×C8×C151C22×C411yescharacteristic
240C2×C8×C151C22×C411yescharacteristic
241C2×C8×C151C2×D411yescharacteristic
242C2×C8×C151C2×D411yescharacteristic
243C2×C8×C151C2×D411yescharacteristic
244C2×C8×C151C2×D411yescharacteristic
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151C22×C411yescharacteristic
250C4⋊C4×C151C22×C411yescharacteristic
251C22⋊C4×C151—21no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C42×C151—21no—
259C42×C151—21no—
260C42×C151—21no—
261C42×C151—21no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151C22×C411yescharacteristic
265C42×C151C22×C411yescharacteristic
266C42×C151C2×D412yes—
267C42×C151C2×D411yescharacteristic
268C42×C151C2×D411yescharacteristic
269C23×C151—21no—
270C23×C151—21no—
271C23×C151—21no—
272C23×C151C2×#4111yescharacteristic
273Q8×C151—21no—
274Q8×C151—21no—
275Q8×C151—21no—
276Q8×C151—21no—
277Q8×C151—21no—
278Q8×C151C4×D412yes—
279D4×C151—22no—
280D4×C151—22no—
281D4×C151—21no—
282D4×C151—21no—
283D4×C151—21no—
284D4×C151—21no—
285D4×C151—21no—
286D4×C151—42no—
287D4×C151—41no—
288D4×C151—41no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—81no—
292D4×C151C4×D412yes—
293C2×C4×C151—21no—
294C2×C4×C151—22no—
295C2×C4×C151—22no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—22no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—42no—
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—81no—
314C2×C4×C151C4×D411yescharacteristic
315C2×C4×C151C4×D411yescharacteristic
316C2×C4×C151C4×D411yescharacteristic
317C2×C4×C151C4×D411yescharacteristic
318C2×C4×C151C23×C411yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C22×D411yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C151H(5,𝔽2)11yescharacteristic
323C2×C4×C1512−1+411yescharacteristic
324C8×C151—21no—
325C8×C151—21no—
326C8×C151—21no—
327C8×C151—21no—
328C8×C151—21no—
329C8×C151—21no—
330C8×C151—21no—
331C8×C151—21no—
332C8×C151—22no—
333C8×C151—41no—
334C8×C151—41no—
335C8×C151—41no—
336C22×C151—21no—
337C22×C151—21no—
338C22×C151—22no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151C2×C4×D411yescharacteristic
348C22×C151#54711yescharacteristic
349C22×C151#55311yescharacteristic
350C4×C151—22no—
351C4×C151—21no—
352C4×C151—21no—
353C4×C151—21no—
354C4×C151—21no—
355C4×C151—42no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—81no—
361C4×C151C2×C4×D411yescharacteristic
362C4×C151#52011yescharacteristic
363C4×C151D4211yescharacteristic
364C4×C151#54811yescharacteristic
365C2×C151—21no—
366C2×C151—21no—
367C2×C151—42no—
368C2×C151—81no—
369C2×C151—81no—
370C2×C151#236111yescharacteristic
371C2×C151#295511yescharacteristic
372C2×C151#295711yescharacteristic
373#23017C15111yesmaximal, characteristic, direct product factor, Sylow
374C151#2301711yescharacteristic, direct product factor, Sylow
375#3035C2×C15111yescharacteristic
376C2×#444C2×C15111yescharacteristic, complemented
377C2×#443C2×C15111yescharacteristic, complemented
378#2935C2×C15111yescharacteristic, complemented
379#2906C2×C15111yescharacteristic, complemented
380#1963C2×C15111yescharacteristic, complemented
381#1950C2×C15111yescharacteristic, complemented
382#1938C2×C15111yescharacteristic, complemented
383#1937C2×C15111yescharacteristic, complemented
384#1876C2×C15111yescharacteristic, complemented
385#1876C2×C15111yescharacteristic, complemented
386#1866C2×C15111yescharacteristic, complemented
387#1866C2×C15111yescharacteristic, complemented
388#1768C2×C15111yescharacteristic, complemented
389#1759C2×C15111yescharacteristic, complemented
390C2×#135C22×C15111yescharacteristic
391C2×#135C22×C15111yescharacteristic
392C2×#131C22×C15111yescharacteristic
393C2×#131C22×C15111yescharacteristic
394C2×#131C22×C15111yescharacteristic
395C2×#131C22×C15111yescharacteristic
396#532C22×C15111yescharacteristic
397C4×#41C22×C15111yescharacteristic
398#464C4×C15111yescharacteristic, complemented
399#464C4×C15111yescharacteristic, complemented
400#463C4×C15111yescharacteristic, complemented
401#463C4×C15111yescharacteristic, complemented
402#462C4×C15111yescharacteristic, complemented
403#461C4×C15111yescharacteristic, complemented
404#460C4×C15111yescharacteristic, complemented
405#459C4×C15111yescharacteristic, complemented
406#444—24no—
407#443—24no—
408#436—21no—
409#435—21no—
410#435—21no—
411C8×D4—21no—
412C2×#108C22×C15111yescharacteristic
413C2×#108C22×C15111yescharacteristic
414#424—21no—
415#424—21no—
416#424C22×C15111yescharacteristic
417#424C22×C15111yescharacteristic
418#423—21no—
419#423C22×C15111yescharacteristic
420C2×C4⋊C8—21no—
421C2×C4⋊C8C22×C15111yescharacteristic
422C2×C4⋊C8C22×C15111yescharacteristic
423C2×#104C22×C15111yescharacteristic
424C2×#104C22×C15111yescharacteristic
425C2×#104C22×C15111yescharacteristic
426C2×#104C22×C15111yescharacteristic
427C2×#104C22×C15111yescharacteristic
428C2×#104C22×C15111yescharacteristic
429#416C22×C15111yescharacteristic
430#416C22×C15111yescharacteristic
431#408C22×C15111yescharacteristic
432#408C22×C15111yescharacteristic
433C4×M16C22×C15111yescharacteristic
434C2×#97C22×C15111yescharacteristic
435C2×C4×C8C22×C15111yescharacteristic
436#376C22×C15111yescharacteristic
437#341C22×C15111yescharacteristic
438#341C22×C15111yescharacteristic
439#339C22×C15111yescharacteristic
440#339C22×C15111yescharacteristic
441#336C22×C15111yescharacteristic
442#336C22×C15111yescharacteristic
443C2×#41C23×C15111yescharacteristic
444C2×#41C23×C15111yescharacteristic
445C2×#41C23×C15111yescharacteristic
446#135—22no—
447#135—22no—
448#135—22no—
449#135—22no—
450C2×Q16C2×C4×C15111yescharacteristic
451C2×Q16C2×C4×C15111yescharacteristic
452C2×SD16C2×C4×C15111yescharacteristic
453C2×SD16C2×C4×C15111yescharacteristic
454C2×SD16C2×C4×C15111yescharacteristic
455C2×SD16C2×C4×C15111yescharacteristic
456C2×D8C2×C4×C15111yescharacteristic
457C2×D8C2×C4×C15111yescharacteristic
458#131—22no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—41no—
463#131—41no—
464#131—41no—
465#131—41no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16C23×C15111yescharacteristic
471C2×M16C23×C15111yescharacteristic
472C2×M16C23×C15111yescharacteristic
473C2×M16C23×C15111yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8C23×C15111yescharacteristic
479C22×C8C23×C15111yescharacteristic
480C22×C8C23×C15111yescharacteristic
481C22×C8C23×C15111yescharacteristic
482C4⋊Q8C2×C4×C15111yescharacteristic
483#127C2×C4×C15111yescharacteristic
484#124C2×C4×C15111yescharacteristic
485#124C2×C4×C15111yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8C2×C4×C15111yescharacteristic
489C4×Q8C2×C4×C15111yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×C4×C15111yescharacteristic
495C4×D4C2×C4×C15111yescharacteristic
496#117—21no—
497#117C23×C15111yescharacteristic
498C2×C42—21no—
499C2×C42C23×C15111yescharacteristic
500C2×C42C23×C15111yescharacteristic
501C2×C42C23×C15111yescharacteristic
502#108—22no—
503#108—22no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—21no—
509C4⋊C8—21no—
510C4⋊C8C2×C4×C15111yescharacteristic
511C4⋊C8C2×C4×C15111yescharacteristic
512C4⋊C8C2×C4×C15111yescharacteristic
513C4⋊C8C2×C4×C15111yescharacteristic
514C4⋊C8D4×C15111yescharacteristic
515C4⋊C8D4×C15111yescharacteristic
516C4⋊C8D4×C15111yescharacteristic
517C4⋊C8D4×C15111yescharacteristic
518#104—22no—
519#104—22no—
520#104—22no—
521#104—41no—
522#104—41no—
523#104D4×C15114yescomplemented
524#103C2×C4×C15111yescharacteristic
525#103C2×C4×C15111yescharacteristic
526#103C2×C4×C15111yescharacteristic
527#103C2×C4×C15111yescharacteristic
528#102C2×C4×C15111yescharacteristic
529#102C2×C4×C15111yescharacteristic
530#102C2×C4×C15111yescharacteristic
531#102C2×C4×C15111yescharacteristic
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536#97—22no—
537#97—21no—
538C4×C8—22no—
539C4×C8—21no—
540#95—21no—
541#95—21no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41C2×D4×C15112yes—
553#41#41×C15112yes—
554C2×Q8C22×C4×C15111yescharacteristic
555C2×Q8C22×C4×C15111yescharacteristic
556C2×Q8C22×C4×C15111yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×C4×C15111yescharacteristic
563C2×D4C22×C4×C15111yescharacteristic
564C2×D4C22×C4×C15111yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4#41×C15111yescharacteristic
573C22×C4#41×C15111yescharacteristic
574C22×C4C24×C15111yescharacteristic
575Q16—22no—
576Q16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581D8—22no—
582D8—22no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—42no—
591M16—42no—
592M16—42no—
593M16—42no—
594M16C2×D4×C15112yes—
595C2×C8—21no—
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×C8—21no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—42no—
610C2×C8—42no—
611C2×C8C22×C4×C15111yescharacteristic
612C2×C8C22×C4×C15111yescharacteristic
613C2×C8C22×C4×C15111yescharacteristic
614C2×C8C22×C4×C15111yescharacteristic
615C2×C8C2×D4×C15111yescharacteristic
616C2×C8C2×D4×C15111yescharacteristic
617C2×C8C2×D4×C15111yescharacteristic
618C2×C8C2×D4×C15111yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C22×C4×C15111yescharacteristic
624C4⋊C4C22×C4×C15111yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42C22×C4×C15111yescharacteristic
639C42C22×C4×C15111yescharacteristic
640C42C2×D4×C15112yes—
641C42C2×D4×C15111yescharacteristic
642C42C2×D4×C15111yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×#41×C15111yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8C4×D4×C15112yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4C4×D4×C15112yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—81no—
688C2×C4C4×D4×C15111yescharacteristic
689C2×C4C4×D4×C15111yescharacteristic
690C2×C4C4×D4×C15111yescharacteristic
691C2×C4C4×D4×C15111yescharacteristic
692C2×C4C23×C4×C15111yescharacteristic
693C2×C4C22×D4×C15111yescharacteristic
694C2×C4C22×D4×C15111yescharacteristic
695C2×C4C2×#41×C15111yescharacteristic
696C2×C4H(5,𝔽2)×C15111yescharacteristic
697C2×C42−1+4×C15111yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—21no—
705C8—21no—
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×C4×D4×C15111yescharacteristic
722C22#547×C15111yescharacteristic
723C22#553×C15111yescharacteristic
724C4—22no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—81no—
735C4C2×C4×D4×C15111yescharacteristic
736C4#520×C15111yescharacteristic
737C4D42×C15111yescharacteristic
738C4#548×C15111yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2#2361×C15111yescharacteristic
745C2#2955×C15111yescharacteristic
746C2#2957×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC22×C151C2×C4×D4
prime radical#3035×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C4⋊C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#444×C151C2semidirect
3. C2×#443×C151C2semidirect
4. #2935×C151C2semidirect
5. #2906×C151C2semidirect
6. #1963×C151C2semidirect
7. #1950×C151C2semidirect
8. #1938×C151C2semidirect
9. #1937×C151C2semidirect
10. #1876×C151C2semidirect
11. #1876×C151C2semidirect
12. #1866×C151C2semidirect
13. #1866×C151C2semidirect
14. #1768×C151C2semidirect
15. #1759×C151C2semidirect
24. #464×C151C4semidirect
25. #464×C151C4semidirect
26. #463×C151C4semidirect
27. #463×C151C4semidirect
28. #462×C151C4semidirect
29. #461×C151C4semidirect
30. #460×C151C4semidirect
31. #459×C151C4semidirect
149. #104×C151D4semidirect
373. #23017C151direct (N × H)
374. C151#23017direct (N × H)
376. C2×#444C2×C151semidirect
377. C2×#443C2×C151semidirect
378. #2935C2×C151semidirect
379. #2906C2×C151semidirect
380. #1963C2×C151semidirect
381. #1950C2×C151semidirect
382. #1938C2×C151semidirect
383. #1937C2×C151semidirect
384. #1876C2×C151semidirect
385. #1876C2×C151semidirect
386. #1866C2×C151semidirect
387. #1866C2×C151semidirect
388. #1768C2×C151semidirect
389. #1759C2×C151semidirect
398. #464C4×C151semidirect
399. #464C4×C151semidirect
400. #463C4×C151semidirect
401. #463C4×C151semidirect
402. #462C4×C151semidirect
403. #461C4×C151semidirect
404. #460C4×C151semidirect
405. #459C4×C151semidirect
523. #104D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3035×C1512
C2×#444×C1512
C2×#443×C1512
#2935×C1512
#2906×C1512
#1963×C1512
#1950×C1512
#1938×C1512
#1937×C1512
#1876×C1512
#1866×C1512
#1768×C1512
#1759×C1512
#23017151