Finite Group Databasebeta

← C151×#24403 #50329328

Subgroups — C151×#24403 #50329328

Order 38656.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C151C211yesmaximal, characteristic
2C2×#473×C151C211yesmaximal, characteristic, complemented
3C2×#471×C151C211yesmaximal, characteristic, complemented
4#3007×C151C211yesmaximal, characteristic, complemented
5C2×#452×C151C211yesmaximal, characteristic, complemented
6#2880×C151C211yesmaximal, characteristic, complemented
7#2052×C151C211yesmaximal, characteristic, complemented
8#2051×C151C211yesmaximal, characteristic, complemented
9#2020×C151C211yesmaximal, characteristic, complemented
10#2019×C151C211yesmaximal, characteristic, complemented
11#1908×C151C211yesmaximal, characteristic, complemented
12#1907×C151C211yesmaximal, characteristic, complemented
13#1901×C151C211yesmaximal, characteristic, complemented
14#1855×C151C211yesmaximal, characteristic, complemented
15#1785×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18#575×C151—24no—
19#575×C151—24no—
20C2×#137×C151—21no—
21C2×#137×C151C2211yescharacteristic
22C2×#137×C151C2211yescharacteristic
23C2×#137×C151C2211yescharacteristic
24C2×#137×C151C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C151—21no—
26C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
28C2×#135×C151—21no—
29C2×#135×C151—21no—
30C22×Q16×C151C2211yescharacteristic, complemented
31C22×SD16×C151C2211yescharacteristic, complemented
32C2×#131×C151C2211yescharacteristic
33C2×#131×C151C2211yescharacteristic
34C22×M16×C151C2211yescharacteristic
35C2×C22⋊Q8×C151C2211yescharacteristic
36#473×C151—24no—
37#471×C151—24no—
38#452×C151—21no—
39#452×C151—21no—
40#452×C151—21no—
41#452×C151—21no—
42#452×C151—21no—
43#452×C151—21no—
44#451×C151—21no—
45#450×C151—21no—
46C2×#108×C151C2211yescharacteristic, complemented
47C2×#108×C151C2211yescharacteristic, complemented
48#417×C151C2211yescharacteristic
49#417×C151C2211yescharacteristic
50C2×#103×C151C2211yescharacteristic, complemented
51C2×#102×C151C2211yescharacteristic, complemented
52C2×#101×C151C2211yescharacteristic, complemented
53C2×#101×C151C2211yescharacteristic, complemented
54C2×#101×C151C2211yescharacteristic, complemented
55C2×#101×C151C2211yescharacteristic, complemented
56C2×#100×C151C2211yescharacteristic, complemented
57C2×#100×C151C2211yescharacteristic, complemented
58#408×C151—21no—
59#408×C151—21no—
60#408×C151C2211yescharacteristic
61#408×C151C2211yescharacteristic
62#407×C151—21no—
63#407×C151C2211yescharacteristic
64#407×C151C2211yescharacteristic
65C2×C22⋊C8×C151—21no—
66C2×C22⋊C8×C151C2211yescharacteristic
67#343×C151C2211yescharacteristic, complemented
68#343×C151C2211yescharacteristic, complemented
69#341×C151C2211yescharacteristic, complemented
70#341×C151C2211yescharacteristic, complemented
71C2×#41×C151—22no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151—22no—
75C2×#41×C151—22no—
76C2×#41×C151—21no—
77C2×#41×C151—21no—
78C2×#41×C151—21no—
79C2×#41×C151—21no—
80C2×#41×C151—22no—
81C2×#41×C151—41no—
82C2×#41×C151—41no—
83C2×#41×C151—41no—
84C2×#41×C151—41no—
85C2×#41×C151D411yescharacteristic
86C2×#41×C151D411yescharacteristic
87C2×#41×C151C2311yescharacteristic
88C2×#41×C151C2311yescharacteristic
89C22×Q8×C151D411yescharacteristic
90C22×Q8×C151C2311yescharacteristic
91C22×Q8×C151C2311yescharacteristic
92C22×D4×C151—21no—
93C22×D4×C151—21no—
94C22×D4×C151D411yescharacteristic
95C22×D4×C151C2311yescharacteristic
96C23×C4×C151—21no—
97C23×C4×C151—21no—
98C23×C4×C151C2311yescharacteristic
99#137×C151—28no—
100#137×C151—22no—
101#137×C151—22no—
102#137×C151—22no—
103#137×C151—22no—
104#137×C151—22no—
105#137×C151—41no—
106#137×C151—41no—
107#137×C151D414yes—
108AGL(1,ℤ/8)×C151—28no—
109AGL(1,ℤ/8)×C151—22no—
110AGL(1,ℤ/8)×C151—22no—
111AGL(1,ℤ/8)×C151—22no—
112AGL(1,ℤ/8)×C151D414yes—
113#135×C151—28no—
114#135×C151—28no—
115C2×Q16×C151—21no—
116C2×Q16×C151—21no—
117C2×Q16×C151—21no—
118C2×Q16×C151—21no—
119C2×Q16×C151—21no—
120C2×Q16×C151—21no—
121C2×Q16×C151—22no—
122C2×Q16×C151—41no—
123C2×SD16×C151—21no—
124C2×SD16×C151—21no—
125C2×SD16×C151—21no—
126C2×SD16×C151—21no—
127C2×SD16×C151—22no—
128C2×SD16×C151—21no—
129C2×SD16×C151—21no—
130C2×SD16×C151—21no—
131C2×SD16×C151—21no—
132C2×SD16×C151—41no—
133C2×D8×C151—21no—
134C2×D8×C151—21no—
135#131×C151—22no—
136#131×C151—22no—
137#131×C151—41no—
138#131×C151—41no—
139C2×M16×C151—21no—
140C2×M16×C151—22no—
141C2×M16×C151—22no—
142C2×M16×C151—21no—
143C2×M16×C151—21no—
144C2×M16×C151C2311yescharacteristic
145C2×M16×C151C2311yescharacteristic
146C2×M16×C151C2311yescharacteristic
147C2×M16×C151C2311yescharacteristic
148C2×M16×C151C2311yescharacteristic
149C2×M16×C151C2311yescharacteristic
150C22×C8×C151—21no—
151C22×C8×C151—21no—
152C22×C8×C151—21no—
153C22×C8×C151C2311yescharacteristic
154C22×C8×C151C2311yescharacteristic
155C22⋊Q8×C151—21no—
156C22⋊Q8×C151—21no—
157C22⋊Q8×C151—21no—
158C22⋊Q8×C151—21no—
159C2×C4⋊C4×C151—21no—
160C2×C4⋊C4×C151C2311yescharacteristic
161C2×C22⋊C4×C151—21no—
162#108×C151—22no—
163#108×C151—22no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#101×C151—22no—
173#101×C151—22no—
174#101×C151—22no—
175#101×C151—41no—
176#100×C151—22no—
177#100×C151—41no—
178C22⋊C8×C151—21no—
179C22⋊C8×C151—21no—
180C22⋊C8×C151—21no—
181C22⋊C8×C151—21no—
182C22⋊C8×C151—21no—
183C22⋊C8×C151—21no—
184C22⋊C8×C151—21no—
185C22⋊C8×C151—21no—
186C22⋊C8×C151D411yescharacteristic
187C22⋊C8×C151D411yescharacteristic
188C22⋊C8×C151D411yescharacteristic
189C22⋊C8×C151D411yescharacteristic
190C24×C151—21no—
191C24×C151—21no—
192C24×C151#4111yescharacteristic
193#41×C151—21no—
194#41×C151—21no—
195#41×C151—24no—
196#41×C151—24no—
197#41×C151—22no—
198#41×C151—22no—
199#41×C151—21no—
200#41×C151—21no—
201#41×C151—21no—
202#41×C151—21no—
203#41×C151—42no—
204#41×C151—42no—
205#41×C151—41no—
206#41×C151—41no—
207#41×C151—42no—
208#41×C151—42no—
209#41×C151—42no—
210#41×C151—42no—
211#41×C151—42no—
212#41×C151—42no—
213#41×C151—42no—
214#41×C151—42no—
215#41×C151C2×D412yes—
216#41×C151C2×D412yes—
217C2×Q8×C151—21no—
218C2×Q8×C151—21no—
219C2×Q8×C151—22no—
220C2×Q8×C151—21no—
221C2×Q8×C151—21no—
222C2×Q8×C151—21no—
223C2×Q8×C151—21no—
224C2×Q8×C151—21no—
225C2×Q8×C151—21no—
226C2×Q8×C151—21no—
227C2×Q8×C151—21no—
228C2×Q8×C151—21no—
229C2×Q8×C151—21no—
230C2×Q8×C151—41no—
231C2×Q8×C151C2×D412yes—
232C2×Q8×C151C2×D411yescharacteristic
233C2×Q8×C151C2×D411yescharacteristic
234C2×D4×C151—21no—
235C2×D4×C151—22no—
236C2×D4×C151—21no—
237C2×D4×C151—21no—
238C2×D4×C151—21no—
239C2×D4×C151—21no—
240C2×D4×C151—21no—
241C2×D4×C151—21no—
242C2×D4×C151—21no—
243C2×D4×C151—21no—
244C2×D4×C151—21no—
245C2×D4×C151—41no—
246C2×D4×C151—42no—
247C2×D4×C151—42no—
248C2×D4×C151—42no—
249C2×D4×C151—42no—
250C2×D4×C151—41no—
251C2×D4×C151—41no—
252C2×D4×C151C2×D412yes—
253C2×D4×C151C2×D411yescharacteristic
254C2×D4×C151C2×D411yescharacteristic
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—42no—
268C22×C4×C151—42no—
269C22×C4×C151—42no—
270C22×C4×C151—42no—
271C22×C4×C151—41no—
272C22×C4×C151—41no—
273C22×C4×C151C2×D411yescharacteristic
274C22×C4×C151C2×D411yescharacteristic
275C22×C4×C151C2×D411yescharacteristic
276C22×C4×C151C2×D411yescharacteristic
277C22×C4×C151#4111yescharacteristic
278C22×C4×C151C2411yescharacteristic
279Q16×C151—24no—
280Q16×C151—24no—
281Q16×C151—42no—
282Q16×C151—42no—
283Q16×C151—42no—
284Q16×C151—42no—
285SD16×C151—24no—
286SD16×C151—24no—
287SD16×C151—24no—
288SD16×C151—24no—
289SD16×C151—42no—
290SD16×C151—42no—
291SD16×C151—42no—
292SD16×C151—42no—
293D8×C151—24no—
294D8×C151—24no—
295M16×C151—24no—
296M16×C151—21no—
297M16×C151—21no—
298M16×C151—21no—
299M16×C151—21no—
300M16×C151—21no—
301M16×C151—21no—
302M16×C151—21no—
303M16×C151—21no—
304M16×C151—21no—
305M16×C151—21no—
306M16×C151—42no—
307M16×C151—42no—
308M16×C151C2×D412yes—
309M16×C151C2×D412yes—
310C2×C8×C151—24no—
311C2×C8×C151—21no—
312C2×C8×C151—21no—
313C2×C8×C151—21no—
314C2×C8×C151—21no—
315C2×C8×C151—21no—
316C2×C8×C151—21no—
317C2×C8×C151—21no—
318C2×C8×C151—21no—
319C2×C8×C151—21no—
320C2×C8×C151—21no—
321C2×C8×C151—42no—
322C2×C8×C151—42no—
323C2×C8×C151C2×D411yescharacteristic
324C2×C8×C151C2×D411yescharacteristic
325C2×C8×C151C2×D411yescharacteristic
326C2×C8×C151C2×D411yescharacteristic
327C4⋊C4×C151—21no—
328C4⋊C4×C151—21no—
329C4⋊C4×C151—41no—
330C4⋊C4×C151—41no—
331C22⋊C4×C151—41no—
332C22⋊C4×C151—41no—
333C23×C151—21no—
334C23×C151—21no—
335C23×C151—21no—
336C23×C151—21no—
337C23×C151—22no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—42no—
341C23×C151—42no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—81no—
345C23×C151—81no—
346C23×C151—81no—
347C23×C151#12111yescharacteristic
348C23×C151#12111yescharacteristic
349C23×C151C2×#4111yescharacteristic
350Q8×C151—21no—
351Q8×C151—21no—
352Q8×C151—22no—
353Q8×C151—21no—
354Q8×C151—22no—
355Q8×C151—42no—
356Q8×C151—41no—
357Q8×C151—41no—
358Q8×C151—41no—
359Q8×C151—41no—
360Q8×C151—41no—
361Q8×C151—41no—
362Q8×C151#12012yes—
363D4×C151—22no—
364D4×C151—22no—
365D4×C151—22no—
366D4×C151—21no—
367D4×C151—21no—
368D4×C151—21no—
369D4×C151—22no—
370D4×C151—42no—
371D4×C151—42no—
372D4×C151—42no—
373D4×C151—44no—
374D4×C151—44no—
375D4×C151—41no—
376D4×C151—41no—
377D4×C151—41no—
378D4×C151—41no—
379D4×C151#12012yes—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—21no—
387C2×C4×C151—22no—
388C2×C4×C151—22no—
389C2×C4×C151—21no—
390C2×C4×C151—21no—
391C2×C4×C151—21no—
392C2×C4×C151—21no—
393C2×C4×C151—21no—
394C2×C4×C151—22no—
395C2×C4×C151—42no—
396C2×C4×C151—42no—
397C2×C4×C151—42no—
398C2×C4×C151—44no—
399C2×C4×C151—44no—
400C2×C4×C151—41no—
401C2×C4×C151—41no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151—41no—
406C2×C4×C151—41no—
407C2×C4×C151—41no—
408C2×C4×C151—81no—
409C2×C4×C151#12111yescharacteristic
410C2×C4×C151#12111yescharacteristic
411C2×C4×C151C22×D411yescharacteristic
412C2×C4×C151C22×D411yescharacteristic
413C2×C4×C151C22×D411yescharacteristic
414C2×C4×C151C22×D411yescharacteristic
415C2×C4×C151H(5,𝔽2)11yescharacteristic
416C2×C4×C151H(5,𝔽2)11yescharacteristic
417C8×C151—22no—
418C8×C151—22no—
419C8×C151—21no—
420C8×C151—21no—
421C8×C151—21no—
422C8×C151—21no—
423C8×C151—41no—
424C8×C151—41no—
425C8×C151—41no—
426C8×C151—41no—
427C22×C151—21no—
428C22×C151—21no—
429C22×C151—21no—
430C22×C151—21no—
431C22×C151—22no—
432C22×C151—21no—
433C22×C151—21no—
434C22×C151—21no—
435C22×C151—21no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—41no—
439C22×C151—42no—
440C22×C151—41no—
441C22×C151—41no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—82no—
445C22×C151—82no—
446C22×C151—84no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151C2×#12111yescharacteristic
450C22×C151#54611yescharacteristic
451C22×C151#54611yescharacteristic
452C4×C151—21no—
453C4×C151—21no—
454C4×C151—22no—
455C4×C151—41no—
456C4×C151—42no—
457C4×C151—81no—
458C4×C151—81no—
459C4×C151C2×#12011yescharacteristic
460C4×C151#53411yescharacteristic
461C4×C151D4211yescharacteristic
462C4×C151D4211yescharacteristic
463C2×C151—21no—
464C2×C151—21no—
465C2×C151—41no—
466C2×C151—41no—
467C2×C151—42no—
468C2×C151—81no—
469C2×C151—82no—
470C2×C151#241011yescharacteristic
471C2×C151#306711yescharacteristic
472C2×C151#306911yescharacteristic
473#24403C15111yesmaximal, characteristic, direct product factor, Sylow
474C151#2440311yescharacteristic, direct product factor, Sylow
475C2×#575C2×C15111yescharacteristic
476C2×#473C2×C15111yescharacteristic, complemented
477C2×#471C2×C15111yescharacteristic, complemented
478#3007C2×C15111yescharacteristic, complemented
479C2×#452C2×C15111yescharacteristic, complemented
480#2880C2×C15111yescharacteristic, complemented
481#2052C2×C15111yescharacteristic, complemented
482#2051C2×C15111yescharacteristic, complemented
483#2020C2×C15111yescharacteristic, complemented
484#2019C2×C15111yescharacteristic, complemented
485#1908C2×C15111yescharacteristic, complemented
486#1907C2×C15111yescharacteristic, complemented
487#1901C2×C15111yescharacteristic, complemented
488#1855C2×C15111yescharacteristic, complemented
489#1785C2×C15111yescharacteristic, complemented
490C22×#41C22×C15111yescharacteristic
491C22×#41C22×C15111yescharacteristic
492#575—24no—
493#575—24no—
494C2×#137—21no—
495C2×#137C22×C15111yescharacteristic
496C2×#137C22×C15111yescharacteristic
497C2×#137C22×C15111yescharacteristic
498C2×#137C22×C15111yescharacteristic
499C2×AGL(1,ℤ/8)—21no—
500C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
501C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
502C2×#135—21no—
503C2×#135—21no—
504C22×Q16C22×C15111yescharacteristic, complemented
505C22×SD16C22×C15111yescharacteristic, complemented
506C2×#131C22×C15111yescharacteristic
507C2×#131C22×C15111yescharacteristic
508C22×M16C22×C15111yescharacteristic
509C2×C22⋊Q8C22×C15111yescharacteristic
510#473—24no—
511#471—24no—
512#452—21no—
513#452—21no—
514#452—21no—
515#452—21no—
516#452—21no—
517#452—21no—
518#451—21no—
519#450—21no—
520C2×#108C22×C15111yescharacteristic, complemented
521C2×#108C22×C15111yescharacteristic, complemented
522#417C22×C15111yescharacteristic
523#417C22×C15111yescharacteristic
524C2×#103C22×C15111yescharacteristic, complemented
525C2×#102C22×C15111yescharacteristic, complemented
526C2×#101C22×C15111yescharacteristic, complemented
527C2×#101C22×C15111yescharacteristic, complemented
528C2×#101C22×C15111yescharacteristic, complemented
529C2×#101C22×C15111yescharacteristic, complemented
530C2×#100C22×C15111yescharacteristic, complemented
531C2×#100C22×C15111yescharacteristic, complemented
532#408—21no—
533#408—21no—
534#408C22×C15111yescharacteristic
535#408C22×C15111yescharacteristic
536#407—21no—
537#407C22×C15111yescharacteristic
538#407C22×C15111yescharacteristic
539C2×C22⋊C8—21no—
540C2×C22⋊C8C22×C15111yescharacteristic
541#343C22×C15111yescharacteristic, complemented
542#343C22×C15111yescharacteristic, complemented
543#341C22×C15111yescharacteristic, complemented
544#341C22×C15111yescharacteristic, complemented
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C15111yescharacteristic
560C2×#41D4×C15111yescharacteristic
561C2×#41C23×C15111yescharacteristic
562C2×#41C23×C15111yescharacteristic
563C22×Q8D4×C15111yescharacteristic
564C22×Q8C23×C15111yescharacteristic
565C22×Q8C23×C15111yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4D4×C15111yescharacteristic
569C22×D4C23×C15111yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C15111yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—22no—
579#137—41no—
580#137—41no—
581#137D4×C15114yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)D4×C15114yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—22no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—41no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—22no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—41no—
607C2×D8—21no—
608C2×D8—21no—
609#131—22no—
610#131—22no—
611#131—41no—
612#131—41no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—21no—
617C2×M16—21no—
618C2×M16C23×C15111yescharacteristic
619C2×M16C23×C15111yescharacteristic
620C2×M16C23×C15111yescharacteristic
621C2×M16C23×C15111yescharacteristic
622C2×M16C23×C15111yescharacteristic
623C2×M16C23×C15111yescharacteristic
624C22×C8—21no—
625C22×C8—21no—
626C22×C8—21no—
627C22×C8C23×C15111yescharacteristic
628C22×C8C23×C15111yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C23×C15111yescharacteristic
635C2×C22⋊C4—21no—
636#108—22no—
637#108—22no—
638#103—21no—
639#103—21no—
640#103—21no—
641#103—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#101—22no—
647#101—22no—
648#101—22no—
649#101—41no—
650#100—22no—
651#100—41no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8D4×C15111yescharacteristic
661C22⋊C8D4×C15111yescharacteristic
662C22⋊C8D4×C15111yescharacteristic
663C22⋊C8D4×C15111yescharacteristic
664C24—21no—
665C24—21no—
666C24#41×C15111yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C15112yes—
690#41C2×D4×C15112yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C15112yes—
706C2×Q8C2×D4×C15111yescharacteristic
707C2×Q8C2×D4×C15111yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C15112yes—
727C2×D4C2×D4×C15111yescharacteristic
728C2×D4C2×D4×C15111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C15111yescharacteristic
748C22×C4C2×D4×C15111yescharacteristic
749C22×C4C2×D4×C15111yescharacteristic
750C22×C4C2×D4×C15111yescharacteristic
751C22×C4#41×C15111yescharacteristic
752C22×C4C24×C15111yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C15112yes—
783M16C2×D4×C15112yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C15111yescharacteristic
798C2×C8C2×D4×C15111yescharacteristic
799C2×C8C2×D4×C15111yescharacteristic
800C2×C8C2×D4×C15111yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#121×C15111yescharacteristic
822C23#121×C15111yescharacteristic
823C23C2×#41×C15111yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8#120×C15112yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#120×C15112yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4#121×C15111yescharacteristic
884C2×C4#121×C15111yescharacteristic
885C2×C4C22×D4×C15111yescharacteristic
886C2×C4C22×D4×C15111yescharacteristic
887C2×C4C22×D4×C15111yescharacteristic
888C2×C4C22×D4×C15111yescharacteristic
889C2×C4H(5,𝔽2)×C15111yescharacteristic
890C2×C4H(5,𝔽2)×C15111yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—22no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#121×C15111yescharacteristic
924C22#546×C15111yescharacteristic
925C22#546×C15111yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#120×C15111yescharacteristic
934C4#534×C15111yescharacteristic
935C4D42×C15111yescharacteristic
936C4D42×C15111yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2#2410×C15111yescharacteristic
945C2#3067×C15111yescharacteristic
946C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#575×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#473×C151C2semidirect
3. C2×#471×C151C2semidirect
4. #3007×C151C2semidirect
5. C2×#452×C151C2semidirect
6. #2880×C151C2semidirect
7. #2052×C151C2semidirect
8. #2051×C151C2semidirect
9. #2020×C151C2semidirect
10. #2019×C151C2semidirect
11. #1908×C151C2semidirect
12. #1907×C151C2semidirect
13. #1901×C151C2semidirect
14. #1855×C151C2semidirect
15. #1785×C151C2semidirect
30. C22×Q16×C151C22semidirect
31. C22×SD16×C151C22semidirect
46. C2×#108×C151C22semidirect
47. C2×#108×C151C22semidirect
50. C2×#103×C151C22semidirect
51. C2×#102×C151C22semidirect
52. C2×#101×C151C22semidirect
53. C2×#101×C151C22semidirect
54. C2×#101×C151C22semidirect
55. C2×#101×C151C22semidirect
56. C2×#100×C151C22semidirect
57. C2×#100×C151C22semidirect
67. #343×C151C22semidirect
68. #343×C151C22semidirect
69. #341×C151C22semidirect
70. #341×C151C22semidirect
473. #24403C151direct (N × H)
474. C151#24403direct (N × H)
476. C2×#473C2×C151semidirect
477. C2×#471C2×C151semidirect
478. #3007C2×C151semidirect
479. C2×#452C2×C151semidirect
480. #2880C2×C151semidirect
481. #2052C2×C151semidirect
482. #2051C2×C151semidirect
483. #2020C2×C151semidirect
484. #2019C2×C151semidirect
485. #1908C2×C151semidirect
486. #1907C2×C151semidirect
487. #1901C2×C151semidirect
488. #1855C2×C151semidirect
489. #1785C2×C151semidirect
504. C22×Q16C22×C151semidirect
505. C22×SD16C22×C151semidirect
520. C2×#108C22×C151semidirect
521. C2×#108C22×C151semidirect
524. C2×#103C22×C151semidirect
525. C2×#102C22×C151semidirect
526. C2×#101C22×C151semidirect
527. C2×#101C22×C151semidirect
528. C2×#101C22×C151semidirect
529. C2×#101C22×C151semidirect
530. C2×#100C22×C151semidirect
531. C2×#100C22×C151semidirect
541. #343C22×C151semidirect
542. #343C22×C151semidirect
543. #341C22×C151semidirect
544. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1512
C2×#473×C1512
C2×#471×C1512
#3007×C1512
C2×#452×C1512
#2880×C1512
#2052×C1512
#2051×C1512
#2020×C1512
#2019×C1512
#1908×C1512
#1907×C1512
#1901×C1512
#1855×C1512
#1785×C1512
#24403151