Finite Group Databasebeta

← C151×#17679 #50322604

Subgroups — C151×#17679 #50322604

Order 38656.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3514×C151C211yesmaximal, characteristic
2#2970×C151C211yesmaximal, characteristic, complemented
3#2923×C151C211yesmaximal, characteristic, complemented
4#1536×C151C211yesmaximal, characteristic, complemented
5#1535×C151C211yesmaximal, characteristic, complemented
6#1535×C151C211yesmaximal, characteristic, complemented
7#1533×C151C211yesmaximal, characteristic, complemented
8#1532×C151C211yesmaximal, characteristic, complemented
9#1532×C151C211yesmaximal, characteristic, complemented
10#1530×C151C211yesmaximal, characteristic, complemented
11#1529×C151C211yesmaximal, characteristic, complemented
12#1527×C151C211yesmaximal, characteristic, complemented
13#1527×C151C211yesmaximal, characteristic, complemented
14#1524×C151C211yesmaximal, characteristic, complemented
15C2×#329×C151C211yesmaximal, characteristic, complemented
16#559×C151C411yescharacteristic
17#556×C151C411yescharacteristic
18#555×C151—21no—
19#551×C151—21no—
20#551×C151—21no—
21D4×Q8×C151C411yescharacteristic
22#548×C151C411yescharacteristic
23#548×C151C411yescharacteristic
24#546×C151—21no—
25#546×C151C411yescharacteristic
26#546×C151C411yescharacteristic
27D42×C151C411yescharacteristic
28#542×C151—21no—
29#538×C151—21no—
30#538×C151—21no—
31#532×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#529×C151C2211yescharacteristic
35C2×#124×C151C2211yescharacteristic
36C2×#124×C151C2211yescharacteristic
37#518×C151—21no—
38C4×#41×C151C2211yescharacteristic
39#446×C151—21no—
40#435×C151—21no—
41#435×C151—21no—
42C8×D4×C151—21no—
43#433×C151—21no—
44#433×C151—21no—
45#432×C151C2211yescharacteristic, complemented
46#432×C151C2211yescharacteristic, complemented
47#432×C151C2211yescharacteristic, complemented
48#432×C151C2211yescharacteristic, complemented
49#432×C151C2211yescharacteristic, complemented
50#432×C151C2211yescharacteristic, complemented
51#432×C151C2211yescharacteristic, complemented
52#424×C151—21no—
53#408×C151—21no—
54C4×M16×C151C2211yescharacteristic, complemented
55C4×M16×C151C2211yescharacteristic, complemented
56C2×#97×C151C2211yescharacteristic, complemented
57C2×#97×C151C2211yescharacteristic, complemented
58C2×#97×C151C2211yescharacteristic, complemented
59#330×C151C2211yescharacteristic, complemented
60#330×C151C2211yescharacteristic, complemented
61#330×C151C2211yescharacteristic, complemented
62#330×C151C2211yescharacteristic, complemented
63#329×C151C2211yescharacteristic
64#329×C151C2211yescharacteristic
65#329×C151C2211yescharacteristic
66#329×C151C2211yescharacteristic
67#329×C151C2211yescharacteristic, complemented
68#329×C151C2211yescharacteristic, complemented
69#329×C151C2211yescharacteristic, complemented
70#329×C151C2211yescharacteristic, complemented
71#329×C151C2211yescharacteristic, complemented
72#329×C151C2211yescharacteristic, complemented
73#329×C151C2211yescharacteristic, complemented
74#329×C151C2211yescharacteristic, complemented
75C2×#41×C151C2×C411yescharacteristic
76C2×#41×C151C2×C411yescharacteristic
77C2×#41×C151D411yescharacteristic
78C22×Q8×C151C2×C411yescharacteristic
79C22×Q8×C151C2×C411yescharacteristic
80C22×D4×C151—21no—
81C22×D4×C151C2×C411yescharacteristic
82C22×D4×C151C2×C411yescharacteristic
83C2×M16×C151—21no—
84C2×M16×C151—21no—
85C22×C8×C151—21no—
86C22×C8×C151—21no—
87C22×C8×C151—21no—
88C4⋊Q8×C151—21no—
89C4⋊Q8×C151C2×C411yescharacteristic
90#127×C151C2×C411yescharacteristic
91#126×C151—21no—
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#126×C151—21no—
96#125×C151C2311yescharacteristic
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151—21no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151—21no—
104#124×C151C2×C411yescharacteristic
105#124×C151C2×C411yescharacteristic
106#124×C151C2×C411yescharacteristic
107#124×C151C2×C411yescharacteristic
108#124×C151C2311yescharacteristic
109#124×C151C2311yescharacteristic
110#124×C151C2311yescharacteristic
111#123×C151—21no—
112#123×C151—21no—
113#123×C151—21no—
114#123×C151—21no—
115#123×C151—21no—
116#123×C151—21no—
117#123×C151—21no—
118C22⋊Q8×C151—21no—
119C22⋊Q8×C151—21no—
120C22⋊Q8×C151—21no—
121C22⋊Q8×C151—21no—
122C22⋊Q8×C151—21no—
123C22⋊Q8×C151C2×C411yescharacteristic
124C22⋊Q8×C151C2×C411yescharacteristic
125C22⋊Q8×C151C2×C411yescharacteristic
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151—21no—
130#121×C151—21no—
131#121×C151—21no—
132#121×C151—21no—
133#121×C151C2×C411yescharacteristic
134#121×C151C2×C411yescharacteristic
135#121×C151C2×C411yescharacteristic
136#120×C151—21no—
137#120×C151—21no—
138#120×C151—21no—
139#120×C151—21no—
140C4×Q8×C151C2×C411yescharacteristic
141C4×Q8×C151C2×C411yescharacteristic
142C4×Q8×C151C2×C411yescharacteristic
143C4×Q8×C151C2×C411yescharacteristic
144C4×Q8×C151D411yescharacteristic
145C4×D4×C151—21no—
146C4×D4×C151—21no—
147C4×D4×C151—21no—
148C4×D4×C151—21no—
149C4×D4×C151—21no—
150C4×D4×C151—21no—
151C4×D4×C151—21no—
152C4×D4×C151—21no—
153C4×D4×C151—21no—
154C4×D4×C151C2×C411yescharacteristic
155C4×D4×C151C2×C411yescharacteristic
156C4×D4×C151C2×C411yescharacteristic
157C4×D4×C151C2×C411yescharacteristic
158C4×D4×C151C2×C411yescharacteristic
159C4×D4×C151C2×C411yescharacteristic
160C4×D4×C151D411yescharacteristic
161C4×D4×C151D411yescharacteristic
162C4×D4×C151D411yescharacteristic
163#117×C151—21no—
164#117×C151—21no—
165#117×C151—21no—
166#117×C151—21no—
167#117×C151D411yescharacteristic
168#117×C151D411yescharacteristic
169#117×C151D411yescharacteristic
170C2×C22⋊C4×C151—21no—
171C2×C22⋊C4×C151—21no—
172C2×C22⋊C4×C151—21no—
173C2×C22⋊C4×C151—21no—
174C2×C22⋊C4×C151—21no—
175C2×C22⋊C4×C151—21no—
176C2×C42×C151C2311yescharacteristic
177C2×C42×C151C2311yescharacteristic
178C2×C42×C151C2311yescharacteristic
179C4⋊C8×C151—21no—
180C4⋊C8×C151—21no—
181C4⋊C8×C151—21no—
182C4⋊C8×C151—21no—
183C4⋊C8×C151—21no—
184C4⋊C8×C151—21no—
185C4⋊C8×C151—21no—
186C22⋊C8×C151—21no—
187C22⋊C8×C151—21no—
188C22⋊C8×C151—21no—
189C22⋊C8×C151—21no—
190C22⋊C8×C151—21no—
191C22⋊C8×C151—21no—
192C22⋊C8×C151—21no—
193#97×C151—21no—
194#97×C151—21no—
195#97×C151—21no—
196#97×C151C2311yescharacteristic
197#97×C151C2311yescharacteristic
198#97×C151C2311yescharacteristic
199#97×C151C2311yescharacteristic
200#97×C151C2311yescharacteristic
201#97×C151C2311yescharacteristic
202#97×C151C2311yescharacteristic
203#97×C151C2311yescharacteristic
204C4×C8×C151—21no—
205C4×C8×C151—21no—
206C24×C151—21no—
207C24×C151—21no—
208#41×C151—42no—
209#41×C151—81no—
210#41×C151—81no—
211C2×Q8×C151—21no—
212C2×Q8×C151—21no—
213C2×Q8×C151—81no—
214C2×Q8×C151—81no—
215C2×Q8×C151C22⋊C411yescharacteristic
216C2×Q8×C151C22×C411yescharacteristic
217C2×Q8×C151C22×C411yescharacteristic
218C2×Q8×C151C22×C411yescharacteristic
219C2×D4×C151—21no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—44no—
229C2×D4×C151—81no—
230C2×D4×C151—81no—
231C2×D4×C151C22⋊C411yescharacteristic
232C2×D4×C151C22⋊C411yescharacteristic
233C2×D4×C151C22⋊C411yescharacteristic
234C2×D4×C151C22×C411yescharacteristic
235C2×D4×C151C22×C411yescharacteristic
236C2×D4×C151C22×C411yescharacteristic
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151C22×C411yescharacteristic
245C22×C4×C151C22×C411yescharacteristic
246C22×C4×C151C22×C411yescharacteristic
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2×D411yescharacteristic
253M16×C151—42no—
254M16×C151—42no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—42no—
264C2×C8×C151—42no—
265C2×C8×C151—42no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151C22⋊C411yescharacteristic
277C4⋊C4×C151C22⋊C411yescharacteristic
278C4⋊C4×C151C22⋊C411yescharacteristic
279C4⋊C4×C151C22⋊C411yescharacteristic
280C4⋊C4×C151C22⋊C411yescharacteristic
281C4⋊C4×C151C22⋊C411yescharacteristic
282C4⋊C4×C151C22×C411yescharacteristic
283C4⋊C4×C151C22×C411yescharacteristic
284C22⋊C4×C151—21no—
285C22⋊C4×C151—21no—
286C22⋊C4×C151—21no—
287C22⋊C4×C151—21no—
288C22⋊C4×C151—21no—
289C22⋊C4×C151—21no—
290C22⋊C4×C151—21no—
291C22⋊C4×C151—21no—
292C22⋊C4×C151—21no—
293C22⋊C4×C151—21no—
294C22⋊C4×C151—21no—
295C22⋊C4×C151—21no—
296C22⋊C4×C151—21no—
297C22⋊C4×C151—21no—
298C22⋊C4×C151—21no—
299C22⋊C4×C151—21no—
300C22⋊C4×C151—21no—
301C22⋊C4×C151—21no—
302C22⋊C4×C151—21no—
303C22⋊C4×C151—21no—
304C22⋊C4×C151—21no—
305C22⋊C4×C151—21no—
306C22⋊C4×C151—21no—
307C22⋊C4×C151C22⋊C411yescharacteristic
308C22⋊C4×C151C22⋊C411yescharacteristic
309C22⋊C4×C151C22⋊C411yescharacteristic
310C22⋊C4×C151C22⋊C411yescharacteristic
311C22⋊C4×C151C22⋊C411yescharacteristic
312C22⋊C4×C151C22⋊C411yescharacteristic
313C42×C151—21no—
314C42×C151—21no—
315C42×C151—21no—
316C42×C151C22×C411yescharacteristic
317C42×C151C22×C411yescharacteristic
318C42×C151C22×C411yescharacteristic
319C42×C151C2×D411yescharacteristic
320C42×C151C2×D411yescharacteristic
321C42×C151C2×D411yescharacteristic
322C42×C151C2×D411yescharacteristic
323C42×C151C2×D411yescharacteristic
324C42×C151C2×D411yescharacteristic
325C42×C151C2411yescharacteristic
326C23×C151—21no—
327C23×C151—21no—
328C23×C151—21no—
329C23×C151—42no—
330C23×C151—42no—
331C23×C151—81no—
332C23×C151—81no—
333C23×C151—81no—
334C23×C151—81no—
335C23×C151C2×C22⋊C411yescharacteristic
336C23×C151C2×C22⋊C411yescharacteristic
337C23×C151C2×C22⋊C411yescharacteristic
338Q8×C151—41no—
339Q8×C151—41no—
340Q8×C151—41no—
341Q8×C151—41no—
342Q8×C151—81no—
343Q8×C151—81no—
344D4×C151—22no—
345D4×C151—22no—
346D4×C151—41no—
347D4×C151—41no—
348D4×C151—41no—
349D4×C151—41no—
350D4×C151—42no—
351D4×C151—42no—
352D4×C151—42no—
353D4×C151—81no—
354D4×C151—81no—
355D4×C151—81no—
356D4×C151—81no—
357D4×C151—81no—
358D4×C151—81no—
359C2×C4×C151—22no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—21no—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—42no—
374C2×C4×C151—81no—
375C2×C4×C151—81no—
376C2×C4×C151—81no—
377C2×C4×C151—81no—
378C2×C4×C151—81no—
379C2×C4×C151—81no—
380C2×C4×C151C2×C22⋊C411yescharacteristic
381C2×C4×C151C2×C22⋊C411yescharacteristic
382C2×C4×C151C2×C22⋊C411yescharacteristic
383C2×C4×C151C2×C22⋊C411yescharacteristic
384C2×C4×C151C2×C22⋊C411yescharacteristic
385C2×C4×C151C2×C22⋊C411yescharacteristic
386C2×C4×C151C2×C22⋊C411yescharacteristic
387C2×C4×C151C2×C22⋊C411yescharacteristic
388C2×C4×C151C2×C22⋊C411yescharacteristic
389C2×C4×C151C23×C411yescharacteristic
390C2×C4×C151C22×D411yescharacteristic
391C2×C4×C151C22×D411yescharacteristic
392C8×C151—22no—
393C8×C151—41no—
394C8×C151—41no—
395C8×C151—41no—
396C8×C151—41no—
397C8×C151—41no—
398C8×C151—41no—
399C8×C151—41no—
400C22×C151—21no—
401C22×C151—21no—
402C22×C151—21no—
403C22×C151—21no—
404C22×C151—21no—
405C22×C151—21no—
406C22×C151—21no—
407C22×C151—21no—
408C22×C151—41no—
409C22×C151—41no—
410C22×C151—41no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—162no—
418C22×C151—162no—
419C22×C151#42112yes—
420C22×C151C22×C22⋊C411yescharacteristic
421C4×C151—21no—
422C4×C151—21no—
423C4×C151—21no—
424C4×C151—21no—
425C4×C151—21no—
426C4×C151—21no—
427C4×C151—21no—
428C4×C151—21no—
429C4×C151—21no—
430C4×C151—21no—
431C4×C151—21no—
432C4×C151—21no—
433C4×C151—41no—
434C4×C151—41no—
435C4×C151—41no—
436C4×C151—41no—
437C4×C151—41no—
438C2×C151—22no—
439C2×C151—41no—
440C2×C151—41no—
441C2×C151—81no—
442C2×C151—81no—
443C2×C151—81no—
444C2×C151#288811yescharacteristic
445C2×C151C2×#42111yescharacteristic
446C2×C151#290111yescharacteristic
447#17679C15111yesmaximal, characteristic, direct product factor, Sylow
448C151#1767911yescharacteristic, direct product factor, Sylow
449#3514C2×C15111yescharacteristic
450#2970C2×C15111yescharacteristic, complemented
451#2923C2×C15111yescharacteristic, complemented
452#1536C2×C15111yescharacteristic, complemented
453#1535C2×C15111yescharacteristic, complemented
454#1535C2×C15111yescharacteristic, complemented
455#1533C2×C15111yescharacteristic, complemented
456#1532C2×C15111yescharacteristic, complemented
457#1532C2×C15111yescharacteristic, complemented
458#1530C2×C15111yescharacteristic, complemented
459#1529C2×C15111yescharacteristic, complemented
460#1527C2×C15111yescharacteristic, complemented
461#1527C2×C15111yescharacteristic, complemented
462#1524C2×C15111yescharacteristic, complemented
463C2×#329C2×C15111yescharacteristic, complemented
464#559C4×C15111yescharacteristic
465#556C4×C15111yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469D4×Q8C4×C15111yescharacteristic
470#548C4×C15111yescharacteristic
471#548C4×C15111yescharacteristic
472#546—21no—
473#546C4×C15111yescharacteristic
474#546C4×C15111yescharacteristic
475D42C4×C15111yescharacteristic
476#542—21no—
477#538—21no—
478#538—21no—
479#532C22×C15111yescharacteristic
480#529C22×C15111yescharacteristic
481#529C22×C15111yescharacteristic
482#529C22×C15111yescharacteristic
483C2×#124C22×C15111yescharacteristic
484C2×#124C22×C15111yescharacteristic
485#518—21no—
486C4×#41C22×C15111yescharacteristic
487#446—21no—
488#435—21no—
489#435—21no—
490C8×D4—21no—
491#433—21no—
492#433—21no—
493#432C22×C15111yescharacteristic, complemented
494#432C22×C15111yescharacteristic, complemented
495#432C22×C15111yescharacteristic, complemented
496#432C22×C15111yescharacteristic, complemented
497#432C22×C15111yescharacteristic, complemented
498#432C22×C15111yescharacteristic, complemented
499#432C22×C15111yescharacteristic, complemented
500#424—21no—
501#408—21no—
502C4×M16C22×C15111yescharacteristic, complemented
503C4×M16C22×C15111yescharacteristic, complemented
504C2×#97C22×C15111yescharacteristic, complemented
505C2×#97C22×C15111yescharacteristic, complemented
506C2×#97C22×C15111yescharacteristic, complemented
507#330C22×C15111yescharacteristic, complemented
508#330C22×C15111yescharacteristic, complemented
509#330C22×C15111yescharacteristic, complemented
510#330C22×C15111yescharacteristic, complemented
511#329C22×C15111yescharacteristic
512#329C22×C15111yescharacteristic
513#329C22×C15111yescharacteristic
514#329C22×C15111yescharacteristic
515#329C22×C15111yescharacteristic, complemented
516#329C22×C15111yescharacteristic, complemented
517#329C22×C15111yescharacteristic, complemented
518#329C22×C15111yescharacteristic, complemented
519#329C22×C15111yescharacteristic, complemented
520#329C22×C15111yescharacteristic, complemented
521#329C22×C15111yescharacteristic, complemented
522#329C22×C15111yescharacteristic, complemented
523C2×#41C2×C4×C15111yescharacteristic
524C2×#41C2×C4×C15111yescharacteristic
525C2×#41D4×C15111yescharacteristic
526C22×Q8C2×C4×C15111yescharacteristic
527C22×Q8C2×C4×C15111yescharacteristic
528C22×D4—21no—
529C22×D4C2×C4×C15111yescharacteristic
530C22×D4C2×C4×C15111yescharacteristic
531C2×M16—21no—
532C2×M16—21no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8C2×C4×C15111yescharacteristic
538#127C2×C4×C15111yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#125C23×C15111yescharacteristic
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#124—21no—
550#124—21no—
551#124—21no—
552#124C2×C4×C15111yescharacteristic
553#124C2×C4×C15111yescharacteristic
554#124C2×C4×C15111yescharacteristic
555#124C2×C4×C15111yescharacteristic
556#124C23×C15111yescharacteristic
557#124C23×C15111yescharacteristic
558#124C23×C15111yescharacteristic
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8C2×C4×C15111yescharacteristic
572C22⋊Q8C2×C4×C15111yescharacteristic
573C22⋊Q8C2×C4×C15111yescharacteristic
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121C2×C4×C15111yescharacteristic
582#121C2×C4×C15111yescharacteristic
583#121C2×C4×C15111yescharacteristic
584#120—21no—
585#120—21no—
586#120—21no—
587#120—21no—
588C4×Q8C2×C4×C15111yescharacteristic
589C4×Q8C2×C4×C15111yescharacteristic
590C4×Q8C2×C4×C15111yescharacteristic
591C4×Q8C2×C4×C15111yescharacteristic
592C4×Q8D4×C15111yescharacteristic
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4C2×C4×C15111yescharacteristic
603C4×D4C2×C4×C15111yescharacteristic
604C4×D4C2×C4×C15111yescharacteristic
605C4×D4C2×C4×C15111yescharacteristic
606C4×D4C2×C4×C15111yescharacteristic
607C4×D4C2×C4×C15111yescharacteristic
608C4×D4D4×C15111yescharacteristic
609C4×D4D4×C15111yescharacteristic
610C4×D4D4×C15111yescharacteristic
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117D4×C15111yescharacteristic
616#117D4×C15111yescharacteristic
617#117D4×C15111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C42C23×C15111yescharacteristic
625C2×C42C23×C15111yescharacteristic
626C2×C42C23×C15111yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640C22⋊C8—21no—
641#97—21no—
642#97—21no—
643#97—21no—
644#97C23×C15111yescharacteristic
645#97C23×C15111yescharacteristic
646#97C23×C15111yescharacteristic
647#97C23×C15111yescharacteristic
648#97C23×C15111yescharacteristic
649#97C23×C15111yescharacteristic
650#97C23×C15111yescharacteristic
651#97C23×C15111yescharacteristic
652C4×C8—21no—
653C4×C8—21no—
654C24—21no—
655C24—21no—
656#41—42no—
657#41—81no—
658#41—81no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—81no—
662C2×Q8—81no—
663C2×Q8C22⋊C4×C15111yescharacteristic
664C2×Q8C22×C4×C15111yescharacteristic
665C2×Q8C22×C4×C15111yescharacteristic
666C2×Q8C22×C4×C15111yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C22⋊C4×C15111yescharacteristic
680C2×D4C22⋊C4×C15111yescharacteristic
681C2×D4C22⋊C4×C15111yescharacteristic
682C2×D4C22×C4×C15111yescharacteristic
683C2×D4C22×C4×C15111yescharacteristic
684C2×D4C22×C4×C15111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C22×C4×C15111yescharacteristic
693C22×C4C22×C4×C15111yescharacteristic
694C22×C4C22×C4×C15111yescharacteristic
695C22×C4C2×D4×C15111yescharacteristic
696C22×C4C2×D4×C15111yescharacteristic
697C22×C4C2×D4×C15111yescharacteristic
698C22×C4C2×D4×C15111yescharacteristic
699C22×C4C2×D4×C15111yescharacteristic
700C22×C4C2×D4×C15111yescharacteristic
701M16—42no—
702M16—42no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—42no—
712C2×C8—42no—
713C2×C8—42no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4C22⋊C4×C15111yescharacteristic
725C4⋊C4C22⋊C4×C15111yescharacteristic
726C4⋊C4C22⋊C4×C15111yescharacteristic
727C4⋊C4C22⋊C4×C15111yescharacteristic
728C4⋊C4C22⋊C4×C15111yescharacteristic
729C4⋊C4C22⋊C4×C15111yescharacteristic
730C4⋊C4C22×C4×C15111yescharacteristic
731C4⋊C4C22×C4×C15111yescharacteristic
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—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4C22⋊C4×C15111yescharacteristic
756C22⋊C4C22⋊C4×C15111yescharacteristic
757C22⋊C4C22⋊C4×C15111yescharacteristic
758C22⋊C4C22⋊C4×C15111yescharacteristic
759C22⋊C4C22⋊C4×C15111yescharacteristic
760C22⋊C4C22⋊C4×C15111yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42C22×C4×C15111yescharacteristic
765C42C22×C4×C15111yescharacteristic
766C42C22×C4×C15111yescharacteristic
767C42C2×D4×C15111yescharacteristic
768C42C2×D4×C15111yescharacteristic
769C42C2×D4×C15111yescharacteristic
770C42C2×D4×C15111yescharacteristic
771C42C2×D4×C15111yescharacteristic
772C42C2×D4×C15111yescharacteristic
773C42C24×C15111yescharacteristic
774C23—21no—
775C23—21no—
776C23—21no—
777C23—42no—
778C23—42no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C2×C22⋊C4×C15111yescharacteristic
784C23C2×C22⋊C4×C15111yescharacteristic
785C23C2×C22⋊C4×C15111yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4C2×C22⋊C4×C15111yescharacteristic
829C2×C4C2×C22⋊C4×C15111yescharacteristic
830C2×C4C2×C22⋊C4×C15111yescharacteristic
831C2×C4C2×C22⋊C4×C15111yescharacteristic
832C2×C4C2×C22⋊C4×C15111yescharacteristic
833C2×C4C2×C22⋊C4×C15111yescharacteristic
834C2×C4C2×C22⋊C4×C15111yescharacteristic
835C2×C4C2×C22⋊C4×C15111yescharacteristic
836C2×C4C2×C22⋊C4×C15111yescharacteristic
837C2×C4C23×C4×C15111yescharacteristic
838C2×C4C22×D4×C15111yescharacteristic
839C2×C4C22×D4×C15111yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—162no—
866C22—162no—
867C22#421×C15112yes—
868C22C22×C22⋊C4×C15111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2#2888×C15111yescharacteristic
893C2C2×#421×C15111yescharacteristic
894C2#2901×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radical#3514×C151C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C4×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2970×C151C2semidirect
3. #2923×C151C2semidirect
4. #1536×C151C2semidirect
5. #1535×C151C2semidirect
6. #1535×C151C2semidirect
7. #1533×C151C2semidirect
8. #1532×C151C2semidirect
9. #1532×C151C2semidirect
10. #1530×C151C2semidirect
11. #1529×C151C2semidirect
12. #1527×C151C2semidirect
13. #1527×C151C2semidirect
14. #1524×C151C2semidirect
15. C2×#329×C151C2semidirect
45. #432×C151C22semidirect
46. #432×C151C22semidirect
47. #432×C151C22semidirect
48. #432×C151C22semidirect
49. #432×C151C22semidirect
50. #432×C151C22semidirect
51. #432×C151C22semidirect
54. C4×M16×C151C22semidirect
55. C4×M16×C151C22semidirect
56. C2×#97×C151C22semidirect
57. C2×#97×C151C22semidirect
58. C2×#97×C151C22semidirect
59. #330×C151C22semidirect
60. #330×C151C22semidirect
61. #330×C151C22semidirect
62. #330×C151C22semidirect
67. #329×C151C22semidirect
68. #329×C151C22semidirect
69. #329×C151C22semidirect
70. #329×C151C22semidirect
71. #329×C151C22semidirect
72. #329×C151C22semidirect
73. #329×C151C22semidirect
74. #329×C151C22semidirect
447. #17679C151direct (N × H)
448. C151#17679direct (N × H)
450. #2970C2×C151semidirect
451. #2923C2×C151semidirect
452. #1536C2×C151semidirect
453. #1535C2×C151semidirect
454. #1535C2×C151semidirect
455. #1533C2×C151semidirect
456. #1532C2×C151semidirect
457. #1532C2×C151semidirect
458. #1530C2×C151semidirect
459. #1529C2×C151semidirect
460. #1527C2×C151semidirect
461. #1527C2×C151semidirect
462. #1524C2×C151semidirect
463. C2×#329C2×C151semidirect
493. #432C22×C151semidirect
494. #432C22×C151semidirect
495. #432C22×C151semidirect
496. #432C22×C151semidirect
497. #432C22×C151semidirect
498. #432C22×C151semidirect
499. #432C22×C151semidirect
502. C4×M16C22×C151semidirect
503. C4×M16C22×C151semidirect
504. C2×#97C22×C151semidirect
505. C2×#97C22×C151semidirect
506. C2×#97C22×C151semidirect
507. #330C22×C151semidirect
508. #330C22×C151semidirect
509. #330C22×C151semidirect
510. #330C22×C151semidirect
515. #329C22×C151semidirect
516. #329C22×C151semidirect
517. #329C22×C151semidirect
518. #329C22×C151semidirect
519. #329C22×C151semidirect
520. #329C22×C151semidirect
521. #329C22×C151semidirect
522. #329C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3514×C1512
#2970×C1512
#2923×C1512
#1536×C1512
#1535×C1512
#1533×C1512
#1532×C1512
#1530×C1512
#1529×C1512
#1527×C1512
#1524×C1512
C2×#329×C1512
#17679151