Finite Group Databasebeta

← C151×#18032 #50322957

Subgroups — C151×#18032 #50322957

Order 38656.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3104×C151C211yesmaximal, characteristic
2#2986×C151C211yesmaximal, characteristic
3#2984×C151C211yesmaximal, characteristic
4#1593×C151C211yesmaximal, characteristic, complemented
5#1591×C151C211yesmaximal, characteristic, complemented
6#1587×C151C211yesmaximal, characteristic, complemented
7#1587×C151C211yesmaximal, characteristic, complemented
8#1584×C151C211yesmaximal, characteristic, complemented
9#1584×C151C211yesmaximal, characteristic, complemented
10#1579×C151C211yesmaximal, characteristic, complemented
11C8×Q16×C151C211yesmaximal, characteristic, complemented
12#1572×C151C211yesmaximal, characteristic
13#1497×C151C211yesmaximal, characteristic
14#1479×C151C211yesmaximal, characteristic
15#1454×C151C211yesmaximal, characteristic
16#533×C151C2211yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18#484×C151C411yescharacteristic
19#484×C151C411yescharacteristic
20#477×C151C411yescharacteristic
21#477×C151C411yescharacteristic
22#462×C151C411yescharacteristic
23#462×C151C411yescharacteristic
24#451×C151C411yescharacteristic
25#451×C151C411yescharacteristic
26#446×C151—21no—
27#446×C151—21no—
28#446×C151—21no—
29#446×C151C2211yescharacteristic
30#446×C151C2211yescharacteristic
31#446×C151C2211yescharacteristic
32#446×C151C2211yescharacteristic
33C8×Q8×C151—21no—
34C8×Q8×C151C2211yescharacteristic
35C8×Q8×C151C2211yescharacteristic
36C8×Q8×C151C2211yescharacteristic
37C8×Q8×C151C2211yescharacteristic
38C4×Q16×C151C2211yescharacteristic
39C4×Q16×C151C2211yescharacteristic
40C4×Q16×C151C2211yescharacteristic
41C4×Q16×C151C2211yescharacteristic
42#433×C151—21no—
43#433×C151—21no—
44#432×C151—21no—
45#432×C151C2211yescharacteristic
46#431×C151—21no—
47#431×C151C2211yescharacteristic
48#431×C151C2211yescharacteristic
49#431×C151C2211yescharacteristic
50#431×C151C2211yescharacteristic
51#335×C151C2211yescharacteristic
52#335×C151C2211yescharacteristic
53#334×C151C2211yescharacteristic
54#334×C151C2211yescharacteristic
55Q8⋊C8×C151C2211yescharacteristic
56Q8⋊C8×C151C2211yescharacteristic
57Q8⋊C8×C151C2211yescharacteristic
58Q8⋊C8×C151C2211yescharacteristic
59Q8⋊C8×C151C2211yescharacteristic
60Q8⋊C8×C151C2211yescharacteristic
61Q8⋊C8×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63#322×C151C2211yescharacteristic
64#322×C151C2211yescharacteristic
65#322×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C22×Q8×C151C2×C411yescharacteristic
68C2×Q16×C151C2×C411yescharacteristic
69C2×Q16×C151C2×C411yescharacteristic
70C2×Q16×C151C2×C411yescharacteristic
71C2×Q16×C151C2×C411yescharacteristic
72C4⋊Q8×C151C2×C411yescharacteristic
73C4⋊Q8×C151C2×C411yescharacteristic
74#125×C151—21no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151C2×C411yescharacteristic
77C22⋊Q8×C151C2×C411yescharacteristic
78C4×Q8×C151—21no—
79C4×Q8×C151—21no—
80C4×Q8×C151—21no—
81C4×Q8×C151C2×C411yescharacteristic
82C4×Q8×C151C2×C411yescharacteristic
83C4×Q8×C151C2311yescharacteristic
84C4×Q8×C151C2311yescharacteristic
85C4×Q8×C151C2311yescharacteristic
86C4×Q8×C151C2311yescharacteristic
87#117×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151C2×C411yescharacteristic
90C2×C42×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151C2×C411yescharacteristic
93#107×C151C2×C411yescharacteristic
94#107×C151C2×C411yescharacteristic
95#107×C151C2×C411yescharacteristic
96C4⋊C8×C151—21no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151—21no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151—21no—
101C4⋊C8×C151—21no—
102C4⋊C8×C151—21no—
103C4⋊C8×C151—21no—
104C4⋊C8×C151—21no—
105C4⋊C8×C151C2×C411yescharacteristic
106C4⋊C8×C151C2×C411yescharacteristic
107C4⋊C8×C151D411yescharacteristic
108C4⋊C8×C151D411yescharacteristic
109C4⋊C8×C151C2311yescharacteristic
110C4⋊C8×C151C2311yescharacteristic
111C4⋊C8×C151C2311yescharacteristic
112C4⋊C8×C151C2311yescharacteristic
113#103×C151C2×C411yescharacteristic
114#103×C151C2×C411yescharacteristic
115#103×C151C2×C411yescharacteristic
116#103×C151C2×C411yescharacteristic
117#103×C151C2×C411yescharacteristic
118#103×C151C2×C411yescharacteristic
119#103×C151C2×C411yescharacteristic
120#103×C151C2×C411yescharacteristic
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123C22⋊C8×C151—21no—
124C22⋊C8×C151C2×C411yescharacteristic
125C22⋊C8×C151C2×C411yescharacteristic
126C22⋊C8×C151D411yescharacteristic
127C22⋊C8×C151D411yescharacteristic
128#97×C151—21no—
129#97×C151—21no—
130#97×C151—21no—
131#97×C151—21no—
132#97×C151—21no—
133C4×C8×C151—21no—
134C4×C8×C151—21no—
135C4×C8×C151—21no—
136C4×C8×C151—21no—
137C4×C8×C151—21no—
138C4×C8×C151C2311yescharacteristic
139C4×C8×C151C2311yescharacteristic
140C4×C8×C151C2311yescharacteristic
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—22no—
147C2×Q8×C151—41no—
148C2×Q8×C151C22×C411yescharacteristic
149C2×Q8×C151C22×C411yescharacteristic
150C2×Q8×C151C22×C411yescharacteristic
151C2×Q8×C151C22×C411yescharacteristic
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151C22×C411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151#4111yescharacteristic
157Q16×C151—22no—
158Q16×C151—22no—
159Q16×C151—41no—
160Q16×C151—41no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151C22×C411yescharacteristic
168C2×C8×C151C22×C411yescharacteristic
169C2×C8×C151C22×C411yescharacteristic
170C2×C8×C151C22×C411yescharacteristic
171C2×C8×C151C2×D411yescharacteristic
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151C22×C411yescharacteristic
188C4⋊C4×C151C22×C411yescharacteristic
189C4⋊C4×C151C22×C411yescharacteristic
190C4⋊C4×C151C22×C411yescharacteristic
191C22⋊C4×C151—21no—
192C22⋊C4×C151—21no—
193C42×C151—21no—
194C42×C151—21no—
195C42×C151—21no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151C22×C411yescharacteristic
200C42×C151C2×D411yescharacteristic
201C42×C151#4111yescharacteristic
202C42×C151C2411yescharacteristic
203C23×C151C4×D411yescharacteristic
204Q8×C151—21no—
205Q8×C151—21no—
206Q8×C151—21no—
207Q8×C151—21no—
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—42no—
212Q8×C151—42no—
213Q8×C151#13112yes—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—41no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151C4×D411yescharacteristic
230C2×C4×C151C4×D411yescharacteristic
231C2×C4×C151C4×D411yescharacteristic
232C2×C4×C151C23×C411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C2×#4111yescharacteristic
235C8×C151—21no—
236C8×C151—21no—
237C8×C151—21no—
238C8×C151—21no—
239C8×C151—21no—
240C8×C151—21no—
241C8×C151—21no—
242C8×C151—21no—
243C8×C151—41no—
244C8×C151—41no—
245C8×C151—41no—
246C8×C151—41no—
247C8×C151—41no—
248C8×C151—41no—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151C2×C4×D411yescharacteristic
253C4×C151—21no—
254C4×C151—22no—
255C4×C151—21no—
256C4×C151—21no—
257C4×C151—21no—
258C4×C151—41no—
259C4×C151—41no—
260C4×C151—41no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—41no—
264C4×C151—41no—
265C4×C151C2×#13111yescharacteristic
266C4×C151#56811yescharacteristic
267C4×C151#57811yescharacteristic
268C4×C151#57811yescharacteristic
269C2×C151—41no—
270C2×C151#293311yescharacteristic
271C2×C151#295011yescharacteristic
272C2×C151#295511yescharacteristic
273#18032C15111yesmaximal, characteristic, direct product factor, Sylow
274C151#1803211yescharacteristic, direct product factor, Sylow
275#3104C2×C15111yescharacteristic
276#2986C2×C15111yescharacteristic
277#2984C2×C15111yescharacteristic
278#1593C2×C15111yescharacteristic, complemented
279#1591C2×C15111yescharacteristic, complemented
280#1587C2×C15111yescharacteristic, complemented
281#1587C2×C15111yescharacteristic, complemented
282#1584C2×C15111yescharacteristic, complemented
283#1584C2×C15111yescharacteristic, complemented
284#1579C2×C15111yescharacteristic, complemented
285C8×Q16C2×C15111yescharacteristic, complemented
286#1572C2×C15111yescharacteristic
287#1497C2×C15111yescharacteristic
288#1479C2×C15111yescharacteristic
289#1454C2×C15111yescharacteristic
290#533C22×C15111yescharacteristic
291C2×C4×Q8C22×C15111yescharacteristic
292#484C4×C15111yescharacteristic
293#484C4×C15111yescharacteristic
294#477C4×C15111yescharacteristic
295#477C4×C15111yescharacteristic
296#462C4×C15111yescharacteristic
297#462C4×C15111yescharacteristic
298#451C4×C15111yescharacteristic
299#451C4×C15111yescharacteristic
300#446—21no—
301#446—21no—
302#446—21no—
303#446C22×C15111yescharacteristic
304#446C22×C15111yescharacteristic
305#446C22×C15111yescharacteristic
306#446C22×C15111yescharacteristic
307C8×Q8—21no—
308C8×Q8C22×C15111yescharacteristic
309C8×Q8C22×C15111yescharacteristic
310C8×Q8C22×C15111yescharacteristic
311C8×Q8C22×C15111yescharacteristic
312C4×Q16C22×C15111yescharacteristic
313C4×Q16C22×C15111yescharacteristic
314C4×Q16C22×C15111yescharacteristic
315C4×Q16C22×C15111yescharacteristic
316#433—21no—
317#433—21no—
318#432—21no—
319#432C22×C15111yescharacteristic
320#431—21no—
321#431C22×C15111yescharacteristic
322#431C22×C15111yescharacteristic
323#431C22×C15111yescharacteristic
324#431C22×C15111yescharacteristic
325#335C22×C15111yescharacteristic
326#335C22×C15111yescharacteristic
327#334C22×C15111yescharacteristic
328#334C22×C15111yescharacteristic
329Q8⋊C8C22×C15111yescharacteristic
330Q8⋊C8C22×C15111yescharacteristic
331Q8⋊C8C22×C15111yescharacteristic
332Q8⋊C8C22×C15111yescharacteristic
333Q8⋊C8C22×C15111yescharacteristic
334Q8⋊C8C22×C15111yescharacteristic
335Q8⋊C8C22×C15111yescharacteristic
336Q8⋊C8C22×C15111yescharacteristic
337#322C22×C15111yescharacteristic
338#322C22×C15111yescharacteristic
339#322C22×C15111yescharacteristic
340C82C22×C15111yescharacteristic
341C22×Q8C2×C4×C15111yescharacteristic
342C2×Q16C2×C4×C15111yescharacteristic
343C2×Q16C2×C4×C15111yescharacteristic
344C2×Q16C2×C4×C15111yescharacteristic
345C2×Q16C2×C4×C15111yescharacteristic
346C4⋊Q8C2×C4×C15111yescharacteristic
347C4⋊Q8C2×C4×C15111yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C2×C4×C15111yescharacteristic
351C22⋊Q8C2×C4×C15111yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C2×C4×C15111yescharacteristic
356C4×Q8C2×C4×C15111yescharacteristic
357C4×Q8C23×C15111yescharacteristic
358C4×Q8C23×C15111yescharacteristic
359C4×Q8C23×C15111yescharacteristic
360C4×Q8C23×C15111yescharacteristic
361#117—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C2×C4×C15111yescharacteristic
364C2×C42—21no—
365C2×C42C23×C15111yescharacteristic
366#107C2×C4×C15111yescharacteristic
367#107C2×C4×C15111yescharacteristic
368#107C2×C4×C15111yescharacteristic
369#107C2×C4×C15111yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8C2×C4×C15111yescharacteristic
380C4⋊C8C2×C4×C15111yescharacteristic
381C4⋊C8D4×C15111yescharacteristic
382C4⋊C8D4×C15111yescharacteristic
383C4⋊C8C23×C15111yescharacteristic
384C4⋊C8C23×C15111yescharacteristic
385C4⋊C8C23×C15111yescharacteristic
386C4⋊C8C23×C15111yescharacteristic
387#103C2×C4×C15111yescharacteristic
388#103C2×C4×C15111yescharacteristic
389#103C2×C4×C15111yescharacteristic
390#103C2×C4×C15111yescharacteristic
391#103C2×C4×C15111yescharacteristic
392#103C2×C4×C15111yescharacteristic
393#103C2×C4×C15111yescharacteristic
394#103C2×C4×C15111yescharacteristic
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8C2×C4×C15111yescharacteristic
399C22⋊C8C2×C4×C15111yescharacteristic
400C22⋊C8D4×C15111yescharacteristic
401C22⋊C8D4×C15111yescharacteristic
402#97—21no—
403#97—21no—
404#97—21no—
405#97—21no—
406#97—21no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8C23×C15111yescharacteristic
413C4×C8C23×C15111yescharacteristic
414C4×C8C23×C15111yescharacteristic
415C4×C8C23×C15111yescharacteristic
416C4×C8C23×C15111yescharacteristic
417C4×C8C23×C15111yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—41no—
422C2×Q8C22×C4×C15111yescharacteristic
423C2×Q8C22×C4×C15111yescharacteristic
424C2×Q8C22×C4×C15111yescharacteristic
425C2×Q8C22×C4×C15111yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4C22×C4×C15111yescharacteristic
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4#41×C15111yescharacteristic
431Q16—22no—
432Q16—22no—
433Q16—41no—
434Q16—41no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8C22×C4×C15111yescharacteristic
442C2×C8C22×C4×C15111yescharacteristic
443C2×C8C22×C4×C15111yescharacteristic
444C2×C8C22×C4×C15111yescharacteristic
445C2×C8C2×D4×C15111yescharacteristic
446C2×C8C2×D4×C15111yescharacteristic
447C2×C8C2×D4×C15111yescharacteristic
448C2×C8C2×D4×C15111yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4C22×C4×C15111yescharacteristic
462C4⋊C4C22×C4×C15111yescharacteristic
463C4⋊C4C22×C4×C15111yescharacteristic
464C4⋊C4C22×C4×C15111yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42C22×C4×C15111yescharacteristic
474C42C2×D4×C15111yescharacteristic
475C42#41×C15111yescharacteristic
476C42C24×C15111yescharacteristic
477C23C4×D4×C15111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—42no—
486Q8—42no—
487Q8#131×C15112yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4C4×D4×C15111yescharacteristic
504C2×C4C4×D4×C15111yescharacteristic
505C2×C4C4×D4×C15111yescharacteristic
506C2×C4C23×C4×C15111yescharacteristic
507C2×C4C22×D4×C15111yescharacteristic
508C2×C4C2×#41×C15111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×D4×C15111yescharacteristic
527C4—21no—
528C4—22no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4C2×#131×C15111yescharacteristic
540C4#568×C15111yescharacteristic
541C4#578×C15111yescharacteristic
542C4#578×C15111yescharacteristic
543C2—41no—
544C2#2933×C15111yescharacteristic
545C2#2950×C15111yescharacteristic
546C2#2955×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
socleC22×C151C2×C4×D4
prime radicalC23×C151C4×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ #431×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1593×C151C2semidirect
5. #1591×C151C2semidirect
6. #1587×C151C2semidirect
7. #1587×C151C2semidirect
8. #1584×C151C2semidirect
9. #1584×C151C2semidirect
10. #1579×C151C2semidirect
11. C8×Q16×C151C2semidirect
273. #18032C151direct (N × H)
274. C151#18032direct (N × H)
278. #1593C2×C151semidirect
279. #1591C2×C151semidirect
280. #1587C2×C151semidirect
281. #1587C2×C151semidirect
282. #1584C2×C151semidirect
283. #1584C2×C151semidirect
284. #1579C2×C151semidirect
285. C8×Q16C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3104×C1512
#2986×C1512
#2984×C1512
#1593×C1512
#1591×C1512
#1587×C1512
#1584×C1512
#1579×C1512
C8×Q16×C1512
#1572×C1512
#1497×C1512
#1479×C1512
#1454×C1512
#18032151