Finite Group Databasebeta

← C151×#17949 #50322874

Subgroups — C151×#17949 #50322874

Order 38656.

568 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3107×C151C211yesmaximal, characteristic
2#2989×C151C211yesmaximal, characteristic
3#2985×C151C211yesmaximal, characteristic, complemented
4#1593×C151C211yesmaximal, characteristic, complemented
5#1592×C151C211yesmaximal, characteristic, complemented
6#1591×C151C211yesmaximal, characteristic, complemented
7#1590×C151C211yesmaximal, characteristic, complemented
8#1588×C151C211yesmaximal, characteristic, complemented
9#1587×C151C211yesmaximal, characteristic, complemented
10#1584×C151C211yesmaximal, characteristic, complemented
11#1583×C151C211yesmaximal, characteristic, complemented
12#1573×C151C211yesmaximal, characteristic, complemented
13#1488×C151C211yesmaximal, characteristic
14#1481×C151C211yesmaximal, characteristic, complemented
15#1454×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17C4×#41×C151C2211yescharacteristic
18#485×C151C411yescharacteristic
19#485×C151C411yescharacteristic
20#475×C151C411yescharacteristic
21#474×C151C411yescharacteristic
22#462×C151C411yescharacteristic
23#461×C151C411yescharacteristic
24#452×C151C411yescharacteristic
25#452×C151C411yescharacteristic
26#446×C151—21no—
27#446×C151—21no—
28#446×C151C2211yescharacteristic
29#446×C151C2211yescharacteristic
30#446×C151C2211yescharacteristic
31#446×C151C2211yescharacteristic
32C8×Q8×C151C2211yescharacteristic
33C8×Q8×C151C2211yescharacteristic
34C4×Q16×C151C2211yescharacteristic
35C4×Q16×C151C2211yescharacteristic
36C4×SD16×C151C2211yescharacteristic
37C4×SD16×C151C2211yescharacteristic
38#436×C151C2211yescharacteristic
39#436×C151C2211yescharacteristic
40#435×C151—21no—
41#435×C151—21no—
42#433×C151—21no—
43#433×C151—21no—
44#432×C151—21no—
45#432×C151C2211yescharacteristic
46#431×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#431×C151C2211yescharacteristic
49#423×C151—21no—
50C2×C4⋊C8×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
61D4⋊C8×C151C2211yescharacteristic
62D4⋊C8×C151C2211yescharacteristic
63#322×C151C2211yescharacteristic
64#322×C151C2211yescharacteristic
65#322×C151C2211yescharacteristic
66C82×C151C2211yescharacteristic
67C2×#41×C151C2×C411yescharacteristic
68C2×Q16×C151C2×C411yescharacteristic
69C2×Q16×C151C2×C411yescharacteristic
70C2×SD16×C151C2×C411yescharacteristic
71C2×SD16×C151C2×C411yescharacteristic
72C2×M16×C151—21no—
73C2×M16×C151—21no—
74C22×C8×C151—21no—
75C4⋊Q8×C151C2×C411yescharacteristic
76C4⋊Q8×C151C2×C411yescharacteristic
77#125×C151—21no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151C2×C411yescharacteristic
80C22⋊Q8×C151C2×C411yescharacteristic
81C4×Q8×C151—21no—
82C4×Q8×C151C2×C411yescharacteristic
83C4×Q8×C151C2311yescharacteristic
84C4×Q8×C151C2311yescharacteristic
85C4×Q8×C151C2311yescharacteristic
86C4×D4×C151—21no—
87C4×D4×C151—21no—
88C4×D4×C151C2×C411yescharacteristic
89C4×D4×C151C2311yescharacteristic
90#117×C151—21no—
91#117×C151—21no—
92#117×C151C2×C411yescharacteristic
93C2×C42×C151—21no—
94C2×C42×C151C2311yescharacteristic
95#107×C151C2×C411yescharacteristic
96#107×C151C2×C411yescharacteristic
97#106×C151C2×C411yescharacteristic
98#106×C151C2×C411yescharacteristic
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×C151—21no—
106C4⋊C8×C151—21no—
107C4⋊C8×C151C2×C411yescharacteristic
108C4⋊C8×C151C2×C411yescharacteristic
109C4⋊C8×C151D411yescharacteristic
110C4⋊C8×C151D411yescharacteristic
111C4⋊C8×C151C2311yescharacteristic
112C4⋊C8×C151C2311yescharacteristic
113C4⋊C8×C151C2311yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115#103×C151C2×C411yescharacteristic
116#103×C151C2×C411yescharacteristic
117#103×C151C2×C411yescharacteristic
118#103×C151C2×C411yescharacteristic
119#103×C151C2×C411yescharacteristic
120#103×C151C2×C411yescharacteristic
121#102×C151C2×C411yescharacteristic
122#102×C151C2×C411yescharacteristic
123C22⋊C8×C151—21no—
124C22⋊C8×C151—21no—
125C22⋊C8×C151—21no—
126C22⋊C8×C151—21no—
127C22⋊C8×C151C2×C411yescharacteristic
128C22⋊C8×C151C2×C411yescharacteristic
129C22⋊C8×C151D411yescharacteristic
130C22⋊C8×C151D411yescharacteristic
131#97×C151—21no—
132#97×C151—21no—
133#97×C151—21no—
134#97×C151—21no—
135#97×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
144#41×C151—41no—
145#41×C151—41no—
146C2×Q8×C151—21no—
147C2×Q8×C151C22×C411yescharacteristic
148C2×Q8×C151C22×C411yescharacteristic
149C2×Q8×C151C22×C411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151C22×C411yescharacteristic
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151C22×C411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151#4111yescharacteristic
158Q16×C151—41no—
159Q16×C151—41no—
160SD16×C151—41no—
161SD16×C151—41no—
162M16×C151—81no—
163M16×C151—81no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—81no—
171C2×C8×C151C22×C411yescharacteristic
172C2×C8×C151C22×C411yescharacteristic
173C2×C8×C151C22×C411yescharacteristic
174C2×C8×C151C22×C411yescharacteristic
175C2×C8×C151C2×D411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
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×C151—21no—
188C4⋊C4×C151C22×C411yescharacteristic
189C4⋊C4×C151C22×C411yescharacteristic
190C4⋊C4×C151C22×C411yescharacteristic
191C4⋊C4×C151C22×C411yescharacteristic
192C22⋊C4×C151—21no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151C22×C411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151#4111yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—21no—
207C23×C151C4×D411yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—81no—
215D4×C151—21no—
216D4×C151—21no—
217D4×C151—42no—
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—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—41no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—81no—
234C2×C4×C151C4×D411yescharacteristic
235C2×C4×C151C4×D411yescharacteristic
236C2×C4×C151C4×D411yescharacteristic
237C2×C4×C151C23×C411yescharacteristic
238C2×C4×C151C22×D411yescharacteristic
239C2×C4×C151C2×#4111yescharacteristic
240C8×C151—21no—
241C8×C151—21no—
242C8×C151—21no—
243C8×C151—21no—
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C22×C151—21no—
255C22×C151—21no—
256C22×C151—21no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151C2×C4×D411yescharacteristic
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—21no—
265C4×C151—41no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151#56811yescharacteristic
273C4×C151#56811yescharacteristic
274C4×C151#57711yescharacteristic
275C4×C151#57811yescharacteristic
276C2×C151—41no—
277C2×C151—81no—
278C2×C151#293011yescharacteristic
279C2×C151#294711yescharacteristic
280C2×C151#295711yescharacteristic
281#17949C15111yesmaximal, characteristic, direct product factor, Sylow
282C151#1794911yescharacteristic, direct product factor, Sylow
283#3107C2×C15111yescharacteristic
284#2989C2×C15111yescharacteristic
285#2985C2×C15111yescharacteristic, complemented
286#1593C2×C15111yescharacteristic, complemented
287#1592C2×C15111yescharacteristic, complemented
288#1591C2×C15111yescharacteristic, complemented
289#1590C2×C15111yescharacteristic, complemented
290#1588C2×C15111yescharacteristic, complemented
291#1587C2×C15111yescharacteristic, complemented
292#1584C2×C15111yescharacteristic, complemented
293#1583C2×C15111yescharacteristic, complemented
294#1573C2×C15111yescharacteristic, complemented
295#1488C2×C15111yescharacteristic
296#1481C2×C15111yescharacteristic, complemented
297#1454C2×C15111yescharacteristic, complemented
298#533C22×C15111yescharacteristic
299C4×#41C22×C15111yescharacteristic
300#485C4×C15111yescharacteristic
301#485C4×C15111yescharacteristic
302#475C4×C15111yescharacteristic
303#474C4×C15111yescharacteristic
304#462C4×C15111yescharacteristic
305#461C4×C15111yescharacteristic
306#452C4×C15111yescharacteristic
307#452C4×C15111yescharacteristic
308#446—21no—
309#446—21no—
310#446C22×C15111yescharacteristic
311#446C22×C15111yescharacteristic
312#446C22×C15111yescharacteristic
313#446C22×C15111yescharacteristic
314C8×Q8C22×C15111yescharacteristic
315C8×Q8C22×C15111yescharacteristic
316C4×Q16C22×C15111yescharacteristic
317C4×Q16C22×C15111yescharacteristic
318C4×SD16C22×C15111yescharacteristic
319C4×SD16C22×C15111yescharacteristic
320#436C22×C15111yescharacteristic
321#436C22×C15111yescharacteristic
322#435—21no—
323#435—21no—
324#433—21no—
325#433—21no—
326#432—21no—
327#432C22×C15111yescharacteristic
328#431C22×C15111yescharacteristic
329#431C22×C15111yescharacteristic
330#431C22×C15111yescharacteristic
331#423—21no—
332C2×C4⋊C8C22×C15111yescharacteristic
333#335C22×C15111yescharacteristic
334#335C22×C15111yescharacteristic
335#334C22×C15111yescharacteristic
336#334C22×C15111yescharacteristic
337Q8⋊C8C22×C15111yescharacteristic
338Q8⋊C8C22×C15111yescharacteristic
339Q8⋊C8C22×C15111yescharacteristic
340Q8⋊C8C22×C15111yescharacteristic
341Q8⋊C8C22×C15111yescharacteristic
342Q8⋊C8C22×C15111yescharacteristic
343D4⋊C8C22×C15111yescharacteristic
344D4⋊C8C22×C15111yescharacteristic
345#322C22×C15111yescharacteristic
346#322C22×C15111yescharacteristic
347#322C22×C15111yescharacteristic
348C82C22×C15111yescharacteristic
349C2×#41C2×C4×C15111yescharacteristic
350C2×Q16C2×C4×C15111yescharacteristic
351C2×Q16C2×C4×C15111yescharacteristic
352C2×SD16C2×C4×C15111yescharacteristic
353C2×SD16C2×C4×C15111yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C22×C8—21no—
357C4⋊Q8C2×C4×C15111yescharacteristic
358C4⋊Q8C2×C4×C15111yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C2×C4×C15111yescharacteristic
362C22⋊Q8C2×C4×C15111yescharacteristic
363C4×Q8—21no—
364C4×Q8C2×C4×C15111yescharacteristic
365C4×Q8C23×C15111yescharacteristic
366C4×Q8C23×C15111yescharacteristic
367C4×Q8C23×C15111yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C2×C4×C15111yescharacteristic
371C4×D4C23×C15111yescharacteristic
372#117—21no—
373#117—21no—
374#117C2×C4×C15111yescharacteristic
375C2×C42—21no—
376C2×C42C23×C15111yescharacteristic
377#107C2×C4×C15111yescharacteristic
378#107C2×C4×C15111yescharacteristic
379#106C2×C4×C15111yescharacteristic
380#106C2×C4×C15111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C2×C4×C15111yescharacteristic
390C4⋊C8C2×C4×C15111yescharacteristic
391C4⋊C8D4×C15111yescharacteristic
392C4⋊C8D4×C15111yescharacteristic
393C4⋊C8C23×C15111yescharacteristic
394C4⋊C8C23×C15111yescharacteristic
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397#103C2×C4×C15111yescharacteristic
398#103C2×C4×C15111yescharacteristic
399#103C2×C4×C15111yescharacteristic
400#103C2×C4×C15111yescharacteristic
401#103C2×C4×C15111yescharacteristic
402#103C2×C4×C15111yescharacteristic
403#102C2×C4×C15111yescharacteristic
404#102C2×C4×C15111yescharacteristic
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C2×C4×C15111yescharacteristic
410C22⋊C8C2×C4×C15111yescharacteristic
411C22⋊C8D4×C15111yescharacteristic
412C22⋊C8D4×C15111yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C15111yescharacteristic
421C4×C8C23×C15111yescharacteristic
422C4×C8C23×C15111yescharacteristic
423C4×C8C23×C15111yescharacteristic
424C4×C8C23×C15111yescharacteristic
425C4×C8C23×C15111yescharacteristic
426#41—41no—
427#41—41no—
428C2×Q8—21no—
429C2×Q8C22×C4×C15111yescharacteristic
430C2×Q8C22×C4×C15111yescharacteristic
431C2×Q8C22×C4×C15111yescharacteristic
432C2×D4—21no—
433C2×D4C22×C4×C15111yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C22×C4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4#41×C15111yescharacteristic
440Q16—41no—
441Q16—41no—
442SD16—41no—
443SD16—41no—
444M16—81no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—81no—
453C2×C8C22×C4×C15111yescharacteristic
454C2×C8C22×C4×C15111yescharacteristic
455C2×C8C22×C4×C15111yescharacteristic
456C2×C8C22×C4×C15111yescharacteristic
457C2×C8C2×D4×C15111yescharacteristic
458C2×C8C2×D4×C15111yescharacteristic
459C2×C8C2×D4×C15111yescharacteristic
460C2×C8C2×D4×C15111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4C22×C4×C15111yescharacteristic
471C4⋊C4C22×C4×C15111yescharacteristic
472C4⋊C4C22×C4×C15111yescharacteristic
473C4⋊C4C22×C4×C15111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42C22×C4×C15111yescharacteristic
485C42C2×D4×C15111yescharacteristic
486C42#41×C15111yescharacteristic
487C42C24×C15111yescharacteristic
488C23—21no—
489C23C4×D4×C15111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—81no—
497D4—21no—
498D4—21no—
499D4—42no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4C4×D4×C15111yescharacteristic
517C2×C4C4×D4×C15111yescharacteristic
518C2×C4C4×D4×C15111yescharacteristic
519C2×C4C23×C4×C15111yescharacteristic
520C2×C4C22×D4×C15111yescharacteristic
521C2×C4C2×#41×C15111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×C4×D4×C15111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4#568×C15111yescharacteristic
555C4#568×C15111yescharacteristic
556C4#577×C15111yescharacteristic
557C4#578×C15111yescharacteristic
558C2—41no—
559C2—81no—
560C2#2930×C15111yescharacteristic
561C2#2947×C15111yescharacteristic
562C2#2957×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
socleC22×C151C2×C4×D4
prime radicalC2×#41×C151C2×C4
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
3. #2985×C151C2semidirect
4. #1593×C151C2semidirect
5. #1592×C151C2semidirect
6. #1591×C151C2semidirect
7. #1590×C151C2semidirect
8. #1588×C151C2semidirect
9. #1587×C151C2semidirect
10. #1584×C151C2semidirect
11. #1583×C151C2semidirect
12. #1573×C151C2semidirect
14. #1481×C151C2semidirect
15. #1454×C151C2semidirect
281. #17949C151direct (N × H)
282. C151#17949direct (N × H)
285. #2985C2×C151semidirect
286. #1593C2×C151semidirect
287. #1592C2×C151semidirect
288. #1591C2×C151semidirect
289. #1590C2×C151semidirect
290. #1588C2×C151semidirect
291. #1587C2×C151semidirect
292. #1584C2×C151semidirect
293. #1583C2×C151semidirect
294. #1573C2×C151semidirect
296. #1481C2×C151semidirect
297. #1454C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3107×C1512
#2989×C1512
#2985×C1512
#1593×C1512
#1592×C1512
#1591×C1512
#1590×C1512
#1588×C1512
#1587×C1512
#1584×C1512
#1583×C1512
#1573×C1512
#1488×C1512
#1481×C1512
#1454×C1512
#17949151