Finite Group Databasebeta

← C151×#18416 #50323341

Subgroups — C151×#18416 #50323341

Order 38656.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3535×C151C211yesmaximal, characteristic, complemented
2#3194×C151C211yesmaximal, characteristic, complemented
3#3187×C151C211yesmaximal, characteristic, complemented
4#2661×C151C211yesmaximal, characteristic, complemented
5#1612×C151C211yesmaximal, characteristic, complemented
6#1611×C151C211yesmaximal, characteristic, complemented
7#1609×C151C211yesmaximal, characteristic, complemented
8#1608×C151C211yesmaximal, characteristic, complemented
9#1600×C151C211yesmaximal, characteristic, complemented
10#1599×C151C211yesmaximal, characteristic, complemented
11#1597×C151C211yesmaximal, characteristic, complemented
12#1596×C151C211yesmaximal, characteristic, complemented
13#1508×C151C211yesmaximal, characteristic, complemented
14#1501×C151C211yesmaximal, characteristic, complemented
15#1468×C151C211yesmaximal, characteristic, complemented
16#563×C151—21no—
17#562×C151—21no—
18#554×C151—21no—
19#552×C151—21no—
20#551×C151—21no—
21#551×C151—21no—
22#547×C151—21no—
23#546×C151—21no—
24#544×C151C2211yescharacteristic
25#543×C151C2211yescharacteristic
26#542×C151—21no—
27#539×C151—21no—
28#539×C151—21no—
29#539×C151C2211yescharacteristic
30#538×C151C2211yescharacteristic
31#536×C151—21no—
32#525×C151C2211yescharacteristic
33C2×#123×C151C2211yescharacteristic
34C2×C22⋊Q8×C151C2211yescharacteristic
35C2×#121×C151C2211yescharacteristic
36#483×C151C2211yescharacteristic
37#483×C151C2211yescharacteristic
38#483×C151C2211yescharacteristic
39#482×C151—21no—
40#481×C151—21no—
41#480×C151C2211yescharacteristic
42#469×C151—21no—
43#468×C151—21no—
44#465×C151—21no—
45#465×C151—21no—
46#450×C151C2211yescharacteristic
47#450×C151C2211yescharacteristic
48#450×C151C2211yescharacteristic
49#449×C151—21no—
50#448×C151—21no—
51#447×C151C2211yescharacteristic
52#407×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#398×C151C2211yescharacteristic
55#397×C151C2211yescharacteristic
56#394×C151—21no—
57#394×C151C2211yescharacteristic
58#392×C151—21no—
59#392×C151C2211yescharacteristic
60#390×C151—21no—
61#388×C151—21no—
62C4×C22⋊C4×C151C2211yescharacteristic
63#328×C151C2211yescharacteristic
64#328×C151C2211yescharacteristic
65#328×C151C2211yescharacteristic
66#328×C151C2211yescharacteristic
67#328×C151C2211yescharacteristic
68#328×C151C2211yescharacteristic
69#327×C151C2211yescharacteristic
70#327×C151C2211yescharacteristic
71#324×C151C2211yescharacteristic
72#324×C151C2211yescharacteristic
73#323×C151C2211yescharacteristic
74#323×C151C2211yescharacteristic
75C2×#41×C151—21no—
76C2×#41×C151D411yescharacteristic, complemented
77C22×Q8×C151D411yescharacteristic, complemented
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151D411yescharacteristic
81C22×D4×C151C2311yescharacteristic
82C23×C4×C151C2311yescharacteristic
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C2×SD16×C151—21no—
86C2×D8×C151—21no—
87C2×M16×C151—21no—
88C22×C8×C151—21no—
89C4⋊Q8×C151—21no—
90C4⋊Q8×C151—21no—
91C4⋊Q8×C151—21no—
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#126×C151—21no—
96#126×C151—21no—
97#126×C151—21no—
98#125×C151—21no—
99#125×C151—21no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151—21no—
103#124×C151—21no—
104#124×C151—21no—
105#124×C151—21no—
106#124×C151—21no—
107#123×C151—21no—
108#123×C151—21no—
109#123×C151—21no—
110#123×C151—21no—
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—
118#123×C151—21no—
119#123×C151—21no—
120#123×C151—21no—
121C22⋊Q8×C151—21no—
122C22⋊Q8×C151—21no—
123C22⋊Q8×C151—21no—
124C22⋊Q8×C151—21no—
125C22⋊Q8×C151—21no—
126C22⋊Q8×C151—21no—
127C22⋊Q8×C151—21no—
128C22⋊Q8×C151—21no—
129C22⋊Q8×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151—21no—
134C22⋊Q8×C151—21no—
135C22⋊Q8×C151D411yescharacteristic, complemented
136C22⋊Q8×C151D411yescharacteristic, complemented
137C22⋊Q8×C151D411yescharacteristic, complemented
138C22⋊Q8×C151C2311yescharacteristic
139C22⋊Q8×C151C2311yescharacteristic
140C22⋊Q8×C151C2311yescharacteristic
141#121×C151—21no—
142#121×C151—21no—
143#121×C151—21no—
144#121×C151—21no—
145#121×C151—21no—
146#121×C151—21no—
147#121×C151—21no—
148#121×C151—21no—
149#121×C151D411yescharacteristic, complemented
150#121×C151C2311yescharacteristic
151#120×C151—21no—
152#120×C151—21no—
153C4×Q8×C151—21no—
154C4×D4×C151—21no—
155C4×D4×C151—21no—
156C4×D4×C151—21no—
157C4×D4×C151—21no—
158C4×D4×C151—21no—
159C4×D4×C151—21no—
160C4×D4×C151—21no—
161#117×C151—21no—
162#117×C151—21no—
163#117×C151—21no—
164#117×C151D411yescharacteristic, complemented
165C2×C4⋊C4×C151—21no—
166C2×C4⋊C4×C151—21no—
167C2×C4⋊C4×C151—21no—
168C2×C4⋊C4×C151D411yescharacteristic
169C2×C4⋊C4×C151D411yescharacteristic, complemented
170C2×C4⋊C4×C151C2311yescharacteristic
171C2×C4⋊C4×C151C2311yescharacteristic
172C2×C22⋊C4×C151—21no—
173C2×C22⋊C4×C151—21no—
174C2×C22⋊C4×C151—21no—
175C2×C22⋊C4×C151—21no—
176C2×C22⋊C4×C151—21no—
177C2×C22⋊C4×C151—21no—
178C2×C22⋊C4×C151—21no—
179C2×C22⋊C4×C151—21no—
180C2×C22⋊C4×C151D411yescharacteristic
181C2×C22⋊C4×C151D411yescharacteristic
182C2×C22⋊C4×C151C2311yescharacteristic
183C2×C42×C151—21no—
184#107×C151—21no—
185#106×C151—21no—
186#106×C151—21no—
187#106×C151—21no—
188#103×C151—21no—
189#103×C151—21no—
190#103×C151—21no—
191#102×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196C22⋊C8×C151—21no—
197C22⋊C8×C151—21no—
198C22⋊C8×C151C2311yescharacteristic
199C22⋊C8×C151C2311yescharacteristic
200C22⋊C8×C151C2311yescharacteristic
201C22⋊C8×C151C2311yescharacteristic
202#95×C151—21no—
203#95×C151—21no—
204#95×C151C2311yescharacteristic
205#95×C151C2311yescharacteristic
206C24×C151—21no—
207C24×C151C2×D411yescharacteristic
208C24×C151C2×D411yescharacteristic
209#41×C151—82no—
210#41×C151—81no—
211C2×Q8×C151—21no—
212C2×Q8×C151—21no—
213C2×Q8×C151—21no—
214C2×Q8×C151—81no—
215C2×Q8×C151C2×D411yescharacteristic
216C2×Q8×C151C2×D411yescharacteristic
217C2×Q8×C151C2×D411yescharacteristic
218C2×D4×C151—21no—
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—42no—
228C2×D4×C151—41no—
229C2×D4×C151—41no—
230C2×D4×C151—81no—
231C2×D4×C151—81no—
232C2×D4×C151—81no—
233C2×D4×C151—81no—
234C2×D4×C151—81no—
235C2×D4×C151—81no—
236C2×D4×C151C2×D411yescharacteristic
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×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—81no—
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2×D411yescharacteristic
253C22×C4×C151C2×D411yescharacteristic
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2411yescharacteristic
257SD16×C151—81no—
258SD16×C151—81no—
259SD16×C151—81no—
260D8×C151—81no—
261M16×C151—81no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—81no—
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×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151—21no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151—21no—
292C4⋊C4×C151—81no—
293C4⋊C4×C151C2×D411yescharacteristic
294C4⋊C4×C151C2×D411yescharacteristic
295C4⋊C4×C151C2×D411yescharacteristic
296C4⋊C4×C151C2×D411yescharacteristic
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×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—21no—
313C22⋊C4×C151—21no—
314C22⋊C4×C151—21no—
315C22⋊C4×C151—21no—
316C22⋊C4×C151—21no—
317C22⋊C4×C151—21no—
318C22⋊C4×C151—21no—
319C22⋊C4×C151—21no—
320C22⋊C4×C151—42no—
321C22⋊C4×C151—42no—
322C22⋊C4×C151—41no—
323C22⋊C4×C151—41no—
324C22⋊C4×C151—81no—
325C22⋊C4×C151—81no—
326C22⋊C4×C151—81no—
327C42×C151—21no—
328C42×C151—21no—
329C42×C151—21no—
330C42×C151—21no—
331C42×C151—21no—
332C42×C151—81no—
333C23×C151—21no—
334C23×C151—21no—
335C23×C151—21no—
336C23×C151—21no—
337C23×C151—21no—
338C23×C151—21no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—41no—
349C23×C151—41no—
350C23×C151#12011yescharacteristic
351C23×C151#12011yescharacteristic
352C23×C151C22×D411yescharacteristic
353Q8×C151—41no—
354Q8×C151—41no—
355Q8×C151—41no—
356Q8×C151—81no—
357Q8×C151—81no—
358Q8×C151—81no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—42no—
365D4×C151—42no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—81no—
369D4×C151—81no—
370D4×C151—81no—
371D4×C151—81no—
372D4×C151—84no—
373D4×C151—82no—
374D4×C151—82no—
375C2×C4×C151—22no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—21no—
379C2×C4×C151—21no—
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—21no—
388C2×C4×C151—41no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—42no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—41no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151—81no—
406C2×C4×C151—81no—
407C2×C4×C151—81no—
408C2×C4×C151—81no—
409C2×C4×C151—81no—
410C2×C4×C151—81no—
411C2×C4×C151#12011yescharacteristic
412C2×C4×C151#12011yescharacteristic
413C2×C4×C151C22×D411yescharacteristic
414C2×C4×C151C22×D411yescharacteristic
415C8×C151—41no—
416C8×C151—41no—
417C8×C151—41no—
418C8×C151—41no—
419C22×C151—21no—
420C22×C151—21no—
421C22×C151—21no—
422C22×C151—21no—
423C22×C151—21no—
424C22×C151—21no—
425C22×C151—21no—
426C22×C151—21no—
427C22×C151—41no—
428C22×C151—41no—
429C22×C151—41no—
430C22×C151—41no—
431C22×C151—41no—
432C22×C151—41no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—81no—
437C22×C151—81no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151C2×#12011yescharacteristic
445C22×C151#57711yescharacteristic
446C22×C151#57711yescharacteristic
447C4×C151—21no—
448C4×C151—21no—
449C4×C151—21no—
450C4×C151—21no—
451C4×C151—42no—
452C4×C151—41no—
453C4×C151—41no—
454C4×C151—41no—
455C4×C151—41no—
456C4×C151—41no—
457C4×C151—41no—
458C4×C151—41no—
459C4×C151—41no—
460C4×C151—41no—
461C4×C151—41no—
462C4×C151—81no—
463C4×C151—81no—
464C2×C151—21no—
465C2×C151—21no—
466C2×C151—41no—
467C2×C151—41no—
468C2×C151—81no—
469C2×C151—81no—
470C2×C151—161no—
471C2×C151#301011yescharacteristic
472C2×C151#301811yescharacteristic
473C2×C151#302611yescharacteristic
474#18416C15111yesmaximal, characteristic, direct product factor, Sylow
475C151#1841611yescharacteristic, direct product factor, Sylow
476#3535C2×C15111yescharacteristic, complemented
477#3194C2×C15111yescharacteristic, complemented
478#3187C2×C15111yescharacteristic, complemented
479#2661C2×C15111yescharacteristic, complemented
480#1612C2×C15111yescharacteristic, complemented
481#1611C2×C15111yescharacteristic, complemented
482#1609C2×C15111yescharacteristic, complemented
483#1608C2×C15111yescharacteristic, complemented
484#1600C2×C15111yescharacteristic, complemented
485#1599C2×C15111yescharacteristic, complemented
486#1597C2×C15111yescharacteristic, complemented
487#1596C2×C15111yescharacteristic, complemented
488#1508C2×C15111yescharacteristic, complemented
489#1501C2×C15111yescharacteristic, complemented
490#1468C2×C15111yescharacteristic, complemented
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C15111yescharacteristic
500#543C22×C15111yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C15111yescharacteristic
505#538C22×C15111yescharacteristic
506#536—21no—
507#525C22×C15111yescharacteristic
508C2×#123C22×C15111yescharacteristic
509C2×C22⋊Q8C22×C15111yescharacteristic
510C2×#121C22×C15111yescharacteristic
511#483C22×C15111yescharacteristic
512#483C22×C15111yescharacteristic
513#483C22×C15111yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C15111yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C15111yescharacteristic
522#450C22×C15111yescharacteristic
523#450C22×C15111yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C15111yescharacteristic
527#407C22×C15111yescharacteristic
528C2×C22⋊C8C22×C15111yescharacteristic
529#398C22×C15111yescharacteristic
530#397C22×C15111yescharacteristic
531#394—21no—
532#394C22×C15111yescharacteristic
533#392—21no—
534#392C22×C15111yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C15111yescharacteristic
538#328C22×C15111yescharacteristic
539#328C22×C15111yescharacteristic
540#328C22×C15111yescharacteristic
541#328C22×C15111yescharacteristic
542#328C22×C15111yescharacteristic
543#328C22×C15111yescharacteristic
544#327C22×C15111yescharacteristic
545#327C22×C15111yescharacteristic
546#324C22×C15111yescharacteristic
547#324C22×C15111yescharacteristic
548#323C22×C15111yescharacteristic
549#323C22×C15111yescharacteristic
550C2×#41—21no—
551C2×#41D4×C15111yescharacteristic, complemented
552C22×Q8D4×C15111yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C15111yescharacteristic
556C22×D4C23×C15111yescharacteristic
557C23×C4C23×C15111yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C15111yescharacteristic, complemented
611C22⋊Q8D4×C15111yescharacteristic, complemented
612C22⋊Q8D4×C15111yescharacteristic, complemented
613C22⋊Q8C23×C15111yescharacteristic
614C22⋊Q8C23×C15111yescharacteristic
615C22⋊Q8C23×C15111yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C15111yescharacteristic, complemented
625#121C23×C15111yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C15111yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C15111yescharacteristic
644C2×C4⋊C4D4×C15111yescharacteristic, complemented
645C2×C4⋊C4C23×C15111yescharacteristic
646C2×C4⋊C4C23×C15111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C15111yescharacteristic
656C2×C22⋊C4D4×C15111yescharacteristic
657C2×C22⋊C4C23×C15111yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C15111yescharacteristic
674C22⋊C8C23×C15111yescharacteristic
675C22⋊C8C23×C15111yescharacteristic
676C22⋊C8C23×C15111yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C15111yescharacteristic
680#95C23×C15111yescharacteristic
681C24—21no—
682C24C2×D4×C15111yescharacteristic
683C24C2×D4×C15111yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C15111yescharacteristic
691C2×Q8C2×D4×C15111yescharacteristic
692C2×Q8C2×D4×C15111yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C15111yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C15111yescharacteristic
724C22×C4C2×D4×C15111yescharacteristic
725C22×C4C2×D4×C15111yescharacteristic
726C22×C4C2×D4×C15111yescharacteristic
727C22×C4C2×D4×C15111yescharacteristic
728C22×C4C2×D4×C15111yescharacteristic
729C22×C4C2×D4×C15111yescharacteristic
730C22×C4C2×D4×C15111yescharacteristic
731C22×C4C24×C15111yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C15111yescharacteristic
769C4⋊C4C2×D4×C15111yescharacteristic
770C4⋊C4C2×D4×C15111yescharacteristic
771C4⋊C4C2×D4×C15111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C15111yescharacteristic
826C23#120×C15111yescharacteristic
827C23C22×D4×C15111yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C15111yescharacteristic
887C2×C4#120×C15111yescharacteristic
888C2×C4C22×D4×C15111yescharacteristic
889C2×C4C22×D4×C15111yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C15111yescharacteristic
920C22#577×C15111yescharacteristic
921C22#577×C15111yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2#3010×C15111yescharacteristic
947C2#3018×C15111yescharacteristic
948C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3535×C151C2semidirect
2. #3194×C151C2semidirect
3. #3187×C151C2semidirect
4. #2661×C151C2semidirect
5. #1612×C151C2semidirect
6. #1611×C151C2semidirect
7. #1609×C151C2semidirect
8. #1608×C151C2semidirect
9. #1600×C151C2semidirect
10. #1599×C151C2semidirect
11. #1597×C151C2semidirect
12. #1596×C151C2semidirect
13. #1508×C151C2semidirect
14. #1501×C151C2semidirect
15. #1468×C151C2semidirect
76. C2×#41×C151D4semidirect
77. C22×Q8×C151D4semidirect
135. C22⋊Q8×C151D4semidirect
136. C22⋊Q8×C151D4semidirect
137. C22⋊Q8×C151D4semidirect
149. #121×C151D4semidirect
164. #117×C151D4semidirect
169. C2×C4⋊C4×C151D4semidirect
474. #18416C151direct (N × H)
475. C151#18416direct (N × H)
476. #3535C2×C151semidirect
477. #3194C2×C151semidirect
478. #3187C2×C151semidirect
479. #2661C2×C151semidirect
480. #1612C2×C151semidirect
481. #1611C2×C151semidirect
482. #1609C2×C151semidirect
483. #1608C2×C151semidirect
484. #1600C2×C151semidirect
485. #1599C2×C151semidirect
486. #1597C2×C151semidirect
487. #1596C2×C151semidirect
488. #1508C2×C151semidirect
489. #1501C2×C151semidirect
490. #1468C2×C151semidirect
551. C2×#41D4×C151semidirect
552. C22×Q8D4×C151semidirect
610. C22⋊Q8D4×C151semidirect
611. C22⋊Q8D4×C151semidirect
612. C22⋊Q8D4×C151semidirect
624. #121D4×C151semidirect
639. #117D4×C151semidirect
644. C2×C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3535×C1512
#3194×C1512
#3187×C1512
#2661×C1512
#1612×C1512
#1611×C1512
#1609×C1512
#1608×C1512
#1600×C1512
#1599×C1512
#1597×C1512
#1596×C1512
#1508×C1512
#1501×C1512
#1468×C1512
#18416151