Finite Group Databasebeta

← C151×#23714 #50328639

Subgroups — C151×#23714 #50328639

Order 38656.

876 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C151C211yesmaximal, characteristic, complemented
2C2×#433×C151C211yesmaximal, characteristic, complemented
3#2324×C151C211yesmaximal, characteristic
4#2323×C151C211yesmaximal, characteristic, complemented
5#2087×C151C211yesmaximal, characteristic, complemented
6#2075×C151C211yesmaximal, characteristic, complemented
7#2067×C151C211yesmaximal, characteristic, complemented
8#2066×C151C211yesmaximal, characteristic, complemented
9#2055×C151C211yesmaximal, characteristic, complemented
10#2036×C151C211yesmaximal, characteristic, complemented
11#2034×C151C211yesmaximal, characteristic
12#2000×C151C211yesmaximal, characteristic
13#1776×C151C211yesmaximal, characteristic, complemented
14C4×#103×C151C211yesmaximal, characteristic, complemented
15C4×#102×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C2×C22⋊Q8×C151C2211yescharacteristic
18C2×#121×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#440×C151—24no—
23#433×C151—24no—
24C2×#107×C151C2211yescharacteristic
25C2×#107×C151C2211yescharacteristic
26C2×#106×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×#97×C151C2211yescharacteristic
38C2×C4×C8×C151C2211yescharacteristic
39#391×C151C2211yescharacteristic
40#390×C151—21no—
41#390×C151C2211yescharacteristic
42#389×C151—21no—
43#389×C151C2211yescharacteristic
44#389×C151C2211yescharacteristic
45#388×C151—21no—
46#388×C151—21no—
47#388×C151—21no—
48#387×C151—21no—
49#386×C151—21no—
50#385×C151—21no—
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151C2311yescharacteristic
64C23×C4×C151—21no—
65C23×C4×C151C2311yescharacteristic
66C2×SD16×C151—22no—
67C2×SD16×C151—22no—
68C2×SD16×C151—22no—
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—22no—
75#121×C151—22no—
76#121×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151—22no—
79C4×D4×C151—22no—
80C4×D4×C151—22no—
81#117×C151—22no—
82#117×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C4⋊C4×C151D411yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151D411yescharacteristic
103C2×C22⋊C4×C151D411yescharacteristic
104C2×C42×C151—21no—
105C2×C42×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108C2×C42×C151C2311yescharacteristic
109#107×C151—22no—
110#107×C151—22no—
111#106×C151—22no—
112C4⋊C8×C151—22no—
113C4⋊C8×C151—22no—
114#103×C151—22no—
115#103×C151—22no—
116#103×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120C22⋊C8×C151—22no—
121C22⋊C8×C151—22no—
122#97×C151D414yescomplemented
123C4×C8×C151—22no—
124#95×C151—21no—
125#95×C151—21no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132C24×C151—21no—
133C24×C151C2×D411yescharacteristic
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151#4112yes—
140C2×D4×C151—24no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—81no—
147C2×D4×C151—81no—
148C2×D4×C151#4112yes—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—42no—
163C22×C4×C151—81no—
164C22×C4×C151—81no—
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2411yescharacteristic
171SD16×C151—28no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151C2×D412yes—
183C2×C8×C151C2×D412yes—
184C4⋊C4×C151—24no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—42no—
198C4⋊C4×C151—81no—
199C4⋊C4×C151—81no—
200C4⋊C4×C151#4112yes—
201C4⋊C4×C151#4112yes—
202C22⋊C4×C151—24no—
203C22⋊C4×C151—24no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—42no—
207C22⋊C4×C151—81no—
208C22⋊C4×C151—81no—
209C22⋊C4×C151—81no—
210C22⋊C4×C151—81no—
211C42×C151—21no—
212C42×C151—21no—
213C42×C151—42no—
214C42×C151—81no—
215C42×C151—81no—
216C42×C151C2×D412yes—
217C42×C151#4112yes—
218C23×C151—21no—
219C23×C151—22no—
220C23×C151—21no—
221C23×C151—21no—
222C23×C151—21no—
223C23×C151—21no—
224C23×C151—21no—
225C23×C151—21no—
226C23×C151—41no—
227C23×C151—41no—
228C23×C151—41no—
229C23×C151—41no—
230C23×C151—41no—
231C23×C151—41no—
232C23×C151C22×D411yescharacteristic
233Q8×C151—22no—
234Q8×C151—22no—
235Q8×C151—41no—
236Q8×C151—41no—
237D4×C151—22no—
238D4×C151—22no—
239D4×C151—41no—
240D4×C151—41no—
241D4×C151—84no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—22no—
250C2×C4×C151—21no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—84no—
281C2×C4×C151#12112yes—
282C2×C4×C151#12112yes—
283C2×C4×C151C22×D411yescharacteristic
284C2×C4×C151C2×#4111yescharacteristic
285C2×C4×C151C2×#4111yescharacteristic
286C2×C4×C151C2×#4111yescharacteristic
287C2×C4×C151C2×#4111yescharacteristic
288C2×C4×C151C2×#4111yescharacteristic
289C8×C151—22no—
290C8×C151—22no—
291C8×C151—41no—
292C8×C151—41no—
293C22×C151—41no—
294C22×C151—41no—
295C22×C151—41no—
296C22×C151—42no—
297C22×C151—41no—
298C22×C151—42no—
299C22×C151—41no—
300C22×C151—42no—
301C22×C151—41no—
302C22×C151—41no—
303C22×C151—81no—
304C22×C151—81no—
305C22×C151—81no—
306C22×C151—81no—
307C22×C151C2×#12111yescharacteristic
308C22×C151#52511yescharacteristic
309C22×C151#52511yescharacteristic
310C22×C151#57611yescharacteristic
311C22×C151#57711yescharacteristic
312C22×C151#57711yescharacteristic
313C22×C151#57811yescharacteristic
314C4×C151—22no—
315C4×C151—22no—
316C4×C151—42no—
317C4×C151—42no—
318C4×C151—41no—
319C4×C151—42no—
320C4×C151—41no—
321C4×C151—41no—
322C4×C151—81no—
323C4×C151—81no—
324C4×C151—81no—
325C4×C151—81no—
326C4×C151#52511yescharacteristic
327C4×C151#52911yescharacteristic
328C4×C151#52911yescharacteristic
329C4×C151#53211yescharacteristic
330C2×C151—81no—
331C2×C151—82no—
332C2×C151#239211yescharacteristic
333C2×C151#306211yescharacteristic
334C2×C151#306311yescharacteristic
335C2×C151#311911yescharacteristic
336C2×C151#312111yescharacteristic
337C2×C151#312311yescharacteristic
338C2×C151#312411yescharacteristic
339#23714C15111yesmaximal, characteristic, direct product factor, Sylow
340C151#2371411yescharacteristic, direct product factor, Sylow
341C2×#440C2×C15111yescharacteristic, complemented
342C2×#433C2×C15111yescharacteristic, complemented
343#2324C2×C15111yescharacteristic
344#2323C2×C15111yescharacteristic, complemented
345#2087C2×C15111yescharacteristic, complemented
346#2075C2×C15111yescharacteristic, complemented
347#2067C2×C15111yescharacteristic, complemented
348#2066C2×C15111yescharacteristic, complemented
349#2055C2×C15111yescharacteristic, complemented
350#2036C2×C15111yescharacteristic, complemented
351#2034C2×C15111yescharacteristic
352#2000C2×C15111yescharacteristic
353#1776C2×C15111yescharacteristic, complemented
354C4×#103C2×C15111yescharacteristic, complemented
355C4×#102C2×C15111yescharacteristic, complemented
356C22×SD16C22×C15111yescharacteristic
357C2×C22⋊Q8C22×C15111yescharacteristic
358C2×#121C22×C15111yescharacteristic
359C2×C4×Q8C22×C15111yescharacteristic
360C2×C4×D4C22×C15111yescharacteristic
361C2×#117C22×C15111yescharacteristic
362#440—24no—
363#433—24no—
364C2×#107C22×C15111yescharacteristic
365C2×#107C22×C15111yescharacteristic
366C2×#106C22×C15111yescharacteristic
367C2×C4⋊C8C22×C15111yescharacteristic
368C2×C4⋊C8C22×C15111yescharacteristic
369C2×#103C22×C15111yescharacteristic
370C2×#103C22×C15111yescharacteristic
371C2×#103C22×C15111yescharacteristic
372C2×#102C22×C15111yescharacteristic
373C2×#102C22×C15111yescharacteristic
374C2×#102C22×C15111yescharacteristic
375C2×C22⋊C8C22×C15111yescharacteristic
376C2×C22⋊C8C22×C15111yescharacteristic
377C2×#97C22×C15111yescharacteristic
378C2×C4×C8C22×C15111yescharacteristic
379#391C22×C15111yescharacteristic
380#390—21no—
381#390C22×C15111yescharacteristic
382#389—21no—
383#389C22×C15111yescharacteristic
384#389C22×C15111yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#387—21no—
389#386—21no—
390#385—21no—
391#380C22×C15111yescharacteristic
392#380C22×C15111yescharacteristic
393C4×C4⋊C4C22×C15111yescharacteristic
394C4×C4⋊C4C22×C15111yescharacteristic
395#340C22×C15111yescharacteristic
396#340C22×C15111yescharacteristic
397#340C22×C15111yescharacteristic
398#340C22×C15111yescharacteristic
399#340C22×C15111yescharacteristic
400#340C22×C15111yescharacteristic
401C22×Q8C23×C15111yescharacteristic
402C22×D4—21no—
403C22×D4C23×C15111yescharacteristic
404C23×C4—21no—
405C23×C4C23×C15111yescharacteristic
406C2×SD16—22no—
407C2×SD16—22no—
408C2×SD16—22no—
409C22×C8C23×C15111yescharacteristic
410C22×C8C23×C15111yescharacteristic
411C22×C8C23×C15111yescharacteristic
412C22×C8C23×C15111yescharacteristic
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415#121—22no—
416#121—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×D4—22no—
420C4×D4—22no—
421#117—22no—
422#117—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4D4×C15111yescharacteristic
428C2×C4⋊C4D4×C15111yescharacteristic
429C2×C4⋊C4C23×C15111yescharacteristic
430C2×C4⋊C4C23×C15111yescharacteristic
431C2×C4⋊C4C23×C15111yescharacteristic
432C2×C4⋊C4C23×C15111yescharacteristic
433C2×C4⋊C4C23×C15111yescharacteristic
434C2×C4⋊C4C23×C15111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4D4×C15111yescharacteristic
443C2×C22⋊C4D4×C15111yescharacteristic
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C23×C15111yescharacteristic
448C2×C42C23×C15111yescharacteristic
449#107—22no—
450#107—22no—
451#106—22no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462#97D4×C15114yescomplemented
463C4×C8—22no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C24—21no—
473C24C2×D4×C15111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#41×C15112yes—
480C2×D4—24no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4#41×C15112yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507C22×C4C2×D4×C15111yescharacteristic
508C22×C4C2×D4×C15111yescharacteristic
509C22×C4C2×D4×C15111yescharacteristic
510C22×C4C24×C15111yescharacteristic
511SD16—28no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8C2×D4×C15112yes—
523C2×C8C2×D4×C15112yes—
524C4⋊C4—24no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4#41×C15112yes—
541C4⋊C4#41×C15112yes—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—81no—
555C42—81no—
556C42C2×D4×C15112yes—
557C42#41×C15112yes—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C15111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—84no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—84no—
621C2×C4#121×C15112yes—
622C2×C4#121×C15112yes—
623C2×C4C22×D4×C15111yescharacteristic
624C2×C4C2×#41×C15111yescharacteristic
625C2×C4C2×#41×C15111yescharacteristic
626C2×C4C2×#41×C15111yescharacteristic
627C2×C4C2×#41×C15111yescharacteristic
628C2×C4C2×#41×C15111yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22—41no—
640C22—42no—
641C22—41no—
642C22—41no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22C2×#121×C15111yescharacteristic
648C22#525×C15111yescharacteristic
649C22#525×C15111yescharacteristic
650C22#576×C15111yescharacteristic
651C22#577×C15111yescharacteristic
652C22#577×C15111yescharacteristic
653C22#578×C15111yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4#525×C15111yescharacteristic
667C4#529×C15111yescharacteristic
668C4#529×C15111yescharacteristic
669C4#532×C15111yescharacteristic
670C2—81no—
671C2—82no—
672C2#2392×C15111yescharacteristic
673C2#3062×C15111yescharacteristic
674C2#3063×C15111yescharacteristic
675C2#3119×C15111yescharacteristic
676C2#3121×C15111yescharacteristic
677C2#3123×C15111yescharacteristic
678C2#3124×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#440×C151C2semidirect
2. C2×#433×C151C2semidirect
4. #2323×C151C2semidirect
5. #2087×C151C2semidirect
6. #2075×C151C2semidirect
7. #2067×C151C2semidirect
8. #2066×C151C2semidirect
9. #2055×C151C2semidirect
10. #2036×C151C2semidirect
13. #1776×C151C2semidirect
14. C4×#103×C151C2semidirect
15. C4×#102×C151C2semidirect
122. #97×C151D4semidirect
339. #23714C151direct (N × H)
340. C151#23714direct (N × H)
341. C2×#440C2×C151semidirect
342. C2×#433C2×C151semidirect
344. #2323C2×C151semidirect
345. #2087C2×C151semidirect
346. #2075C2×C151semidirect
347. #2067C2×C151semidirect
348. #2066C2×C151semidirect
349. #2055C2×C151semidirect
350. #2036C2×C151semidirect
353. #1776C2×C151semidirect
354. C4×#103C2×C151semidirect
355. C4×#102C2×C151semidirect
462. #97D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#440×C1512
C2×#433×C1512
#2324×C1512
#2323×C1512
#2087×C1512
#2075×C1512
#2067×C1512
#2066×C1512
#2055×C1512
#2036×C1512
#2034×C1512
#2000×C1512
#1776×C1512
C4×#103×C1512
C4×#102×C1512
#23714151