Finite Group Databasebeta

← C151×#24362 #50329287

Subgroups — C151×#24362 #50329287

Order 38656.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C151C211yesmaximal, characteristic, complemented
2C2×#464×C151C211yesmaximal, characteristic, complemented
3C2×#460×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5#2431×C151C211yesmaximal, characteristic, complemented
6#2341×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#2012×C151C211yesmaximal, characteristic, complemented
10#2011×C151C211yesmaximal, characteristic, complemented
11#1893×C151C211yesmaximal, characteristic, complemented
12#1880×C151C211yesmaximal, characteristic, complemented
13#1878×C151C211yesmaximal, characteristic, complemented
14#1850×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C2×#135×C151—24no—
19C2×#135×C151—24no—
20C2×#135×C151—24no—
21C22×Q16×C151C2211yescharacteristic
22C22×SD16×C151C2211yescharacteristic
23C22×SD16×C151C2211yescharacteristic
24C22×SD16×C151C2211yescharacteristic
25C22×D8×C151C2211yescharacteristic
26C22×D8×C151C2211yescharacteristic
27C23×C8×C151C2211yescharacteristic
28C2×#127×C151C2211yescharacteristic
29C2×#124×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×C4×Q8×C151C2211yescharacteristic
32C2×C4×Q8×C151C2211yescharacteristic
33#464×C151—24no—
34#460×C151—24no—
35#449×C151—24no—
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47#392×C151—21no—
48#392×C151—21no—
49#391×C151C2211yescharacteristic
50#390×C151—21no—
51#390×C151—21no—
52#390×C151C2211yescharacteristic
53#390×C151C2211yescharacteristic
54#390×C151C2211yescharacteristic
55#386×C151—21no—
56#386×C151—21no—
57#380×C151—21no—
58#380×C151C2211yescharacteristic
59C4×C22⋊C4×C151—21no—
60C4×C22⋊C4×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63#336×C151C2211yescharacteristic
64#336×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—22no—
72C2×#41×C151—41no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C2×#41×C151—41no—
76C2×#41×C151D414yescomplemented
77C22×Q8×C151C2311yescharacteristic
78C22×Q8×C151C2311yescharacteristic
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151C2311yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C23×C4×C151—21no—
88C23×C4×C151—21no—
89C23×C4×C151C2311yescharacteristic
90#135×C151—232no—
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151D414yescomplemented
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—22no—
100C2×SD16×C151—22no—
101C2×SD16×C151—22no—
102C2×SD16×C151D414yescomplemented
103C2×D8×C151—22no—
104C2×D8×C151—22no—
105C2×D8×C151—22no—
106C2×D8×C151—22no—
107C2×D8×C151—41no—
108C2×D8×C151—41no—
109C22×C8×C151—22no—
110C22×C8×C151—22no—
111C22×C8×C151—22no—
112C22×C8×C151C2311yescharacteristic
113C22×C8×C151C2311yescharacteristic
114C22×C8×C151C2311yescharacteristic
115C22×C8×C151C2311yescharacteristic
116#127×C151—22no—
117#127×C151—41no—
118#124×C151—22no—
119#124×C151—41no—
120#121×C151—22no—
121#121×C151—22no—
122C4×Q8×C151—22no—
123C4×Q8×C151—22no—
124C4×Q8×C151—41no—
125C4×Q8×C151—41no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151D411yescharacteristic
142C2×C22⋊C4×C151D411yescharacteristic
143C2×C42×C151—21no—
144C2×C42×C151—21no—
145C2×C42×C151C2311yescharacteristic
146C2×C42×C151C2311yescharacteristic
147C4⋊C8×C151—22no—
148C4⋊C8×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—41no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—41no—
157C22⋊C8×C151—22no—
158#95×C151—21no—
159#95×C151—21no—
160#95×C151—21no—
161#95×C151D411yescharacteristic
162#95×C151D411yescharacteristic
163C24×C151—21no—
164C24×C151—21no—
165C24×C151—21no—
166C24×C151C2×D411yescharacteristic
167#41×C151—28no—
168#41×C151—28no—
169#41×C151—44no—
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151C2×D412yes—
184C2×Q8×C151C2×D412yes—
185C2×Q8×C151C2×D412yes—
186C2×Q8×C151C2×D412yes—
187C2×D4×C151—24no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—81no—
215C2×D4×C151—81no—
216C2×D4×C151—81no—
217C2×D4×C151—81no—
218C2×D4×C151C2×D412yes—
219C2×D4×C151C2×D412yes—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—24no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—42no—
231C22×C4×C151—42no—
232C22×C4×C151—42no—
233C22×C4×C151—42no—
234C22×C4×C151—42no—
235C22×C4×C151C2×D411yescharacteristic
236C22×C4×C151C2×D411yescharacteristic
237C22×C4×C151C2×D411yescharacteristic
238C22×C4×C151C2×D411yescharacteristic
239C22×C4×C151C2×D412yes—
240C22×C4×C151C2×D411yescharacteristic
241C22×C4×C151#4112yes—
242C22×C4×C151C2411yescharacteristic
243Q16×C151—28no—
244SD16×C151—28no—
245SD16×C151—28no—
246SD16×C151—44no—
247D8×C151—28no—
248D8×C151—44no—
249C2×C8×C151—28no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151C2×D412yes—
261C2×C8×C151C2×D412yes—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—42no—
269C4⋊C4×C151—42no—
270C22⋊C4×C151—22no—
271C22⋊C4×C151—41no—
272C22⋊C4×C151—42no—
273C22⋊C4×C151—42no—
274C22⋊C4×C151—42no—
275C22⋊C4×C151—42no—
276C22⋊C4×C151—42no—
277C22⋊C4×C151—81no—
278C22⋊C4×C151—81no—
279C22⋊C4×C151—81no—
280C22⋊C4×C151—81no—
281C22⋊C4×C151—81no—
282C42×C151—21no—
283C42×C151—21no—
284C42×C151—21no—
285C42×C151—21no—
286C42×C151—42no—
287C42×C151—42no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—22no—
295C23×C151—22no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151#12112yes—
316C23×C151C22×D411yescharacteristic
317Q8×C151—22no—
318Q8×C151—22no—
319Q8×C151—22no—
320Q8×C151—22no—
321Q8×C151—22no—
322Q8×C151—41no—
323Q8×C151—41no—
324Q8×C151#12014yes—
325D4×C151—22no—
326D4×C151—22no—
327D4×C151—22no—
328D4×C151—22no—
329D4×C151—48no—
330D4×C151—48no—
331D4×C151—41no—
332D4×C151—41no—
333D4×C151—41no—
334D4×C151—41no—
335D4×C151—41no—
336D4×C151—41no—
337D4×C151—41no—
338D4×C151—41no—
339D4×C151—84no—
340D4×C151—84no—
341D4×C151—84no—
342C2×C4×C151—22no—
343C2×C4×C151—22no—
344C2×C4×C151—22no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—22no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—21no—
363C2×C4×C151—48no—
364C2×C4×C151—48no—
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—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151#12112yes—
377C2×C4×C151#13512yescomplemented
378C2×C4×C151C22×D411yescharacteristic
379C2×C4×C151C22×D411yescharacteristic
380C2×C4×C151C22×D411yescharacteristic
381C2×C4×C151C2×#4111yescharacteristic
382C2×C4×C151H(5,𝔽2)11yescharacteristic
383C2×C4×C151H(5,𝔽2)11yescharacteristic
384C8×C151—22no—
385C8×C151—22no—
386C8×C151—41no—
387C8×C151—41no—
388C22×C151—22no—
389C22×C151—22no—
390C22×C151—22no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—41no—
394C22×C151—41no—
395C22×C151—42no—
396C22×C151—42no—
397C22×C151—42no—
398C22×C151—42no—
399C22×C151—42no—
400C22×C151—42no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151—81no—
404C22×C151—81no—
405C22×C151—81no—
406C22×C151—81no—
407C22×C151—81no—
408C22×C151—81no—
409C22×C151—81no—
410C22×C151—81no—
411C22×C151—81no—
412C22×C151—81no—
413C22×C151—81no—
414C22×C151—81no—
415C22×C151—81no—
416C22×C151C2×#12111yescharacteristic
417C22×C151D4211yescharacteristic
418C22×C151D4211yescharacteristic
419C22×C151C2×#13511yescharacteristic
420C22×C151#57511yescharacteristic
421C22×C151#57611yescharacteristic
422C22×C151#57711yescharacteristic
423C4×C151—22no—
424C4×C151—24no—
425C4×C151—22no—
426C4×C151—42no—
427C4×C151—41no—
428C4×C151—41no—
429C4×C151—41no—
430C4×C151—81no—
431C4×C151—81no—
432C4×C151—81no—
433C4×C151C2×#12011yescharacteristic
434C4×C151#53411yescharacteristic
435C4×C151#54611yescharacteristic
436C4×C151#54611yescharacteristic
437C2×C151—42no—
438C2×C151—82no—
439C2×C151—82no—
440C2×C151—161no—
441C2×C151#241011yescharacteristic
442C2×C151#303511yescharacteristic
443C2×C151#304511yescharacteristic
444C2×C151#326811yescharacteristic
445C2×C151#327111yescharacteristic
446C2×C151#328211yescharacteristic
447C2×C151#328711yescharacteristic
448#24362C15111yesmaximal, characteristic, direct product factor, Sylow
449C151#2436211yescharacteristic, direct product factor, Sylow
450C22×#135C2×C15111yescharacteristic, complemented
451C2×#464C2×C15111yescharacteristic, complemented
452C2×#460C2×C15111yescharacteristic, complemented
453C2×#449C2×C15111yescharacteristic, complemented
454#2431C2×C15111yescharacteristic, complemented
455#2341C2×C15111yescharacteristic, complemented
456#2055C2×C15111yescharacteristic, complemented
457#2054C2×C15111yescharacteristic, complemented
458#2012C2×C15111yescharacteristic, complemented
459#2011C2×C15111yescharacteristic, complemented
460#1893C2×C15111yescharacteristic, complemented
461#1880C2×C15111yescharacteristic, complemented
462#1878C2×C15111yescharacteristic, complemented
463#1850C2×C15111yescharacteristic, complemented
464#1788C2×C15111yescharacteristic, complemented
465C22×#41C22×C15111yescharacteristic
466C22×#41C22×C15111yescharacteristic
467C2×#135—24no—
468C2×#135—24no—
469C2×#135—24no—
470C22×Q16C22×C15111yescharacteristic
471C22×SD16C22×C15111yescharacteristic
472C22×SD16C22×C15111yescharacteristic
473C22×SD16C22×C15111yescharacteristic
474C22×D8C22×C15111yescharacteristic
475C22×D8C22×C15111yescharacteristic
476C23×C8C22×C15111yescharacteristic
477C2×#127C22×C15111yescharacteristic
478C2×#124C22×C15111yescharacteristic
479C2×#121C22×C15111yescharacteristic
480C2×C4×Q8C22×C15111yescharacteristic
481C2×C4×Q8C22×C15111yescharacteristic
482#464—24no—
483#460—24no—
484#449—24no—
485C2×C4⋊C8C22×C15111yescharacteristic
486C2×C4⋊C8C22×C15111yescharacteristic
487C2×#103C22×C15111yescharacteristic
488C2×#103C22×C15111yescharacteristic
489C2×#103C22×C15111yescharacteristic
490C2×#102C22×C15111yescharacteristic
491C2×#102C22×C15111yescharacteristic
492C2×#102C22×C15111yescharacteristic
493C2×#102C22×C15111yescharacteristic
494C2×#102C22×C15111yescharacteristic
495C2×C22⋊C8C22×C15111yescharacteristic
496#392—21no—
497#392—21no—
498#391C22×C15111yescharacteristic
499#390—21no—
500#390—21no—
501#390C22×C15111yescharacteristic
502#390C22×C15111yescharacteristic
503#390C22×C15111yescharacteristic
504#386—21no—
505#386—21no—
506#380—21no—
507#380C22×C15111yescharacteristic
508C4×C22⋊C4—21no—
509C4×C22⋊C4C22×C15111yescharacteristic
510#340C22×C15111yescharacteristic
511#340C22×C15111yescharacteristic
512#336C22×C15111yescharacteristic
513#336C22×C15111yescharacteristic
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41D4×C15114yescomplemented
526C22×Q8C23×C15111yescharacteristic
527C22×Q8C23×C15111yescharacteristic
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C23×C15111yescharacteristic
534C22×D4C23×C15111yescharacteristic
535C22×D4C23×C15111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C15111yescharacteristic
539#135—232no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16D4×C15114yescomplemented
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16D4×C15114yescomplemented
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8C23×C15111yescharacteristic
562C22×C8C23×C15111yescharacteristic
563C22×C8C23×C15111yescharacteristic
564C22×C8C23×C15111yescharacteristic
565#127—22no—
566#127—41no—
567#124—22no—
568#124—41no—
569#121—22no—
570#121—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4C23×C15111yescharacteristic
578C2×C4⋊C4C23×C15111yescharacteristic
579C2×C4⋊C4C23×C15111yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C15111yescharacteristic
591C2×C22⋊C4D4×C15111yescharacteristic
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C23×C15111yescharacteristic
595C2×C42C23×C15111yescharacteristic
596C4⋊C8—22no—
597C4⋊C8—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95D4×C15111yescharacteristic
611#95D4×C15111yescharacteristic
612C24—21no—
613C24—21no—
614C24—21no—
615C24C2×D4×C15111yescharacteristic
616#41—28no—
617#41—28no—
618#41—44no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×D4×C15112yes—
633C2×Q8C2×D4×C15112yes—
634C2×Q8C2×D4×C15112yes—
635C2×Q8C2×D4×C15112yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C15112yes—
668C2×D4C2×D4×C15112yes—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4C2×D4×C15111yescharacteristic
685C22×C4C2×D4×C15111yescharacteristic
686C22×C4C2×D4×C15111yescharacteristic
687C22×C4C2×D4×C15111yescharacteristic
688C22×C4C2×D4×C15112yes—
689C22×C4C2×D4×C15111yescharacteristic
690C22×C4#41×C15112yes—
691C22×C4C24×C15111yescharacteristic
692Q16—28no—
693SD16—28no—
694SD16—28no—
695SD16—44no—
696D8—28no—
697D8—44no—
698C2×C8—28no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8C2×D4×C15112yes—
710C2×C8C2×D4×C15112yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—42no—
736C42—42no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23#121×C15112yes—
765C23C22×D4×C15111yescharacteristic
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8#120×C15114yes—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4—84no—
790D4—84no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4#121×C15112yes—
826C2×C4#135×C15112yescomplemented
827C2×C4C22×D4×C15111yescharacteristic
828C2×C4C22×D4×C15111yescharacteristic
829C2×C4C22×D4×C15111yescharacteristic
830C2×C4C2×#41×C15111yescharacteristic
831C2×C4H(5,𝔽2)×C15111yescharacteristic
832C2×C4H(5,𝔽2)×C15111yescharacteristic
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×#121×C15111yescharacteristic
866C22D42×C15111yescharacteristic
867C22D42×C15111yescharacteristic
868C22C2×#135×C15111yescharacteristic
869C22#575×C15111yescharacteristic
870C22#576×C15111yescharacteristic
871C22#577×C15111yescharacteristic
872C4—22no—
873C4—24no—
874C4—22no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C2×#120×C15111yescharacteristic
883C4#534×C15111yescharacteristic
884C4#546×C15111yescharacteristic
885C4#546×C15111yescharacteristic
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2#2410×C15111yescharacteristic
891C2#3035×C15111yescharacteristic
892C2#3045×C15111yescharacteristic
893C2#3268×C15111yescharacteristic
894C2#3271×C15111yescharacteristic
895C2#3282×C15111yescharacteristic
896C2#3287×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C151C2semidirect
2. C2×#464×C151C2semidirect
3. C2×#460×C151C2semidirect
4. C2×#449×C151C2semidirect
5. #2431×C151C2semidirect
6. #2341×C151C2semidirect
7. #2055×C151C2semidirect
8. #2054×C151C2semidirect
9. #2012×C151C2semidirect
10. #2011×C151C2semidirect
11. #1893×C151C2semidirect
12. #1880×C151C2semidirect
13. #1878×C151C2semidirect
14. #1850×C151C2semidirect
15. #1788×C151C2semidirect
76. C2×#41×C151D4semidirect
93. C2×Q16×C151D4semidirect
102. C2×SD16×C151D4semidirect
377. C2×C4×C151#135semidirect
448. #24362C151direct (N × H)
449. C151#24362direct (N × H)
450. C22×#135C2×C151semidirect
451. C2×#464C2×C151semidirect
452. C2×#460C2×C151semidirect
453. C2×#449C2×C151semidirect
454. #2431C2×C151semidirect
455. #2341C2×C151semidirect
456. #2055C2×C151semidirect
457. #2054C2×C151semidirect
458. #2012C2×C151semidirect
459. #2011C2×C151semidirect
460. #1893C2×C151semidirect
461. #1880C2×C151semidirect
462. #1878C2×C151semidirect
463. #1850C2×C151semidirect
464. #1788C2×C151semidirect
525. C2×#41D4×C151semidirect
542. C2×Q16D4×C151semidirect
551. C2×SD16D4×C151semidirect
826. C2×C4#135×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1512
C2×#464×C1512
C2×#460×C1512
C2×#449×C1512
#2431×C1512
#2341×C1512
#2055×C1512
#2054×C1512
#2012×C1512
#2011×C1512
#1893×C1512
#1880×C1512
#1878×C1512
#1850×C1512
#1788×C1512
#24362151