Finite Group Databasebeta

← C149×#17513 #49196462

Subgroups — C149×#17513 #49196462

Order 38144.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3475×C149C211yesmaximal, characteristic
2#2965×C149C211yesmaximal, characteristic, complemented
3#2925×C149C211yesmaximal, characteristic, complemented
4#1497×C149C211yesmaximal, characteristic, complemented
5#1495×C149C211yesmaximal, characteristic, complemented
6#1494×C149C211yesmaximal, characteristic, complemented
7#1490×C149C211yesmaximal, characteristic, complemented
8#1489×C149C211yesmaximal, characteristic, complemented
9#1488×C149C211yesmaximal, characteristic, complemented
10#1485×C149C211yesmaximal, characteristic, complemented
11#1483×C149C211yesmaximal, characteristic, complemented
12#1482×C149C211yesmaximal, characteristic, complemented
13#1478×C149C211yesmaximal, characteristic, complemented
14#1477×C149C211yesmaximal, characteristic, complemented
15#1476×C149C211yesmaximal, characteristic, complemented
16#556×C149C411yescharacteristic
17#555×C149C411yescharacteristic
18#554×C149C411yescharacteristic
19#553×C149—21no—
20#552×C149—21no—
21#552×C149C411yescharacteristic
22#552×C149C411yescharacteristic
23#551×C149—21no—
24#551×C149—21no—
25#547×C149C411yescharacteristic
26#546×C149C411yescharacteristic
27#546×C149C411yescharacteristic
28#533×C149C2211yescharacteristic
29#529×C149—21no—
30#529×C149—21no—
31#529×C149C2211yescharacteristic
32#529×C149C2211yescharacteristic
33#525×C149—21no—
34C4×#41×C149C2211yescharacteristic
35C4×#41×C149C2211yescharacteristic
36C4×#41×C149C2211yescharacteristic
37C2×C4×D4×C149C2211yescharacteristic
38C2×#117×C149—21no—
39#446×C149—21no—
40#436×C149—21no—
41#435×C149—21no—
42#435×C149—21no—
43#433×C149—21no—
44#433×C149—21no—
45#432×C149C2211yescharacteristic
46#432×C149C2211yescharacteristic, complemented
47#431×C149C2211yescharacteristic
48#431×C149C2211yescharacteristic
49#431×C149C2211yescharacteristic, complemented
50#431×C149C2211yescharacteristic, complemented
51#431×C149C2211yescharacteristic, complemented
52#423×C149C2211yescharacteristic, complemented
53C2×C4⋊C8×C149C2211yescharacteristic, complemented
54#408×C149—21no—
55#405×C149—21no—
56C4×M16×C149C2211yescharacteristic
57C4×M16×C149C2211yescharacteristic, complemented
58C2×C4×C8×C149C2211yescharacteristic, complemented
59Q8⋊C8×C149C2211yescharacteristic, complemented
60Q8⋊C8×C149C2211yescharacteristic, complemented
61Q8⋊C8×C149C2211yescharacteristic, complemented
62Q8⋊C8×C149C2211yescharacteristic, complemented
63Q8⋊C8×C149C2211yescharacteristic, complemented
64Q8⋊C8×C149C2211yescharacteristic, complemented
65Q8⋊C8×C149C2211yescharacteristic, complemented
66Q8⋊C8×C149C2211yescharacteristic, complemented
67D4⋊C8×C149C2211yescharacteristic
68D4⋊C8×C149C2211yescharacteristic
69D4⋊C8×C149C2211yescharacteristic
70D4⋊C8×C149C2211yescharacteristic
71D4⋊C8×C149C2211yescharacteristic
72D4⋊C8×C149C2211yescharacteristic
73D4⋊C8×C149C2211yescharacteristic
74D4⋊C8×C149C2211yescharacteristic
75C2×#41×C149C2×C411yescharacteristic
76C2×#41×C149C2×C411yescharacteristic
77C2×#41×C149D411yescharacteristic
78C22×D4×C149C2×C411yescharacteristic
79C23×C4×C149—21no—
80C2×M16×C149—21no—
81C2×M16×C149—21no—
82C2×M16×C149—21no—
83C22×C8×C149—21no—
84C22×C8×C149—21no—
85C4⋊Q8×C149C2×C411yescharacteristic
86C4⋊Q8×C149C2×C411yescharacteristic
87#126×C149—21no—
88#126×C149—21no—
89#126×C149—21no—
90#126×C149—21no—
91#126×C149—21no—
92#126×C149—21no—
93#125×C149—21no—
94#125×C149—21no—
95#125×C149—21no—
96#125×C149C2×C411yescharacteristic
97#125×C149C2×C411yescharacteristic
98#124×C149—21no—
99#124×C149—21no—
100#124×C149C2×C411yescharacteristic
101#124×C149C2×C411yescharacteristic
102#123×C149—21no—
103#123×C149—21no—
104#123×C149—21no—
105#123×C149—21no—
106#123×C149—21no—
107#123×C149—21no—
108#123×C149—21no—
109#123×C149—21no—
110C22⋊Q8×C149—21no—
111C22⋊Q8×C149—21no—
112C22⋊Q8×C149—21no—
113C22⋊Q8×C149—21no—
114C22⋊Q8×C149—21no—
115C22⋊Q8×C149C2×C411yescharacteristic
116C22⋊Q8×C149C2×C411yescharacteristic
117C22⋊Q8×C149C2×C411yescharacteristic
118C22⋊Q8×C149C2×C411yescharacteristic
119#121×C149—21no—
120#121×C149—21no—
121#121×C149—21no—
122#121×C149—21no—
123#121×C149C2×C411yescharacteristic
124#121×C149C2×C411yescharacteristic
125#120×C149—21no—
126#120×C149—21no—
127C4×Q8×C149—21no—
128C4×Q8×C149C2×C411yescharacteristic
129C4×Q8×C149C2×C411yescharacteristic
130C4×Q8×C149C2×C411yescharacteristic
131C4×Q8×C149D411yescharacteristic
132C4×Q8×C149C2311yescharacteristic
133C4×Q8×C149C2311yescharacteristic
134C4×D4×C149—21no—
135C4×D4×C149—21no—
136C4×D4×C149—21no—
137C4×D4×C149—21no—
138C4×D4×C149—21no—
139C4×D4×C149—21no—
140C4×D4×C149—21no—
141C4×D4×C149—21no—
142C4×D4×C149C2×C411yescharacteristic
143C4×D4×C149C2×C411yescharacteristic
144C4×D4×C149C2×C411yescharacteristic
145C4×D4×C149C2×C411yescharacteristic
146C4×D4×C149C2×C411yescharacteristic
147C4×D4×C149C2×C411yescharacteristic
148C4×D4×C149C2×C411yescharacteristic
149C4×D4×C149D411yescharacteristic
150C4×D4×C149D411yescharacteristic
151C4×D4×C149D411yescharacteristic
152C4×D4×C149C2311yescharacteristic
153C4×D4×C149C2311yescharacteristic
154#117×C149—21no—
155#117×C149—21no—
156#117×C149—21no—
157#117×C149—21no—
158#117×C149—21no—
159#117×C149—21no—
160#117×C149—21no—
161#117×C149—21no—
162#117×C149—21no—
163#117×C149C2×C411yescharacteristic
164#117×C149C2×C411yescharacteristic
165#117×C149D411yescharacteristic
166#117×C149D411yescharacteristic
167#117×C149D411yescharacteristic
168C2×C4⋊C4×C149—21no—
169C2×C4⋊C4×C149—21no—
170C2×C4⋊C4×C149C2×C411yescharacteristic
171C2×C22⋊C4×C149—21no—
172C2×C22⋊C4×C149—21no—
173C2×C22⋊C4×C149—21no—
174C2×C42×C149—21no—
175C2×C42×C149—21no—
176C2×C42×C149C2311yescharacteristic
177C2×C42×C149C2311yescharacteristic
178C2×C42×C149C2311yescharacteristic
179C4⋊C8×C149—21no—
180C4⋊C8×C149—21no—
181C4⋊C8×C149—21no—
182C4⋊C8×C149—21no—
183C4⋊C8×C149—21no—
184C4⋊C8×C149C2311yescharacteristic
185C4⋊C8×C149C2311yescharacteristic
186C4⋊C8×C149C2311yescharacteristic
187C4⋊C8×C149C2311yescharacteristic
188C22⋊C8×C149—21no—
189C22⋊C8×C149—21no—
190C22⋊C8×C149—21no—
191C22⋊C8×C149—21no—
192C22⋊C8×C149—21no—
193C22⋊C8×C149—21no—
194C22⋊C8×C149—21no—
195#97×C149—21no—
196#97×C149—21no—
197#97×C149—21no—
198#97×C149—21no—
199C4×C8×C149—21no—
200C4×C8×C149—21no—
201C4×C8×C149—21no—
202C4×C8×C149C2311yescharacteristic
203C4×C8×C149C2311yescharacteristic
204C4×C8×C149C2311yescharacteristic
205C4×C8×C149C2311yescharacteristic
206C24×C149—21no—
207#41×C149—22no—
208#41×C149—22no—
209#41×C149—41no—
210#41×C149—41no—
211#41×C149—41no—
212#41×C149—41no—
213C2×Q8×C149—21no—
214C2×Q8×C149C22⋊C411yescharacteristic
215C2×Q8×C149C22×C411yescharacteristic
216C2×Q8×C149C22×C411yescharacteristic
217C2×D4×C149—22no—
218C2×D4×C149—21no—
219C2×D4×C149—21no—
220C2×D4×C149—21no—
221C2×D4×C149—21no—
222C2×D4×C149—21no—
223C2×D4×C149—41no—
224C2×D4×C149C22⋊C411yescharacteristic
225C2×D4×C149C22⋊C411yescharacteristic
226C2×D4×C149C22⋊C411yescharacteristic
227C2×D4×C149C22×C411yescharacteristic
228C2×D4×C149C22×C411yescharacteristic
229C22×C4×C149—21no—
230C22×C4×C149—21no—
231C22×C4×C149—21no—
232C22×C4×C149—21no—
233C22×C4×C149—21no—
234C22×C4×C149—21no—
235C22×C4×C149—21no—
236C22×C4×C149—21no—
237C22×C4×C149—21no—
238C22×C4×C149—42no—
239C22×C4×C149—42no—
240C22×C4×C149C22×C411yescharacteristic
241C22×C4×C149C22×C411yescharacteristic
242C22×C4×C149C22×C411yescharacteristic
243C22×C4×C149C2×D411yescharacteristic
244C22×C4×C149C2×D411yescharacteristic
245C22×C4×C149C2×D411yescharacteristic
246C22×C4×C149C2×D411yescharacteristic
247C22×C4×C149C2×D411yescharacteristic
248C22×C4×C149C2×D411yescharacteristic
249M16×C149—42no—
250M16×C149—42no—
251M16×C149—42no—
252C2×C8×C149—21no—
253C2×C8×C149—21no—
254C2×C8×C149—21no—
255C2×C8×C149—21no—
256C2×C8×C149—21no—
257C2×C8×C149—21no—
258C2×C8×C149—21no—
259C2×C8×C149—21no—
260C2×C8×C149—42no—
261C2×C8×C149—42no—
262C4⋊C4×C149—21no—
263C4⋊C4×C149—21no—
264C4⋊C4×C149—21no—
265C4⋊C4×C149—21no—
266C4⋊C4×C149—21no—
267C4⋊C4×C149—21no—
268C4⋊C4×C149—21no—
269C4⋊C4×C149—21no—
270C4⋊C4×C149—21no—
271C4⋊C4×C149—21no—
272C4⋊C4×C149—21no—
273C4⋊C4×C149—21no—
274C4⋊C4×C149—21no—
275C4⋊C4×C149—21no—
276C4⋊C4×C149—21no—
277C4⋊C4×C149—21no—
278C4⋊C4×C149C22⋊C411yescharacteristic
279C4⋊C4×C149C22⋊C411yescharacteristic
280C4⋊C4×C149C22⋊C411yescharacteristic
281C4⋊C4×C149C22⋊C411yescharacteristic
282C4⋊C4×C149C22⋊C411yescharacteristic
283C4⋊C4×C149C22⋊C411yescharacteristic
284C4⋊C4×C149C22×C411yescharacteristic
285C4⋊C4×C149C22×C411yescharacteristic
286C4⋊C4×C149C22×C411yescharacteristic
287C4⋊C4×C149C22×C411yescharacteristic
288C22⋊C4×C149—21no—
289C22⋊C4×C149—21no—
290C22⋊C4×C149—21no—
291C22⋊C4×C149—21no—
292C22⋊C4×C149—21no—
293C22⋊C4×C149—21no—
294C22⋊C4×C149—21no—
295C22⋊C4×C149—21no—
296C22⋊C4×C149—21no—
297C22⋊C4×C149—21no—
298C22⋊C4×C149—21no—
299C22⋊C4×C149—21no—
300C22⋊C4×C149—21no—
301C22⋊C4×C149—21no—
302C22⋊C4×C149—21no—
303C22⋊C4×C149—21no—
304C22⋊C4×C149—21no—
305C22⋊C4×C149—21no—
306C22⋊C4×C149C22⋊C411yescharacteristic
307C22⋊C4×C149C22⋊C411yescharacteristic
308C22⋊C4×C149C22⋊C411yescharacteristic
309C22⋊C4×C149C22⋊C411yescharacteristic
310C22⋊C4×C149C22⋊C411yescharacteristic
311C22⋊C4×C149C22⋊C411yescharacteristic
312C42×C149—21no—
313C42×C149—21no—
314C42×C149—21no—
315C42×C149—21no—
316C42×C149—21no—
317C42×C149—21no—
318C42×C149C22×C411yescharacteristic
319C42×C149C22×C411yescharacteristic
320C42×C149C22×C411yescharacteristic
321C42×C149C2×D411yescharacteristic
322C42×C149C2×D411yescharacteristic
323C42×C149C2×D411yescharacteristic
324C42×C149C2×D411yescharacteristic
325C42×C149C2×D411yescharacteristic
326C42×C149C2×D411yescharacteristic
327C42×C149C2411yescharacteristic
328C23×C149—21no—
329C23×C149—21no—
330C23×C149—42no—
331C23×C149—42no—
332C23×C149—81no—
333C23×C149C2×C22⋊C411yescharacteristic
334C23×C149C2×C22⋊C411yescharacteristic
335C23×C149C2×C22⋊C411yescharacteristic
336Q8×C149—21no—
337Q8×C149—21no—
338Q8×C149—21no—
339Q8×C149—21no—
340Q8×C149—41no—
341Q8×C149—81no—
342D4×C149—21no—
343D4×C149—21no—
344D4×C149—21no—
345D4×C149—41no—
346D4×C149—41no—
347D4×C149—41no—
348D4×C149—42no—
349D4×C149—42no—
350D4×C149—42no—
351D4×C149—81no—
352D4×C149—81no—
353D4×C149#13112yes—
354C2×C4×C149—21no—
355C2×C4×C149—21no—
356C2×C4×C149—21no—
357C2×C4×C149—21no—
358C2×C4×C149—21no—
359C2×C4×C149—21no—
360C2×C4×C149—21no—
361C2×C4×C149—21no—
362C2×C4×C149—21no—
363C2×C4×C149—21no—
364C2×C4×C149—21no—
365C2×C4×C149—21no—
366C2×C4×C149—21no—
367C2×C4×C149—21no—
368C2×C4×C149—21no—
369C2×C4×C149—21no—
370C2×C4×C149—21no—
371C2×C4×C149—21no—
372C2×C4×C149—41no—
373C2×C4×C149—41no—
374C2×C4×C149—41no—
375C2×C4×C149—42no—
376C2×C4×C149—42no—
377C2×C4×C149—42no—
378C2×C4×C149—42no—
379C2×C4×C149—42no—
380C2×C4×C149—41no—
381C2×C4×C149—41no—
382C2×C4×C149—41no—
383C2×C4×C149—41no—
384C2×C4×C149—81no—
385C2×C4×C149—81no—
386C2×C4×C149C2×C22⋊C411yescharacteristic
387C2×C4×C149C2×C22⋊C411yescharacteristic
388C2×C4×C149C2×C22⋊C411yescharacteristic
389C2×C4×C149C2×C22⋊C411yescharacteristic
390C2×C4×C149C2×C22⋊C411yescharacteristic
391C2×C4×C149C2×C22⋊C411yescharacteristic
392C2×C4×C149C2×C22⋊C411yescharacteristic
393C2×C4×C149C2×C22⋊C411yescharacteristic
394C2×C4×C149C2×C22⋊C411yescharacteristic
395C2×C4×C149C23×C411yescharacteristic
396C2×C4×C149C22×D411yescharacteristic
397C2×C4×C149C22×D411yescharacteristic
398C8×C149—22no—
399C8×C149—41no—
400C8×C149—41no—
401C8×C149—41no—
402C8×C149—41no—
403C8×C149—41no—
404C8×C149—41no—
405C8×C149—41no—
406C22×C149—21no—
407C22×C149—21no—
408C22×C149—21no—
409C22×C149—22no—
410C22×C149—21no—
411C22×C149—21no—
412C22×C149—21no—
413C22×C149—21no—
414C22×C149—21no—
415C22×C149—21no—
416C22×C149—41no—
417C22×C149—41no—
418C22×C149—41no—
419C22×C149—41no—
420C22×C149—41no—
421C22×C149—84no—
422C22×C149C22×C22⋊C411yescharacteristic
423C4×C149—21no—
424C4×C149—21no—
425C4×C149—21no—
426C4×C149—21no—
427C4×C149—21no—
428C4×C149—21no—
429C4×C149—21no—
430C4×C149—21no—
431C4×C149—21no—
432C4×C149—21no—
433C4×C149—41no—
434C4×C149—41no—
435C4×C149—41no—
436C4×C149—41no—
437C4×C149—41no—
438C4×C149—41no—
439C4×C149C2×#13111yescharacteristic
440C4×C149#56811yescharacteristic
441C4×C149#57511yescharacteristic
442C4×C149#57511yescharacteristic
443C2×C149—41no—
444C2×C149—41no—
445C2×C149—41no—
446C2×C149—42no—
447C2×C149—81no—
448C2×C149#288011yescharacteristic
449C2×C149#289611yescharacteristic
450C2×C149#290111yescharacteristic
451#17513C14911yesmaximal, characteristic, direct product factor, Sylow
452C149#1751311yescharacteristic, direct product factor, Sylow
453#3475C2×C14911yescharacteristic
454#2965C2×C14911yescharacteristic, complemented
455#2925C2×C14911yescharacteristic, complemented
456#1497C2×C14911yescharacteristic, complemented
457#1495C2×C14911yescharacteristic, complemented
458#1494C2×C14911yescharacteristic, complemented
459#1490C2×C14911yescharacteristic, complemented
460#1489C2×C14911yescharacteristic, complemented
461#1488C2×C14911yescharacteristic, complemented
462#1485C2×C14911yescharacteristic, complemented
463#1483C2×C14911yescharacteristic, complemented
464#1482C2×C14911yescharacteristic, complemented
465#1478C2×C14911yescharacteristic, complemented
466#1477C2×C14911yescharacteristic, complemented
467#1476C2×C14911yescharacteristic, complemented
468#556C4×C14911yescharacteristic
469#555C4×C14911yescharacteristic
470#554C4×C14911yescharacteristic
471#553—21no—
472#552—21no—
473#552C4×C14911yescharacteristic
474#552C4×C14911yescharacteristic
475#551—21no—
476#551—21no—
477#547C4×C14911yescharacteristic
478#546C4×C14911yescharacteristic
479#546C4×C14911yescharacteristic
480#533C22×C14911yescharacteristic
481#529—21no—
482#529—21no—
483#529C22×C14911yescharacteristic
484#529C22×C14911yescharacteristic
485#525—21no—
486C4×#41C22×C14911yescharacteristic
487C4×#41C22×C14911yescharacteristic
488C4×#41C22×C14911yescharacteristic
489C2×C4×D4C22×C14911yescharacteristic
490C2×#117—21no—
491#446—21no—
492#436—21no—
493#435—21no—
494#435—21no—
495#433—21no—
496#433—21no—
497#432C22×C14911yescharacteristic
498#432C22×C14911yescharacteristic, complemented
499#431C22×C14911yescharacteristic
500#431C22×C14911yescharacteristic
501#431C22×C14911yescharacteristic, complemented
502#431C22×C14911yescharacteristic, complemented
503#431C22×C14911yescharacteristic, complemented
504#423C22×C14911yescharacteristic, complemented
505C2×C4⋊C8C22×C14911yescharacteristic, complemented
506#408—21no—
507#405—21no—
508C4×M16C22×C14911yescharacteristic
509C4×M16C22×C14911yescharacteristic, complemented
510C2×C4×C8C22×C14911yescharacteristic, complemented
511Q8⋊C8C22×C14911yescharacteristic, complemented
512Q8⋊C8C22×C14911yescharacteristic, complemented
513Q8⋊C8C22×C14911yescharacteristic, complemented
514Q8⋊C8C22×C14911yescharacteristic, complemented
515Q8⋊C8C22×C14911yescharacteristic, complemented
516Q8⋊C8C22×C14911yescharacteristic, complemented
517Q8⋊C8C22×C14911yescharacteristic, complemented
518Q8⋊C8C22×C14911yescharacteristic, complemented
519D4⋊C8C22×C14911yescharacteristic
520D4⋊C8C22×C14911yescharacteristic
521D4⋊C8C22×C14911yescharacteristic
522D4⋊C8C22×C14911yescharacteristic
523D4⋊C8C22×C14911yescharacteristic
524D4⋊C8C22×C14911yescharacteristic
525D4⋊C8C22×C14911yescharacteristic
526D4⋊C8C22×C14911yescharacteristic
527C2×#41C2×C4×C14911yescharacteristic
528C2×#41C2×C4×C14911yescharacteristic
529C2×#41D4×C14911yescharacteristic
530C22×D4C2×C4×C14911yescharacteristic
531C23×C4—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—21no—
535C22×C8—21no—
536C22×C8—21no—
537C4⋊Q8C2×C4×C14911yescharacteristic
538C4⋊Q8C2×C4×C14911yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125C2×C4×C14911yescharacteristic
549#125C2×C4×C14911yescharacteristic
550#124—21no—
551#124—21no—
552#124C2×C4×C14911yescharacteristic
553#124C2×C4×C14911yescharacteristic
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C2×C4×C14911yescharacteristic
568C22⋊Q8C2×C4×C14911yescharacteristic
569C22⋊Q8C2×C4×C14911yescharacteristic
570C22⋊Q8C2×C4×C14911yescharacteristic
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121C2×C4×C14911yescharacteristic
576#121C2×C4×C14911yescharacteristic
577#120—21no—
578#120—21no—
579C4×Q8—21no—
580C4×Q8C2×C4×C14911yescharacteristic
581C4×Q8C2×C4×C14911yescharacteristic
582C4×Q8C2×C4×C14911yescharacteristic
583C4×Q8D4×C14911yescharacteristic
584C4×Q8C23×C14911yescharacteristic
585C4×Q8C23×C14911yescharacteristic
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C2×C4×C14911yescharacteristic
595C4×D4C2×C4×C14911yescharacteristic
596C4×D4C2×C4×C14911yescharacteristic
597C4×D4C2×C4×C14911yescharacteristic
598C4×D4C2×C4×C14911yescharacteristic
599C4×D4C2×C4×C14911yescharacteristic
600C4×D4C2×C4×C14911yescharacteristic
601C4×D4D4×C14911yescharacteristic
602C4×D4D4×C14911yescharacteristic
603C4×D4D4×C14911yescharacteristic
604C4×D4C23×C14911yescharacteristic
605C4×D4C23×C14911yescharacteristic
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C2×C4×C14911yescharacteristic
616#117C2×C4×C14911yescharacteristic
617#117D4×C14911yescharacteristic
618#117D4×C14911yescharacteristic
619#117D4×C14911yescharacteristic
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×C4×C14911yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C23×C14911yescharacteristic
629C2×C42C23×C14911yescharacteristic
630C2×C42C23×C14911yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635C4⋊C8—21no—
636C4⋊C8C23×C14911yescharacteristic
637C4⋊C8C23×C14911yescharacteristic
638C4⋊C8C23×C14911yescharacteristic
639C4⋊C8C23×C14911yescharacteristic
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647#97—21no—
648#97—21no—
649#97—21no—
650#97—21no—
651C4×C8—21no—
652C4×C8—21no—
653C4×C8—21no—
654C4×C8C23×C14911yescharacteristic
655C4×C8C23×C14911yescharacteristic
656C4×C8C23×C14911yescharacteristic
657C4×C8C23×C14911yescharacteristic
658C24—21no—
659#41—22no—
660#41—22no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665C2×Q8—21no—
666C2×Q8C22⋊C4×C14911yescharacteristic
667C2×Q8C22×C4×C14911yescharacteristic
668C2×Q8C22×C4×C14911yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C22⋊C4×C14911yescharacteristic
677C2×D4C22⋊C4×C14911yescharacteristic
678C2×D4C22⋊C4×C14911yescharacteristic
679C2×D4C22×C4×C14911yescharacteristic
680C2×D4C22×C4×C14911yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4C22×C4×C14911yescharacteristic
693C22×C4C22×C4×C14911yescharacteristic
694C22×C4C22×C4×C14911yescharacteristic
695C22×C4C2×D4×C14911yescharacteristic
696C22×C4C2×D4×C14911yescharacteristic
697C22×C4C2×D4×C14911yescharacteristic
698C22×C4C2×D4×C14911yescharacteristic
699C22×C4C2×D4×C14911yescharacteristic
700C22×C4C2×D4×C14911yescharacteristic
701M16—42no—
702M16—42no—
703M16—42no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C22⋊C4×C14911yescharacteristic
731C4⋊C4C22⋊C4×C14911yescharacteristic
732C4⋊C4C22⋊C4×C14911yescharacteristic
733C4⋊C4C22⋊C4×C14911yescharacteristic
734C4⋊C4C22⋊C4×C14911yescharacteristic
735C4⋊C4C22⋊C4×C14911yescharacteristic
736C4⋊C4C22×C4×C14911yescharacteristic
737C4⋊C4C22×C4×C14911yescharacteristic
738C4⋊C4C22×C4×C14911yescharacteristic
739C4⋊C4C22×C4×C14911yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4C22⋊C4×C14911yescharacteristic
759C22⋊C4C22⋊C4×C14911yescharacteristic
760C22⋊C4C22⋊C4×C14911yescharacteristic
761C22⋊C4C22⋊C4×C14911yescharacteristic
762C22⋊C4C22⋊C4×C14911yescharacteristic
763C22⋊C4C22⋊C4×C14911yescharacteristic
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42C22×C4×C14911yescharacteristic
771C42C22×C4×C14911yescharacteristic
772C42C22×C4×C14911yescharacteristic
773C42C2×D4×C14911yescharacteristic
774C42C2×D4×C14911yescharacteristic
775C42C2×D4×C14911yescharacteristic
776C42C2×D4×C14911yescharacteristic
777C42C2×D4×C14911yescharacteristic
778C42C2×D4×C14911yescharacteristic
779C42C24×C14911yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23C2×C22⋊C4×C14911yescharacteristic
786C23C2×C22⋊C4×C14911yescharacteristic
787C23C2×C22⋊C4×C14911yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—41no—
793Q8—81no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4#131×C14912yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C2×C22⋊C4×C14911yescharacteristic
839C2×C4C2×C22⋊C4×C14911yescharacteristic
840C2×C4C2×C22⋊C4×C14911yescharacteristic
841C2×C4C2×C22⋊C4×C14911yescharacteristic
842C2×C4C2×C22⋊C4×C14911yescharacteristic
843C2×C4C2×C22⋊C4×C14911yescharacteristic
844C2×C4C2×C22⋊C4×C14911yescharacteristic
845C2×C4C2×C22⋊C4×C14911yescharacteristic
846C2×C4C2×C22⋊C4×C14911yescharacteristic
847C2×C4C23×C4×C14911yescharacteristic
848C2×C4C22×D4×C14911yescharacteristic
849C2×C4C22×D4×C14911yescharacteristic
850C8—22no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—41no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—84no—
874C22C22×C22⋊C4×C14911yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4C2×#131×C14911yescharacteristic
892C4#568×C14911yescharacteristic
893C4#575×C14911yescharacteristic
894C4#575×C14911yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—42no—
899C2—81no—
900C2#2880×C14911yescharacteristic
901C2#2896×C14911yescharacteristic
902C2#2901×C14911yescharacteristic
subgroupG/H
centerC2×C4×C149C22×D4
commutatorC2×C4C23×C4×C149
Frattini, cosocleC42C24×C149
socleC22×C149C22×C22⋊C4
prime radical#3475×C149C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C149 ◁ C4×#41×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2965×C149C2semidirect
3. #2925×C149C2semidirect
4. #1497×C149C2semidirect
5. #1495×C149C2semidirect
6. #1494×C149C2semidirect
7. #1490×C149C2semidirect
8. #1489×C149C2semidirect
9. #1488×C149C2semidirect
10. #1485×C149C2semidirect
11. #1483×C149C2semidirect
12. #1482×C149C2semidirect
13. #1478×C149C2semidirect
14. #1477×C149C2semidirect
15. #1476×C149C2semidirect
46. #432×C149C22semidirect
49. #431×C149C22semidirect
50. #431×C149C22semidirect
51. #431×C149C22semidirect
52. #423×C149C22semidirect
53. C2×C4⋊C8×C149C22semidirect
57. C4×M16×C149C22semidirect
58. C2×C4×C8×C149C22semidirect
59. Q8⋊C8×C149C22semidirect
60. Q8⋊C8×C149C22semidirect
61. Q8⋊C8×C149C22semidirect
62. Q8⋊C8×C149C22semidirect
63. Q8⋊C8×C149C22semidirect
64. Q8⋊C8×C149C22semidirect
65. Q8⋊C8×C149C22semidirect
66. Q8⋊C8×C149C22semidirect
451. #17513C149direct (N × H)
452. C149#17513direct (N × H)
454. #2965C2×C149semidirect
455. #2925C2×C149semidirect
456. #1497C2×C149semidirect
457. #1495C2×C149semidirect
458. #1494C2×C149semidirect
459. #1490C2×C149semidirect
460. #1489C2×C149semidirect
461. #1488C2×C149semidirect
462. #1485C2×C149semidirect
463. #1483C2×C149semidirect
464. #1482C2×C149semidirect
465. #1478C2×C149semidirect
466. #1477C2×C149semidirect
467. #1476C2×C149semidirect
498. #432C22×C149semidirect
501. #431C22×C149semidirect
502. #431C22×C149semidirect
503. #431C22×C149semidirect
504. #423C22×C149semidirect
505. C2×C4⋊C8C22×C149semidirect
509. C4×M16C22×C149semidirect
510. C2×C4×C8C22×C149semidirect
511. Q8⋊C8C22×C149semidirect
512. Q8⋊C8C22×C149semidirect
513. Q8⋊C8C22×C149semidirect
514. Q8⋊C8C22×C149semidirect
515. Q8⋊C8C22×C149semidirect
516. Q8⋊C8C22×C149semidirect
517. Q8⋊C8C22×C149semidirect
518. Q8⋊C8C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3475×C1492
#2965×C1492
#2925×C1492
#1497×C1492
#1495×C1492
#1494×C1492
#1490×C1492
#1489×C1492
#1488×C1492
#1485×C1492
#1483×C1492
#1482×C1492
#1478×C1492
#1477×C1492
#1476×C1492
#17513149