Finite Group Databasebeta

← C149×#17775 #49196724

Subgroups — C149×#17775 #49196724

Order 38144.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C149C211yesmaximal, characteristic
2#2990×C149C211yesmaximal, characteristic, complemented
3#2990×C149C211yesmaximal, characteristic, complemented
4#1559×C149C211yesmaximal, characteristic, complemented
5#1557×C149C211yesmaximal, characteristic, complemented
6#1556×C149C211yesmaximal, characteristic, complemented
7#1554×C149C211yesmaximal, characteristic, complemented
8#1553×C149C211yesmaximal, characteristic, complemented
9#1551×C149C211yesmaximal, characteristic, complemented
10#1551×C149C211yesmaximal, characteristic, complemented
11#1550×C149C211yesmaximal, characteristic, complemented
12#1547×C149C211yesmaximal, characteristic, complemented
13#1542×C149C211yesmaximal, characteristic, complemented
14#1540×C149C211yesmaximal, characteristic, complemented
15C2×#332×C149C211yesmaximal, characteristic, complemented
16#556×C149—21no—
17#555×C149—21no—
18#554×C149—21no—
19#553×C149—21no—
20#553×C149—21no—
21#548×C149—21no—
22#548×C149—21no—
23#547×C149—21no—
24#542×C149C412yes—
25#542×C149C412yes—
26#537×C149C412yes—
27#533×C149C2211yescharacteristic
28#533×C149C2211yescharacteristic
29#532×C149C2211yescharacteristic
30#532×C149C2211yescharacteristic
31#532×C149C2211yescharacteristic
32C2×C4⋊Q8×C149C2211yescharacteristic
33#520×C149C412yes—
34C4×#41×C149C2211yescharacteristic
35#446×C149—21no—
36#446×C149—21no—
37#435×C149—21no—
38#435×C149—21no—
39#435×C149—21no—
40#435×C149—21no—
41C8×D4×C149—21no—
42C8×D4×C149—21no—
43#432×C149C2211yescharacteristic
44#432×C149C2211yescharacteristic
45#432×C149C2211yescharacteristic
46#432×C149C2211yescharacteristic
47#431×C149C2211yescharacteristic
48#431×C149C2211yescharacteristic
49#423×C149C2211yescharacteristic
50#423×C149C2211yescharacteristic
51C2×C4⋊C8×C149C2211yescharacteristic
52C2×C4⋊C8×C149C2211yescharacteristic
53C2×C4⋊C8×C149C2211yescharacteristic
54C2×C4⋊C8×C149C2211yescharacteristic
55#333×C149C2211yescharacteristic
56#333×C149C2211yescharacteristic
57#333×C149C2211yescharacteristic
58#333×C149C2211yescharacteristic
59#332×C149C2211yescharacteristic
60#332×C149C2211yescharacteristic
61#332×C149C2211yescharacteristic
62#332×C149C2211yescharacteristic
63#332×C149C2211yescharacteristic
64#332×C149C2211yescharacteristic
65#332×C149C2211yescharacteristic
66#332×C149C2211yescharacteristic
67#331×C149C2211yescharacteristic
68#331×C149C2211yescharacteristic
69#331×C149C2211yescharacteristic
70#331×C149C2211yescharacteristic
71C2×#41×C149—21no—
72C2×#41×C149—21no—
73C2×#41×C149C2×C412yes—
74C2×#41×C149C2×C411yescharacteristic
75C22×Q8×C149—21no—
76C2×M16×C149—21no—
77C2×M16×C149—21no—
78C22×C8×C149—21no—
79C22×C8×C149—21no—
80C22×C8×C149—21no—
81C22×C8×C149—21no—
82C4⋊Q8×C149—21no—
83C4⋊Q8×C149—21no—
84C4⋊Q8×C149C2×C412yes—
85C4⋊Q8×C149C2311yescharacteristic
86C4⋊Q8×C149C2311yescharacteristic
87C4⋊Q8×C149C2311yescharacteristic
88#127×C149C2311yescharacteristic
89#126×C149—22no—
90#126×C149—22no—
91#125×C149—21no—
92#125×C149—21no—
93#124×C149—22no—
94#124×C149—22no—
95#124×C149—21no—
96#124×C149—21no—
97#124×C149C2×C412yes—
98#123×C149—22no—
99#123×C149—22no—
100C22⋊Q8×C149—22no—
101C22⋊Q8×C149—21no—
102C22⋊Q8×C149—21no—
103C22⋊Q8×C149—22no—
104C22⋊Q8×C149—22no—
105C22⋊Q8×C149C2×C412yes—
106C22⋊Q8×C149C2×C412yes—
107#121×C149—22no—
108#121×C149—22no—
109#121×C149—22no—
110#121×C149—21no—
111#121×C149—21no—
112#121×C149—21no—
113#121×C149—21no—
114#121×C149C2×C412yes—
115#121×C149C2×C412yes—
116C4×Q8×C149—21no—
117C4×Q8×C149—21no—
118C4×Q8×C149C2×C412yes—
119C4×Q8×C149C2×C412yes—
120C4×Q8×C149D411yescharacteristic
121C4×Q8×C149D411yescharacteristic
122C4×D4×C149—22no—
123C4×D4×C149—22no—
124C4×D4×C149—21no—
125C4×D4×C149—21no—
126C4×D4×C149—21no—
127C4×D4×C149—21no—
128C4×D4×C149C2×C412yes—
129C4×D4×C149C2×C412yes—
130C4×D4×C149D411yescharacteristic
131C4×D4×C149D411yescharacteristic
132C4×D4×C149D411yescharacteristic
133C4×D4×C149D411yescharacteristic
134C4×D4×C149D411yescharacteristic
135C4×D4×C149D411yescharacteristic
136#117×C149—21no—
137#117×C149—21no—
138#117×C149—22no—
139#117×C149C2×C411yescharacteristic
140#117×C149C2×C411yescharacteristic
141#117×C149C2×C411yescharacteristic
142C2×C4⋊C4×C149—21no—
143C2×C4⋊C4×C149—22no—
144C2×C4⋊C4×C149C2×C412yes—
145C2×C42×C149C2311yescharacteristic
146C2×C42×C149C2311yescharacteristic
147C2×C42×C149C2311yescharacteristic
148C4⋊C8×C149—21no—
149C4⋊C8×C149—21no—
150C4⋊C8×C149—21no—
151C4⋊C8×C149—21no—
152C4⋊C8×C149—21no—
153C4⋊C8×C149—21no—
154C4⋊C8×C149C2311yescharacteristic
155C4⋊C8×C149C2311yescharacteristic
156C4⋊C8×C149C2311yescharacteristic
157C4⋊C8×C149C2311yescharacteristic
158C4⋊C8×C149C2311yescharacteristic
159C4⋊C8×C149C2311yescharacteristic
160C4⋊C8×C149C2311yescharacteristic
161C4⋊C8×C149C2311yescharacteristic
162C22⋊C8×C149—21no—
163C22⋊C8×C149—21no—
164C22⋊C8×C149—21no—
165C22⋊C8×C149—21no—
166C22⋊C8×C149—21no—
167C22⋊C8×C149—21no—
168#97×C149—21no—
169#97×C149—21no—
170#97×C149—21no—
171#97×C149—21no—
172C4×C8×C149—21no—
173C4×C8×C149—21no—
174#41×C149—42no—
175#41×C149—44no—
176#41×C149—81no—
177#41×C149—81no—
178#41×C149—81no—
179#41×C149—81no—
180C2×Q8×C149—22no—
181C2×Q8×C149—21no—
182C2×Q8×C149—21no—
183C2×Q8×C149—81no—
184C2×Q8×C149—81no—
185C2×Q8×C149C22⋊C411yescharacteristic
186C2×Q8×C149C22×C412yes—
187C2×D4×C149—22no—
188C2×D4×C149—22no—
189C2×D4×C149—22no—
190C2×D4×C149—21no—
191C2×D4×C149—21no—
192C2×D4×C149C22⋊C411yescharacteristic
193C2×D4×C149C22⋊C411yescharacteristic
194C2×D4×C149C22⋊C411yescharacteristic
195C2×D4×C149C22×C412yes—
196C22×C4×C149—22no—
197C22×C4×C149—22no—
198C22×C4×C149—22no—
199C22×C4×C149—22no—
200C22×C4×C149C22×C411yescharacteristic
201C22×C4×C149C22×C411yescharacteristic
202C22×C4×C149C22×C411yescharacteristic
203C22×C4×C149C2×D411yescharacteristic
204C22×C4×C149C2×D411yescharacteristic
205C22×C4×C149C2×D411yescharacteristic
206C22×C4×C149C2×D411yescharacteristic
207C22×C4×C149C2×D411yescharacteristic
208C22×C4×C149C2×D411yescharacteristic
209M16×C149—81no—
210M16×C149—81no—
211C2×C8×C149—21no—
212C2×C8×C149—21no—
213C2×C8×C149—21no—
214C2×C8×C149—21no—
215C2×C8×C149—21no—
216C2×C8×C149—21no—
217C2×C8×C149—21no—
218C2×C8×C149—21no—
219C2×C8×C149—81no—
220C2×C8×C149—81no—
221C2×C8×C149—81no—
222C2×C8×C149—81no—
223C4⋊C4×C149—22no—
224C4⋊C4×C149—22no—
225C4⋊C4×C149—22no—
226C4⋊C4×C149—22no—
227C4⋊C4×C149—22no—
228C4⋊C4×C149—22no—
229C4⋊C4×C149—21no—
230C4⋊C4×C149—21no—
231C4⋊C4×C149—21no—
232C4⋊C4×C149—21no—
233C4⋊C4×C149C22⋊C411yescharacteristic
234C4⋊C4×C149C22⋊C411yescharacteristic
235C4⋊C4×C149C22⋊C411yescharacteristic
236C4⋊C4×C149C22⋊C411yescharacteristic
237C4⋊C4×C149C22⋊C411yescharacteristic
238C4⋊C4×C149C22⋊C411yescharacteristic
239C4⋊C4×C149C22×C412yes—
240C4⋊C4×C149C22×C412yes—
241C22⋊C4×C149—22no—
242C22⋊C4×C149—22no—
243C22⋊C4×C149—22no—
244C22⋊C4×C149—22no—
245C22⋊C4×C149—22no—
246C22⋊C4×C149—22no—
247C22⋊C4×C149—22no—
248C22⋊C4×C149—22no—
249C22⋊C4×C149C22⋊C411yescharacteristic
250C22⋊C4×C149C22⋊C411yescharacteristic
251C22⋊C4×C149C22⋊C411yescharacteristic
252C22⋊C4×C149C22⋊C411yescharacteristic
253C22⋊C4×C149C22⋊C411yescharacteristic
254C22⋊C4×C149C22⋊C411yescharacteristic
255C42×C149—22no—
256C42×C149—22no—
257C42×C149C22×C411yescharacteristic
258C42×C149C22×C411yescharacteristic
259C42×C149C22×C411yescharacteristic
260C42×C149C2×D411yescharacteristic
261C42×C149C2×D411yescharacteristic
262C42×C149C2×D411yescharacteristic
263C42×C149C2×D411yescharacteristic
264C42×C149C2×D411yescharacteristic
265C42×C149C2×D411yescharacteristic
266C42×C149C2411yescharacteristic
267C23×C149—22no—
268C23×C149C2×C22⋊C411yescharacteristic
269C23×C149C2×C22⋊C411yescharacteristic
270C23×C149C2×C22⋊C411yescharacteristic
271Q8×C149—41no—
272Q8×C149—42no—
273Q8×C149—41no—
274Q8×C149—41no—
275Q8×C149—41no—
276Q8×C149—41no—
277Q8×C149—82no—
278D4×C149—22no—
279D4×C149—22no—
280D4×C149—41no—
281D4×C149—42no—
282D4×C149—44no—
283D4×C149—41no—
284D4×C149—41no—
285D4×C149—41no—
286D4×C149—41no—
287D4×C149—82no—
288D4×C149—82no—
289C2×C4×C149—22no—
290C2×C4×C149—21no—
291C2×C4×C149—21no—
292C2×C4×C149—21no—
293C2×C4×C149—21no—
294C2×C4×C149—21no—
295C2×C4×C149—21no—
296C2×C4×C149—21no—
297C2×C4×C149—21no—
298C2×C4×C149—21no—
299C2×C4×C149—21no—
300C2×C4×C149—21no—
301C2×C4×C149—21no—
302C2×C4×C149—22no—
303C2×C4×C149—22no—
304C2×C4×C149—22no—
305C2×C4×C149—41no—
306C2×C4×C149—41no—
307C2×C4×C149—44no—
308C2×C4×C149—82no—
309C2×C4×C149—82no—
310C2×C4×C149—82no—
311C2×C4×C149C2×C22⋊C411yescharacteristic
312C2×C4×C149C2×C22⋊C411yescharacteristic
313C2×C4×C149C2×C22⋊C411yescharacteristic
314C2×C4×C149C2×C22⋊C411yescharacteristic
315C2×C4×C149C2×C22⋊C411yescharacteristic
316C2×C4×C149C2×C22⋊C411yescharacteristic
317C2×C4×C149C2×C22⋊C411yescharacteristic
318C2×C4×C149C2×C22⋊C411yescharacteristic
319C2×C4×C149C2×C22⋊C411yescharacteristic
320C2×C4×C149C23×C411yescharacteristic
321C2×C4×C149C22×D411yescharacteristic
322C2×C4×C149C22×D411yescharacteristic
323C8×C149—41no—
324C8×C149—41no—
325C8×C149—41no—
326C8×C149—41no—
327C8×C149—41no—
328C8×C149—41no—
329C8×C149—41no—
330C8×C149—41no—
331C22×C149—21no—
332C22×C149—21no—
333C22×C149—21no—
334C22×C149—21no—
335C22×C149—21no—
336C22×C149—21no—
337C22×C149—21no—
338C22×C149—21no—
339C22×C149—42no—
340C22×C149—42no—
341C22×C149—42no—
342C22×C149#41312yes—
343C22×C149C22×C22⋊C411yescharacteristic
344C4×C149—21no—
345C4×C149—21no—
346C4×C149—21no—
347C4×C149—21no—
348C4×C149—21no—
349C4×C149—21no—
350C4×C149—21no—
351C4×C149—21no—
352C4×C149—21no—
353C4×C149—21no—
354C4×C149—42no—
355C4×C149—42no—
356C4×C149—42no—
357C4×C149#57611yescharacteristic
358C4×C149#57711yescharacteristic
359C4×C149#57711yescharacteristic
360C4×C149#57811yescharacteristic
361C2×C149—22no—
362C2×C149—41no—
363C2×C149—41no—
364C2×C149—82no—
365C2×C149C2×#41311yescharacteristic
366C2×C149#289711yescharacteristic
367C2×C149#289811yescharacteristic
368#17775C14911yesmaximal, characteristic, direct product factor, Sylow
369C149#1777511yescharacteristic, direct product factor, Sylow
370#3511C2×C14911yescharacteristic
371#2990C2×C14911yescharacteristic, complemented
372#2990C2×C14911yescharacteristic, complemented
373#1559C2×C14911yescharacteristic, complemented
374#1557C2×C14911yescharacteristic, complemented
375#1556C2×C14911yescharacteristic, complemented
376#1554C2×C14911yescharacteristic, complemented
377#1553C2×C14911yescharacteristic, complemented
378#1551C2×C14911yescharacteristic, complemented
379#1551C2×C14911yescharacteristic, complemented
380#1550C2×C14911yescharacteristic, complemented
381#1547C2×C14911yescharacteristic, complemented
382#1542C2×C14911yescharacteristic, complemented
383#1540C2×C14911yescharacteristic, complemented
384C2×#332C2×C14911yescharacteristic, complemented
385#556—21no—
386#555—21no—
387#554—21no—
388#553—21no—
389#553—21no—
390#548—21no—
391#548—21no—
392#547—21no—
393#542C4×C14912yes—
394#542C4×C14912yes—
395#537C4×C14912yes—
396#533C22×C14911yescharacteristic
397#533C22×C14911yescharacteristic
398#532C22×C14911yescharacteristic
399#532C22×C14911yescharacteristic
400#532C22×C14911yescharacteristic
401C2×C4⋊Q8C22×C14911yescharacteristic
402#520C4×C14912yes—
403C4×#41C22×C14911yescharacteristic
404#446—21no—
405#446—21no—
406#435—21no—
407#435—21no—
408#435—21no—
409#435—21no—
410C8×D4—21no—
411C8×D4—21no—
412#432C22×C14911yescharacteristic
413#432C22×C14911yescharacteristic
414#432C22×C14911yescharacteristic
415#432C22×C14911yescharacteristic
416#431C22×C14911yescharacteristic
417#431C22×C14911yescharacteristic
418#423C22×C14911yescharacteristic
419#423C22×C14911yescharacteristic
420C2×C4⋊C8C22×C14911yescharacteristic
421C2×C4⋊C8C22×C14911yescharacteristic
422C2×C4⋊C8C22×C14911yescharacteristic
423C2×C4⋊C8C22×C14911yescharacteristic
424#333C22×C14911yescharacteristic
425#333C22×C14911yescharacteristic
426#333C22×C14911yescharacteristic
427#333C22×C14911yescharacteristic
428#332C22×C14911yescharacteristic
429#332C22×C14911yescharacteristic
430#332C22×C14911yescharacteristic
431#332C22×C14911yescharacteristic
432#332C22×C14911yescharacteristic
433#332C22×C14911yescharacteristic
434#332C22×C14911yescharacteristic
435#332C22×C14911yescharacteristic
436#331C22×C14911yescharacteristic
437#331C22×C14911yescharacteristic
438#331C22×C14911yescharacteristic
439#331C22×C14911yescharacteristic
440C2×#41—21no—
441C2×#41—21no—
442C2×#41C2×C4×C14912yes—
443C2×#41C2×C4×C14911yescharacteristic
444C22×Q8—21no—
445C2×M16—21no—
446C2×M16—21no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C2×C4×C14912yes—
454C4⋊Q8C23×C14911yescharacteristic
455C4⋊Q8C23×C14911yescharacteristic
456C4⋊Q8C23×C14911yescharacteristic
457#127C23×C14911yescharacteristic
458#126—22no—
459#126—22no—
460#125—21no—
461#125—21no—
462#124—22no—
463#124—22no—
464#124—21no—
465#124—21no—
466#124C2×C4×C14912yes—
467#123—22no—
468#123—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8C2×C4×C14912yes—
475C22⋊Q8C2×C4×C14912yes—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121C2×C4×C14912yes—
484#121C2×C4×C14912yes—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8C2×C4×C14912yes—
488C4×Q8C2×C4×C14912yes—
489C4×Q8D4×C14911yescharacteristic
490C4×Q8D4×C14911yescharacteristic
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4C2×C4×C14912yes—
498C4×D4C2×C4×C14912yes—
499C4×D4D4×C14911yescharacteristic
500C4×D4D4×C14911yescharacteristic
501C4×D4D4×C14911yescharacteristic
502C4×D4D4×C14911yescharacteristic
503C4×D4D4×C14911yescharacteristic
504C4×D4D4×C14911yescharacteristic
505#117—21no—
506#117—21no—
507#117—22no—
508#117C2×C4×C14911yescharacteristic
509#117C2×C4×C14911yescharacteristic
510#117C2×C4×C14911yescharacteristic
511C2×C4⋊C4—21no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4C2×C4×C14912yes—
514C2×C42C23×C14911yescharacteristic
515C2×C42C23×C14911yescharacteristic
516C2×C42C23×C14911yescharacteristic
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—21no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8C23×C14911yescharacteristic
524C4⋊C8C23×C14911yescharacteristic
525C4⋊C8C23×C14911yescharacteristic
526C4⋊C8C23×C14911yescharacteristic
527C4⋊C8C23×C14911yescharacteristic
528C4⋊C8C23×C14911yescharacteristic
529C4⋊C8C23×C14911yescharacteristic
530C4⋊C8C23×C14911yescharacteristic
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537#97—21no—
538#97—21no—
539#97—21no—
540#97—21no—
541C4×C8—21no—
542C4×C8—21no—
543#41—42no—
544#41—44no—
545#41—81no—
546#41—81no—
547#41—81no—
548#41—81no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—81no—
553C2×Q8—81no—
554C2×Q8C22⋊C4×C14911yescharacteristic
555C2×Q8C22×C4×C14912yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C22⋊C4×C14911yescharacteristic
562C2×D4C22⋊C4×C14911yescharacteristic
563C2×D4C22⋊C4×C14911yescharacteristic
564C2×D4C22×C4×C14912yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4C22×C4×C14911yescharacteristic
570C22×C4C22×C4×C14911yescharacteristic
571C22×C4C22×C4×C14911yescharacteristic
572C22×C4C2×D4×C14911yescharacteristic
573C22×C4C2×D4×C14911yescharacteristic
574C22×C4C2×D4×C14911yescharacteristic
575C22×C4C2×D4×C14911yescharacteristic
576C22×C4C2×D4×C14911yescharacteristic
577C22×C4C2×D4×C14911yescharacteristic
578M16—81no—
579M16—81no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—81no—
589C2×C8—81no—
590C2×C8—81no—
591C2×C8—81no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4C22⋊C4×C14911yescharacteristic
603C4⋊C4C22⋊C4×C14911yescharacteristic
604C4⋊C4C22⋊C4×C14911yescharacteristic
605C4⋊C4C22⋊C4×C14911yescharacteristic
606C4⋊C4C22⋊C4×C14911yescharacteristic
607C4⋊C4C22⋊C4×C14911yescharacteristic
608C4⋊C4C22×C4×C14912yes—
609C4⋊C4C22×C4×C14912yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4C22⋊C4×C14911yescharacteristic
619C22⋊C4C22⋊C4×C14911yescharacteristic
620C22⋊C4C22⋊C4×C14911yescharacteristic
621C22⋊C4C22⋊C4×C14911yescharacteristic
622C22⋊C4C22⋊C4×C14911yescharacteristic
623C22⋊C4C22⋊C4×C14911yescharacteristic
624C42—22no—
625C42—22no—
626C42C22×C4×C14911yescharacteristic
627C42C22×C4×C14911yescharacteristic
628C42C22×C4×C14911yescharacteristic
629C42C2×D4×C14911yescharacteristic
630C42C2×D4×C14911yescharacteristic
631C42C2×D4×C14911yescharacteristic
632C42C2×D4×C14911yescharacteristic
633C42C2×D4×C14911yescharacteristic
634C42C2×D4×C14911yescharacteristic
635C42C24×C14911yescharacteristic
636C23—22no—
637C23C2×C22⋊C4×C14911yescharacteristic
638C23C2×C22⋊C4×C14911yescharacteristic
639C23C2×C22⋊C4×C14911yescharacteristic
640Q8—41no—
641Q8—42no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—82no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—42no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—82no—
657D4—82no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—44no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C2×C22⋊C4×C14911yescharacteristic
681C2×C4C2×C22⋊C4×C14911yescharacteristic
682C2×C4C2×C22⋊C4×C14911yescharacteristic
683C2×C4C2×C22⋊C4×C14911yescharacteristic
684C2×C4C2×C22⋊C4×C14911yescharacteristic
685C2×C4C2×C22⋊C4×C14911yescharacteristic
686C2×C4C2×C22⋊C4×C14911yescharacteristic
687C2×C4C2×C22⋊C4×C14911yescharacteristic
688C2×C4C2×C22⋊C4×C14911yescharacteristic
689C2×C4C23×C4×C14911yescharacteristic
690C2×C4C22×D4×C14911yescharacteristic
691C2×C4C22×D4×C14911yescharacteristic
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22#413×C14912yes—
712C22C22×C22⋊C4×C14911yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4#576×C14911yescharacteristic
727C4#577×C14911yescharacteristic
728C4#577×C14911yescharacteristic
729C4#578×C14911yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—82no—
734C2C2×#413×C14911yescharacteristic
735C2#2897×C14911yescharacteristic
736C2#2898×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C22×C22⋊C4
commutatorC2×C4C23×C4×C149
Frattini, cosocleC42C24×C149
prime radical#3511×C149C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C4×#41×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2990×C149C2semidirect
3. #2990×C149C2semidirect
4. #1559×C149C2semidirect
5. #1557×C149C2semidirect
6. #1556×C149C2semidirect
7. #1554×C149C2semidirect
8. #1553×C149C2semidirect
9. #1551×C149C2semidirect
10. #1551×C149C2semidirect
11. #1550×C149C2semidirect
12. #1547×C149C2semidirect
13. #1542×C149C2semidirect
14. #1540×C149C2semidirect
15. C2×#332×C149C2semidirect
368. #17775C149direct (N × H)
369. C149#17775direct (N × H)
371. #2990C2×C149semidirect
372. #2990C2×C149semidirect
373. #1559C2×C149semidirect
374. #1557C2×C149semidirect
375. #1556C2×C149semidirect
376. #1554C2×C149semidirect
377. #1553C2×C149semidirect
378. #1551C2×C149semidirect
379. #1551C2×C149semidirect
380. #1550C2×C149semidirect
381. #1547C2×C149semidirect
382. #1542C2×C149semidirect
383. #1540C2×C149semidirect
384. C2×#332C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3511×C1492
#2990×C1492
#1559×C1492
#1557×C1492
#1556×C1492
#1554×C1492
#1553×C1492
#1551×C1492
#1550×C1492
#1547×C1492
#1542×C1492
#1540×C1492
C2×#332×C1492
#17775149