Finite Group Databasebeta

← C149×#18415 #49197364

Subgroups — C149×#18415 #49197364

Order 38144.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C149C211yesmaximal, characteristic
2#3196×C149C211yesmaximal, characteristic, complemented
3#3187×C149C211yesmaximal, characteristic, complemented
4#2663×C149C211yesmaximal, characteristic, complemented
5#1618×C149C211yesmaximal, characteristic, complemented
6#1616×C149C211yesmaximal, characteristic, complemented
7#1615×C149C211yesmaximal, characteristic, complemented
8#1613×C149C211yesmaximal, characteristic, complemented
9#1606×C149C211yesmaximal, characteristic, complemented
10#1604×C149C211yesmaximal, characteristic, complemented
11#1603×C149C211yesmaximal, characteristic, complemented
12#1601×C149C211yesmaximal, characteristic, complemented
13#1507×C149C211yesmaximal, characteristic, complemented
14#1501×C149C211yesmaximal, characteristic, complemented
15#1468×C149C211yesmaximal, characteristic, complemented
16#562×C149—21no—
17#560×C149—21no—
18#553×C149—21no—
19#551×C149—21no—
20#546×C149—21no—
21#546×C149—21no—
22#546×C149—21no—
23D42×C149—21no—
24#540×C149—21no—
25#539×C149—21no—
26#539×C149C2211yescharacteristic
27#538×C149—21no—
28#538×C149C2211yescharacteristic
29#537×C149C2211yescharacteristic
30#534×C149—21no—
31#534×C149C2211yescharacteristic
32#525×C149C2211yescharacteristic
33C2×#123×C149C2211yescharacteristic
34C2×C22⋊Q8×C149C2211yescharacteristic, complemented
35C2×#121×C149C2211yescharacteristic
36#485×C149—21no—
37#484×C149C2211yescharacteristic, complemented
38#483×C149—21no—
39#481×C149C2211yescharacteristic
40#481×C149C2211yescharacteristic, complemented
41#481×C149C2211yescharacteristic, complemented
42#470×C149—21no—
43#468×C149—21no—
44#465×C149—21no—
45#465×C149—21no—
46#452×C149—21no—
47#451×C149C2211yescharacteristic, complemented
48#450×C149—21no—
49#448×C149C2211yescharacteristic
50#448×C149C2211yescharacteristic, complemented
51#448×C149C2211yescharacteristic, complemented
52#407×C149C2211yescharacteristic, complemented
53C2×C22⋊C8×C149C2211yescharacteristic, complemented
54#400×C149C2211yescharacteristic, complemented
55#399×C149C2211yescharacteristic, complemented
56#397×C149—21no—
57#395×C149C2211yescharacteristic, complemented
58#394×C149—21no—
59#393×C149C2211yescharacteristic, complemented
60#389×C149—21no—
61#388×C149—21no—
62C4×C22⋊C4×C149C2211yescharacteristic, complemented
63#328×C149C2211yescharacteristic, complemented
64#328×C149C2211yescharacteristic, complemented
65#327×C149C2211yescharacteristic
66#327×C149C2211yescharacteristic
67#327×C149C2211yescharacteristic, complemented
68#327×C149C2211yescharacteristic, complemented
69#327×C149C2211yescharacteristic, complemented
70#327×C149C2211yescharacteristic, complemented
71#324×C149C2211yescharacteristic, complemented
72#324×C149C2211yescharacteristic, complemented
73#323×C149C2211yescharacteristic, complemented
74#323×C149C2211yescharacteristic, complemented
75C2×#41×C149—21no—
76C2×#41×C149D411yescharacteristic
77C22×Q8×C149C2311yescharacteristic
78C22×D4×C149—21no—
79C22×D4×C149—21no—
80C22×D4×C149—21no—
81C22×D4×C149D411yescharacteristic
82C22×D4×C149D411yescharacteristic
83C23×C4×C149C2311yescharacteristic
84C2×Q16×C149—21no—
85C2×SD16×C149—21no—
86C2×SD16×C149—21no—
87C2×SD16×C149—21no—
88C2×M16×C149—21no—
89C22×C8×C149—21no—
90#127×C149—21no—
91#126×C149—21no—
92#126×C149—21no—
93#126×C149—21no—
94#126×C149—21no—
95#125×C149—21no—
96#125×C149—21no—
97#124×C149—21no—
98#124×C149—21no—
99#124×C149—21no—
100#123×C149—21no—
101#123×C149—21no—
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—
110#123×C149—21no—
111#123×C149—21no—
112#123×C149—21no—
113#123×C149—21no—
114C22⋊Q8×C149—21no—
115C22⋊Q8×C149—21no—
116C22⋊Q8×C149—21no—
117C22⋊Q8×C149—21no—
118C22⋊Q8×C149—21no—
119C22⋊Q8×C149—21no—
120C22⋊Q8×C149—21no—
121C22⋊Q8×C149—21no—
122C22⋊Q8×C149—21no—
123C22⋊Q8×C149D411yescharacteristic
124C22⋊Q8×C149C2311yescharacteristic
125#121×C149—21no—
126#121×C149—21no—
127#121×C149—21no—
128#121×C149—21no—
129#121×C149—21no—
130#121×C149—21no—
131#121×C149—21no—
132#121×C149—21no—
133#121×C149—21no—
134#121×C149—21no—
135#121×C149—21no—
136#121×C149—21no—
137#121×C149—21no—
138#121×C149—21no—
139#121×C149—21no—
140#121×C149D411yescharacteristic
141#121×C149D411yescharacteristic
142#121×C149D411yescharacteristic
143#121×C149C2311yescharacteristic
144#121×C149C2311yescharacteristic
145#121×C149C2311yescharacteristic
146#120×C149—21no—
147#120×C149—21no—
148#120×C149—21no—
149#120×C149—21no—
150#120×C149—21no—
151#120×C149—21no—
152#120×C149—21no—
153#120×C149—21no—
154C4×D4×C149—21no—
155C4×D4×C149—21no—
156C4×D4×C149—21no—
157C4×D4×C149—21no—
158C4×D4×C149—21no—
159C4×D4×C149—21no—
160C4×D4×C149—21no—
161C4×D4×C149—21no—
162#117×C149—21no—
163#117×C149D411yescharacteristic
164C2×C4⋊C4×C149—21no—
165C2×C4⋊C4×C149—21no—
166C2×C4⋊C4×C149—21no—
167C2×C4⋊C4×C149D411yescharacteristic
168C2×C4⋊C4×C149D411yescharacteristic
169C2×C4⋊C4×C149C2311yescharacteristic
170C2×C4⋊C4×C149C2311yescharacteristic
171C2×C22⋊C4×C149—21no—
172C2×C22⋊C4×C149—21no—
173C2×C22⋊C4×C149—21no—
174C2×C22⋊C4×C149—21no—
175C2×C22⋊C4×C149—21no—
176C2×C22⋊C4×C149—21no—
177C2×C22⋊C4×C149—21no—
178C2×C22⋊C4×C149D411yescharacteristic
179C2×C22⋊C4×C149D411yescharacteristic
180C2×C22⋊C4×C149C2311yescharacteristic
181C2×C42×C149—21no—
182#107×C149—21no—
183#106×C149—21no—
184#106×C149—21no—
185#106×C149—21no—
186#103×C149—21no—
187#103×C149—21no—
188#103×C149—21no—
189#103×C149—21no—
190#103×C149—21no—
191#102×C149—21no—
192#102×C149—21no—
193#102×C149—21no—
194C22⋊C8×C149—21no—
195C22⋊C8×C149—21no—
196C22⋊C8×C149C2311yescharacteristic
197C22⋊C8×C149C2311yescharacteristic
198C22⋊C8×C149C2311yescharacteristic
199C22⋊C8×C149C2311yescharacteristic
200#95×C149—21no—
201#95×C149—21no—
202#95×C149—21no—
203#95×C149—21no—
204#95×C149C2311yescharacteristic
205#95×C149C2311yescharacteristic
206C24×C149—21no—
207C24×C149—21no—
208C24×C149C2×D411yescharacteristic
209C24×C149C2×D411yescharacteristic
210#41×C149—81no—
211#41×C149—81no—
212#41×C149—81no—
213C2×Q8×C149—21no—
214C2×Q8×C149—21no—
215C2×Q8×C149—21no—
216C2×Q8×C149—81no—
217C2×Q8×C149C2×D411yescharacteristic
218C2×D4×C149—21no—
219C2×D4×C149—21no—
220C2×D4×C149—21no—
221C2×D4×C149—21no—
222C2×D4×C149—21no—
223C2×D4×C149—21no—
224C2×D4×C149—21no—
225C2×D4×C149—21no—
226C2×D4×C149—21no—
227C2×D4×C149—21no—
228C2×D4×C149—21no—
229C2×D4×C149—21no—
230C2×D4×C149—21no—
231C2×D4×C149—21no—
232C2×D4×C149—21no—
233C2×D4×C149—21no—
234C2×D4×C149—21no—
235C2×D4×C149—81no—
236C2×D4×C149—81no—
237C2×D4×C149—81no—
238C2×D4×C149—81no—
239C2×D4×C149—81no—
240C2×D4×C149—81no—
241C2×D4×C149—82no—
242C2×D4×C149C2×D411yescharacteristic
243C2×D4×C149C2×D411yescharacteristic
244C2×D4×C149C2×D411yescharacteristic
245C22×C4×C149—21no—
246C22×C4×C149—21no—
247C22×C4×C149—21no—
248C22×C4×C149—21no—
249C22×C4×C149—21no—
250C22×C4×C149—21no—
251C22×C4×C149—21no—
252C22×C4×C149—21no—
253C22×C4×C149—21no—
254C22×C4×C149—21no—
255C22×C4×C149—21no—
256C22×C4×C149—81no—
257C22×C4×C149C2×D411yescharacteristic
258C22×C4×C149C2×D411yescharacteristic
259C22×C4×C149C2×D411yescharacteristic
260C22×C4×C149C2×D411yescharacteristic
261C22×C4×C149C2×D411yescharacteristic
262C22×C4×C149C2×D411yescharacteristic
263C22×C4×C149C2×D411yescharacteristic
264C22×C4×C149C2×D411yescharacteristic
265C22×C4×C149C2411yescharacteristic
266Q16×C149—81no—
267SD16×C149—81no—
268SD16×C149—81no—
269SD16×C149—81no—
270M16×C149—81no—
271C2×C8×C149—21no—
272C2×C8×C149—21no—
273C2×C8×C149—21no—
274C2×C8×C149—21no—
275C2×C8×C149—81no—
276C4⋊C4×C149—21no—
277C4⋊C4×C149—21no—
278C4⋊C4×C149—21no—
279C4⋊C4×C149—21no—
280C4⋊C4×C149—21no—
281C4⋊C4×C149—21no—
282C4⋊C4×C149—21no—
283C4⋊C4×C149—21no—
284C4⋊C4×C149—21no—
285C4⋊C4×C149—21no—
286C4⋊C4×C149—21no—
287C4⋊C4×C149—21no—
288C4⋊C4×C149—21no—
289C4⋊C4×C149—21no—
290C4⋊C4×C149—21no—
291C4⋊C4×C149—42no—
292C4⋊C4×C149—41no—
293C4⋊C4×C149—41no—
294C4⋊C4×C149—81no—
295C4⋊C4×C149C2×D411yescharacteristic
296C4⋊C4×C149C2×D411yescharacteristic
297C4⋊C4×C149C2×D411yescharacteristic
298C4⋊C4×C149C2×D411yescharacteristic
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×C149—21no—
307C22⋊C4×C149—21no—
308C22⋊C4×C149—21no—
309C22⋊C4×C149—21no—
310C22⋊C4×C149—21no—
311C22⋊C4×C149—21no—
312C22⋊C4×C149—21no—
313C22⋊C4×C149—21no—
314C22⋊C4×C149—21no—
315C22⋊C4×C149—21no—
316C22⋊C4×C149—21no—
317C22⋊C4×C149—21no—
318C22⋊C4×C149—21no—
319C22⋊C4×C149—21no—
320C22⋊C4×C149—21no—
321C22⋊C4×C149—21no—
322C22⋊C4×C149—21no—
323C22⋊C4×C149—21no—
324C22⋊C4×C149—42no—
325C22⋊C4×C149—42no—
326C22⋊C4×C149—41no—
327C22⋊C4×C149—41no—
328C22⋊C4×C149—81no—
329C42×C149—21no—
330C42×C149—21no—
331C42×C149—21no—
332C42×C149—81no—
333C23×C149—21no—
334C23×C149—21no—
335C23×C149—21no—
336C23×C149—21no—
337C23×C149—21no—
338C23×C149—21no—
339C23×C149—21no—
340C23×C149—21no—
341C23×C149—41no—
342C23×C149—41no—
343C23×C149—42no—
344C23×C149—41no—
345C23×C149—41no—
346C23×C149—81no—
347C23×C149—81no—
348C23×C149—81no—
349C23×C149—81no—
350C23×C149—81no—
351C23×C149#12011yescharacteristic
352C23×C149#12011yescharacteristic
353C23×C149C22×D411yescharacteristic
354Q8×C149—41no—
355Q8×C149—41no—
356Q8×C149—41no—
357Q8×C149—41no—
358Q8×C149—41no—
359Q8×C149—81no—
360D4×C149—41no—
361D4×C149—41no—
362D4×C149—41no—
363D4×C149—42no—
364D4×C149—42no—
365D4×C149—41no—
366D4×C149—41no—
367D4×C149—41no—
368D4×C149—41no—
369D4×C149—41no—
370D4×C149—41no—
371D4×C149—81no—
372D4×C149—81no—
373D4×C149—81no—
374D4×C149—81no—
375D4×C149—81no—
376D4×C149—81no—
377D4×C149—81no—
378D4×C149—81no—
379D4×C149—81no—
380D4×C149—81no—
381D4×C149—81no—
382D4×C149—81no—
383C2×C4×C149—22no—
384C2×C4×C149—21no—
385C2×C4×C149—21no—
386C2×C4×C149—21no—
387C2×C4×C149—21no—
388C2×C4×C149—21no—
389C2×C4×C149—21no—
390C2×C4×C149—21no—
391C2×C4×C149—21no—
392C2×C4×C149—21no—
393C2×C4×C149—21no—
394C2×C4×C149—41no—
395C2×C4×C149—41no—
396C2×C4×C149—41no—
397C2×C4×C149—41no—
398C2×C4×C149—41no—
399C2×C4×C149—41no—
400C2×C4×C149—41no—
401C2×C4×C149—41no—
402C2×C4×C149—41no—
403C2×C4×C149—41no—
404C2×C4×C149—41no—
405C2×C4×C149—41no—
406C2×C4×C149—41no—
407C2×C4×C149—41no—
408C2×C4×C149—41no—
409C2×C4×C149—41no—
410C2×C4×C149—41no—
411C2×C4×C149—41no—
412C2×C4×C149—41no—
413C2×C4×C149—81no—
414C2×C4×C149—81no—
415C2×C4×C149—81no—
416C2×C4×C149—81no—
417C2×C4×C149—81no—
418C2×C4×C149—81no—
419C2×C4×C149—81no—
420C2×C4×C149#12011yescharacteristic
421C2×C4×C149#12011yescharacteristic
422C2×C4×C149C22×D411yescharacteristic
423C2×C4×C149C22×D411yescharacteristic
424C8×C149—41no—
425C8×C149—41no—
426C8×C149—41no—
427C8×C149—41no—
428C22×C149—21no—
429C22×C149—21no—
430C22×C149—21no—
431C22×C149—21no—
432C22×C149—21no—
433C22×C149—21no—
434C22×C149—21no—
435C22×C149—21no—
436C22×C149—41no—
437C22×C149—41no—
438C22×C149—41no—
439C22×C149—41no—
440C22×C149—41no—
441C22×C149—41no—
442C22×C149—41no—
443C22×C149—41no—
444C22×C149—41no—
445C22×C149—41no—
446C22×C149—41no—
447C22×C149—41no—
448C22×C149—81no—
449C22×C149—81no—
450C22×C149—81no—
451C22×C149—81no—
452C22×C149—162no—
453C22×C149—162no—
454C22×C149C2×#12011yescharacteristic
455C22×C149#57711yescharacteristic
456C22×C149#57711yescharacteristic
457C4×C149—21no—
458C4×C149—21no—
459C4×C149—21no—
460C4×C149—21no—
461C4×C149—42no—
462C4×C149—41no—
463C4×C149—41no—
464C4×C149—41no—
465C4×C149—41no—
466C4×C149—41no—
467C4×C149—41no—
468C4×C149—41no—
469C4×C149—41no—
470C4×C149—81no—
471C4×C149—81no—
472C4×C149—81no—
473C2×C149—21no—
474C2×C149—21no—
475C2×C149—41no—
476C2×C149—41no—
477C2×C149—81no—
478C2×C149—81no—
479C2×C149—81no—
480C2×C149—81no—
481C2×C149#300911yescharacteristic
482C2×C149#301811yescharacteristic
483C2×C149#302611yescharacteristic
484#18415C14911yesmaximal, characteristic, direct product factor, Sylow
485C149#1841511yescharacteristic, direct product factor, Sylow
486#3534C2×C14911yescharacteristic
487#3196C2×C14911yescharacteristic, complemented
488#3187C2×C14911yescharacteristic, complemented
489#2663C2×C14911yescharacteristic, complemented
490#1618C2×C14911yescharacteristic, complemented
491#1616C2×C14911yescharacteristic, complemented
492#1615C2×C14911yescharacteristic, complemented
493#1613C2×C14911yescharacteristic, complemented
494#1606C2×C14911yescharacteristic, complemented
495#1604C2×C14911yescharacteristic, complemented
496#1603C2×C14911yescharacteristic, complemented
497#1601C2×C14911yescharacteristic, complemented
498#1507C2×C14911yescharacteristic, complemented
499#1501C2×C14911yescharacteristic, complemented
500#1468C2×C14911yescharacteristic, complemented
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C14911yescharacteristic
512#538—21no—
513#538C22×C14911yescharacteristic
514#537C22×C14911yescharacteristic
515#534—21no—
516#534C22×C14911yescharacteristic
517#525C22×C14911yescharacteristic
518C2×#123C22×C14911yescharacteristic
519C2×C22⋊Q8C22×C14911yescharacteristic, complemented
520C2×#121C22×C14911yescharacteristic
521#485—21no—
522#484C22×C14911yescharacteristic, complemented
523#483—21no—
524#481C22×C14911yescharacteristic
525#481C22×C14911yescharacteristic, complemented
526#481C22×C14911yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C14911yescharacteristic, complemented
533#450—21no—
534#448C22×C14911yescharacteristic
535#448C22×C14911yescharacteristic, complemented
536#448C22×C14911yescharacteristic, complemented
537#407C22×C14911yescharacteristic, complemented
538C2×C22⋊C8C22×C14911yescharacteristic, complemented
539#400C22×C14911yescharacteristic, complemented
540#399C22×C14911yescharacteristic, complemented
541#397—21no—
542#395C22×C14911yescharacteristic, complemented
543#394—21no—
544#393C22×C14911yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C14911yescharacteristic, complemented
548#328C22×C14911yescharacteristic, complemented
549#328C22×C14911yescharacteristic, complemented
550#327C22×C14911yescharacteristic
551#327C22×C14911yescharacteristic
552#327C22×C14911yescharacteristic, complemented
553#327C22×C14911yescharacteristic, complemented
554#327C22×C14911yescharacteristic, complemented
555#327C22×C14911yescharacteristic, complemented
556#324C22×C14911yescharacteristic, complemented
557#324C22×C14911yescharacteristic, complemented
558#323C22×C14911yescharacteristic, complemented
559#323C22×C14911yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C14911yescharacteristic
562C22×Q8C23×C14911yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C14911yescharacteristic
567C22×D4D4×C14911yescharacteristic
568C23×C4C23×C14911yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—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—
596#123—21no—
597#123—21no—
598#123—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⋊Q8D4×C14911yescharacteristic
609C22⋊Q8C23×C14911yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
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#121—21no—
625#121D4×C14911yescharacteristic
626#121D4×C14911yescharacteristic
627#121D4×C14911yescharacteristic
628#121C23×C14911yescharacteristic
629#121C23×C14911yescharacteristic
630#121C23×C14911yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C14911yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C14911yescharacteristic
653C2×C4⋊C4D4×C14911yescharacteristic
654C2×C4⋊C4C23×C14911yescharacteristic
655C2×C4⋊C4C23×C14911yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C14911yescharacteristic
664C2×C22⋊C4D4×C14911yescharacteristic
665C2×C22⋊C4C23×C14911yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C14911yescharacteristic
682C22⋊C8C23×C14911yescharacteristic
683C22⋊C8C23×C14911yescharacteristic
684C22⋊C8C23×C14911yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C14911yescharacteristic
690#95C23×C14911yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C14911yescharacteristic
694C24C2×D4×C14911yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C14911yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C14911yescharacteristic
728C2×D4C2×D4×C14911yescharacteristic
729C2×D4C2×D4×C14911yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C14911yescharacteristic
743C22×C4C2×D4×C14911yescharacteristic
744C22×C4C2×D4×C14911yescharacteristic
745C22×C4C2×D4×C14911yescharacteristic
746C22×C4C2×D4×C14911yescharacteristic
747C22×C4C2×D4×C14911yescharacteristic
748C22×C4C2×D4×C14911yescharacteristic
749C22×C4C2×D4×C14911yescharacteristic
750C22×C4C24×C14911yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C14911yescharacteristic
781C4⋊C4C2×D4×C14911yescharacteristic
782C4⋊C4C2×D4×C14911yescharacteristic
783C4⋊C4C2×D4×C14911yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C14911yescharacteristic
837C23#120×C14911yescharacteristic
838C23C22×D4×C14911yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C14911yescharacteristic
906C2×C4#120×C14911yescharacteristic
907C2×C4C22×D4×C14911yescharacteristic
908C2×C4C22×D4×C14911yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C14911yescharacteristic
940C22#577×C14911yescharacteristic
941C22#577×C14911yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2#3009×C14911yescharacteristic
967C2#3018×C14911yescharacteristic
968C2#3026×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC22×C4C24×C149
prime radical#3534×C149C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3196×C149C2semidirect
3. #3187×C149C2semidirect
4. #2663×C149C2semidirect
5. #1618×C149C2semidirect
6. #1616×C149C2semidirect
7. #1615×C149C2semidirect
8. #1613×C149C2semidirect
9. #1606×C149C2semidirect
10. #1604×C149C2semidirect
11. #1603×C149C2semidirect
12. #1601×C149C2semidirect
13. #1507×C149C2semidirect
14. #1501×C149C2semidirect
15. #1468×C149C2semidirect
34. C2×C22⋊Q8×C149C22semidirect
37. #484×C149C22semidirect
40. #481×C149C22semidirect
41. #481×C149C22semidirect
47. #451×C149C22semidirect
50. #448×C149C22semidirect
51. #448×C149C22semidirect
52. #407×C149C22semidirect
53. C2×C22⋊C8×C149C22semidirect
54. #400×C149C22semidirect
55. #399×C149C22semidirect
57. #395×C149C22semidirect
59. #393×C149C22semidirect
62. C4×C22⋊C4×C149C22semidirect
63. #328×C149C22semidirect
64. #328×C149C22semidirect
67. #327×C149C22semidirect
68. #327×C149C22semidirect
69. #327×C149C22semidirect
70. #327×C149C22semidirect
71. #324×C149C22semidirect
72. #324×C149C22semidirect
73. #323×C149C22semidirect
74. #323×C149C22semidirect
484. #18415C149direct (N × H)
485. C149#18415direct (N × H)
487. #3196C2×C149semidirect
488. #3187C2×C149semidirect
489. #2663C2×C149semidirect
490. #1618C2×C149semidirect
491. #1616C2×C149semidirect
492. #1615C2×C149semidirect
493. #1613C2×C149semidirect
494. #1606C2×C149semidirect
495. #1604C2×C149semidirect
496. #1603C2×C149semidirect
497. #1601C2×C149semidirect
498. #1507C2×C149semidirect
499. #1501C2×C149semidirect
500. #1468C2×C149semidirect
519. C2×C22⋊Q8C22×C149semidirect
522. #484C22×C149semidirect
525. #481C22×C149semidirect
526. #481C22×C149semidirect
532. #451C22×C149semidirect
535. #448C22×C149semidirect
536. #448C22×C149semidirect
537. #407C22×C149semidirect
538. C2×C22⋊C8C22×C149semidirect
539. #400C22×C149semidirect
540. #399C22×C149semidirect
542. #395C22×C149semidirect
544. #393C22×C149semidirect
547. C4×C22⋊C4C22×C149semidirect
548. #328C22×C149semidirect
549. #328C22×C149semidirect
552. #327C22×C149semidirect
553. #327C22×C149semidirect
554. #327C22×C149semidirect
555. #327C22×C149semidirect
556. #324C22×C149semidirect
557. #324C22×C149semidirect
558. #323C22×C149semidirect
559. #323C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3534×C1492
#3196×C1492
#3187×C1492
#2663×C1492
#1618×C1492
#1616×C1492
#1615×C1492
#1613×C1492
#1606×C1492
#1604×C1492
#1603×C1492
#1601×C1492
#1507×C1492
#1501×C1492
#1468×C1492
#18415149