Finite Group Databasebeta

← C149×#18262 #49197211

Subgroups — C149×#18262 #49197211

Order 38144.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C149C211yesmaximal, characteristic
2#3094×C149C211yesmaximal, characteristic, complemented
3#3091×C149C211yesmaximal, characteristic, complemented
4#2498×C149C211yesmaximal, characteristic, complemented
5#1618×C149C211yesmaximal, characteristic, complemented
6#1616×C149C211yesmaximal, characteristic, complemented
7#1615×C149C211yesmaximal, characteristic, complemented
8#1613×C149C211yesmaximal, characteristic, complemented
9#1612×C149C211yesmaximal, characteristic, complemented
10#1610×C149C211yesmaximal, characteristic, complemented
11#1609×C149C211yesmaximal, characteristic, complemented
12#1607×C149C211yesmaximal, characteristic, complemented
13#1504×C149C211yesmaximal, characteristic, complemented
14C2×#327×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×#121×C149C2211yescharacteristic
35C2×#117×C149C2211yescharacteristic, complemented
36#485×C149—21no—
37#484×C149C2211yescharacteristic, complemented
38#483×C149C2211yescharacteristic, complemented
39#482×C149—21no—
40#482×C149—21no—
41#482×C149—21no—
42#481×C149C2211yescharacteristic
43#481×C149C2211yescharacteristic, complemented
44#481×C149C2211yescharacteristic, complemented
45#480×C149C2211yescharacteristic
46#480×C149C2211yescharacteristic, complemented
47#480×C149C2211yescharacteristic, complemented
48#428×C149—21no—
49#427×C149—21no—
50#418×C149—21no—
51#416×C149—21no—
52#407×C149C2211yescharacteristic, complemented
53C2×C22⋊C8×C149C2211yescharacteristic, complemented
54#400×C149C2211yescharacteristic, complemented
55#399×C149C2211yescharacteristic, complemented
56#398×C149C2211yescharacteristic, complemented
57#397×C149C2211yescharacteristic, complemented
58#388×C149—21no—
59#387×C149—21no—
60#386×C149—21no—
61#380×C149—21no—
62C2×#95×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×D4×C149—21no—
78C22×D4×C149—21no—
79C22×D4×C149—21no—
80C22×D4×C149D411yescharacteristic
81C22×D4×C149D411yescharacteristic
82C23×C4×C149—21no—
83C23×C4×C149C2311yescharacteristic
84C2×M16×C149—21no—
85C22×C8×C149—21no—
86#127×C149—21no—
87#126×C149—21no—
88#126×C149—21no—
89#126×C149—21no—
90#126×C149—21no—
91#125×C149—21no—
92#125×C149—21no—
93#124×C149—21no—
94#124×C149—21no—
95#124×C149—21no—
96#123×C149—21no—
97#123×C149—21no—
98#123×C149—21no—
99#123×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—
110C22⋊Q8×C149—21no—
111C22⋊Q8×C149—21no—
112C22⋊Q8×C149—21no—
113C22⋊Q8×C149—21no—
114C22⋊Q8×C149—21no—
115C22⋊Q8×C149D411yescharacteristic
116C22⋊Q8×C149C2311yescharacteristic
117#121×C149—21no—
118#121×C149—21no—
119#121×C149—21no—
120#121×C149—21no—
121#121×C149—21no—
122#121×C149—21no—
123#121×C149—21no—
124#121×C149—21no—
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×C149D411yescharacteristic
133#121×C149D411yescharacteristic
134#121×C149D411yescharacteristic
135#121×C149C2311yescharacteristic
136#121×C149C2311yescharacteristic
137#121×C149C2311yescharacteristic
138#120×C149—21no—
139#120×C149—21no—
140#120×C149—21no—
141#120×C149—21no—
142#120×C149—21no—
143#120×C149—21no—
144#120×C149—21no—
145#120×C149—21no—
146C4×D4×C149—21no—
147C4×D4×C149—21no—
148C4×D4×C149—21no—
149C4×D4×C149—21no—
150C4×D4×C149—21no—
151C4×D4×C149—21no—
152C4×D4×C149—21no—
153C4×D4×C149—21no—
154#117×C149—21no—
155#117×C149—21no—
156#117×C149—21no—
157#117×C149—21no—
158#117×C149—21no—
159#117×C149D411yescharacteristic
160C2×C4⋊C4×C149—21no—
161C2×C4⋊C4×C149—21no—
162C2×C4⋊C4×C149D411yescharacteristic
163C2×C4⋊C4×C149D411yescharacteristic
164C2×C4⋊C4×C149C2311yescharacteristic
165C2×C4⋊C4×C149C2311yescharacteristic
166C2×C4⋊C4×C149C2311yescharacteristic
167C2×C22⋊C4×C149—21no—
168C2×C22⋊C4×C149—21no—
169C2×C22⋊C4×C149—21no—
170C2×C22⋊C4×C149—21no—
171C2×C22⋊C4×C149—21no—
172C2×C22⋊C4×C149—21no—
173C2×C22⋊C4×C149D411yescharacteristic
174C2×C22⋊C4×C149D411yescharacteristic
175C2×C22⋊C4×C149C2311yescharacteristic
176C2×C42×C149—21no—
177#107×C149—21no—
178#107×C149—21no—
179#107×C149—21no—
180#107×C149—21no—
181#106×C149—21no—
182#106×C149—21no—
183#106×C149—21no—
184#106×C149—21no—
185#103×C149—21no—
186#103×C149—21no—
187#102×C149—21no—
188#102×C149—21no—
189#102×C149—21no—
190#102×C149—21no—
191#102×C149—21no—
192#102×C149—21no—
193C22⋊C8×C149—21no—
194C22⋊C8×C149—21no—
195C22⋊C8×C149C2311yescharacteristic
196C22⋊C8×C149C2311yescharacteristic
197C22⋊C8×C149C2311yescharacteristic
198C22⋊C8×C149C2311yescharacteristic
199#95×C149—21no—
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—42no—
211#41×C149—81no—
212#41×C149—81no—
213C2×Q8×C149—21no—
214C2×Q8×C149C2×D411yescharacteristic
215C2×D4×C149—21no—
216C2×D4×C149—21no—
217C2×D4×C149—21no—
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—42no—
233C2×D4×C149—42no—
234C2×D4×C149—81no—
235C2×D4×C149—81no—
236C2×D4×C149—81no—
237C2×D4×C149—81no—
238C2×D4×C149—82no—
239C2×D4×C149C2×D411yescharacteristic
240C2×D4×C149C2×D411yescharacteristic
241C2×D4×C149C2×D411yescharacteristic
242C22×C4×C149—21no—
243C22×C4×C149—21no—
244C22×C4×C149—21no—
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—42no—
254C22×C4×C149—42no—
255C22×C4×C149—42no—
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
266M16×C149—42no—
267C2×C8×C149—21no—
268C2×C8×C149—21no—
269C2×C8×C149—21no—
270C2×C8×C149—21no—
271C2×C8×C149—42no—
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×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—42no—
290C4⋊C4×C149—81no—
291C4⋊C4×C149C2×D411yescharacteristic
292C4⋊C4×C149C2×D411yescharacteristic
293C4⋊C4×C149C2×D411yescharacteristic
294C4⋊C4×C149C2×D411yescharacteristic
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×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—42no—
321C22⋊C4×C149—41no—
322C22⋊C4×C149—41no—
323C22⋊C4×C149—81no—
324C42×C149—21no—
325C42×C149—21no—
326C42×C149—21no—
327C42×C149—41no—
328C42×C149—41no—
329C23×C149—21no—
330C23×C149—21no—
331C23×C149—22no—
332C23×C149—21no—
333C23×C149—21no—
334C23×C149—21no—
335C23×C149—21no—
336C23×C149—21no—
337C23×C149—21no—
338C23×C149—41no—
339C23×C149—41no—
340C23×C149—41no—
341C23×C149—42no—
342C23×C149—81no—
343C23×C149—81no—
344C23×C149—81no—
345C23×C149—81no—
346C23×C149—81no—
347C23×C149#12011yescharacteristic
348C23×C149#12011yescharacteristic
349C23×C149C22×D411yescharacteristic
350Q8×C149—41no—
351Q8×C149—81no—
352D4×C149—41no—
353D4×C149—41no—
354D4×C149—41no—
355D4×C149—41no—
356D4×C149—41no—
357D4×C149—41no—
358D4×C149—41no—
359D4×C149—41no—
360D4×C149—41no—
361D4×C149—42no—
362D4×C149—42no—
363D4×C149—81no—
364D4×C149—81no—
365D4×C149—81no—
366D4×C149—81no—
367D4×C149—81no—
368D4×C149—81no—
369D4×C149—81no—
370D4×C149—81no—
371D4×C149—81no—
372D4×C149—81no—
373D4×C149—81no—
374D4×C149—81no—
375C2×C4×C149—22no—
376C2×C4×C149—22no—
377C2×C4×C149—22no—
378C2×C4×C149—21no—
379C2×C4×C149—21no—
380C2×C4×C149—21no—
381C2×C4×C149—21no—
382C2×C4×C149—21no—
383C2×C4×C149—21no—
384C2×C4×C149—21no—
385C2×C4×C149—21no—
386C2×C4×C149—21no—
387C2×C4×C149—21no—
388C2×C4×C149—41no—
389C2×C4×C149—41no—
390C2×C4×C149—41no—
391C2×C4×C149—41no—
392C2×C4×C149—41no—
393C2×C4×C149—41no—
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—81no—
406C2×C4×C149—81no—
407C2×C4×C149—81no—
408C2×C4×C149—81no—
409C2×C4×C149—81no—
410C2×C4×C149—81no—
411C2×C4×C149—81no—
412C2×C4×C149—84no—
413C2×C4×C149#12011yescharacteristic
414C2×C4×C149#12011yescharacteristic
415C2×C4×C149C22×D411yescharacteristic
416C2×C4×C149C22×D411yescharacteristic
417C8×C149—41no—
418C8×C149—41no—
419C8×C149—41no—
420C8×C149—41no—
421C22×C149—21no—
422C22×C149—21no—
423C22×C149—21no—
424C22×C149—21no—
425C22×C149—21no—
426C22×C149—21no—
427C22×C149—21no—
428C22×C149—42no—
429C22×C149—42no—
430C22×C149—41no—
431C22×C149—41no—
432C22×C149—41no—
433C22×C149—41no—
434C22×C149—41no—
435C22×C149—41no—
436C22×C149—41no—
437C22×C149—41no—
438C22×C149—41no—
439C22×C149—41no—
440C22×C149—41no—
441C22×C149—41no—
442C22×C149—81no—
443C22×C149—81no—
444C22×C149—162no—
445C22×C149—162no—
446C22×C149#45812yes—
447C22×C149C2×#12011yescharacteristic
448C22×C149#57611yescharacteristic
449C22×C149#57711yescharacteristic
450C4×C149—21no—
451C4×C149—21no—
452C4×C149—21no—
453C4×C149—21no—
454C4×C149—42no—
455C4×C149—41no—
456C4×C149—41no—
457C4×C149—41no—
458C4×C149—41no—
459C4×C149—41no—
460C4×C149—41no—
461C4×C149—41no—
462C4×C149—41no—
463C4×C149—81no—
464C4×C149—81no—
465C4×C149—81no—
466C2×C149—21no—
467C2×C149—21no—
468C2×C149—22no—
469C2×C149—41no—
470C2×C149—81no—
471C2×C149—81no—
472C2×C149—81no—
473C2×C149—81no—
474C2×C149#301211yescharacteristic
475C2×C149#301811yescharacteristic
476C2×C149C2×#45811yescharacteristic
477#18262C14911yesmaximal, characteristic, direct product factor, Sylow
478C149#1826211yescharacteristic, direct product factor, Sylow
479#3534C2×C14911yescharacteristic
480#3094C2×C14911yescharacteristic, complemented
481#3091C2×C14911yescharacteristic, complemented
482#2498C2×C14911yescharacteristic, complemented
483#1618C2×C14911yescharacteristic, complemented
484#1616C2×C14911yescharacteristic, complemented
485#1615C2×C14911yescharacteristic, complemented
486#1613C2×C14911yescharacteristic, complemented
487#1612C2×C14911yescharacteristic, complemented
488#1610C2×C14911yescharacteristic, complemented
489#1609C2×C14911yescharacteristic, complemented
490#1607C2×C14911yescharacteristic, complemented
491#1504C2×C14911yescharacteristic, complemented
492C2×#327C2×C14911yescharacteristic, complemented
493#1468C2×C14911yescharacteristic, complemented
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C14911yescharacteristic
505#538—21no—
506#538C22×C14911yescharacteristic
507#537C22×C14911yescharacteristic
508#534—21no—
509#534C22×C14911yescharacteristic
510#525C22×C14911yescharacteristic
511C2×#123C22×C14911yescharacteristic
512C2×#121C22×C14911yescharacteristic
513C2×#117C22×C14911yescharacteristic, complemented
514#485—21no—
515#484C22×C14911yescharacteristic, complemented
516#483C22×C14911yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C14911yescharacteristic
521#481C22×C14911yescharacteristic, complemented
522#481C22×C14911yescharacteristic, complemented
523#480C22×C14911yescharacteristic
524#480C22×C14911yescharacteristic, complemented
525#480C22×C14911yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C14911yescharacteristic, complemented
531C2×C22⋊C8C22×C14911yescharacteristic, complemented
532#400C22×C14911yescharacteristic, complemented
533#399C22×C14911yescharacteristic, complemented
534#398C22×C14911yescharacteristic, complemented
535#397C22×C14911yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C14911yescharacteristic, complemented
541#328C22×C14911yescharacteristic, complemented
542#328C22×C14911yescharacteristic, complemented
543#327C22×C14911yescharacteristic
544#327C22×C14911yescharacteristic
545#327C22×C14911yescharacteristic, complemented
546#327C22×C14911yescharacteristic, complemented
547#327C22×C14911yescharacteristic, complemented
548#327C22×C14911yescharacteristic, complemented
549#324C22×C14911yescharacteristic, complemented
550#324C22×C14911yescharacteristic, complemented
551#323C22×C14911yescharacteristic, complemented
552#323C22×C14911yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C14911yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C14911yescharacteristic
559C22×D4D4×C14911yescharacteristic
560C23×C4—21no—
561C23×C4C23×C14911yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C14911yescharacteristic
594C22⋊Q8C23×C14911yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C14911yescharacteristic
611#121D4×C14911yescharacteristic
612#121D4×C14911yescharacteristic
613#121C23×C14911yescharacteristic
614#121C23×C14911yescharacteristic
615#121C23×C14911yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C14911yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C14911yescharacteristic
641C2×C4⋊C4D4×C14911yescharacteristic
642C2×C4⋊C4C23×C14911yescharacteristic
643C2×C4⋊C4C23×C14911yescharacteristic
644C2×C4⋊C4C23×C14911yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C14911yescharacteristic
652C2×C22⋊C4D4×C14911yescharacteristic
653C2×C22⋊C4C23×C14911yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C14911yescharacteristic
674C22⋊C8C23×C14911yescharacteristic
675C22⋊C8C23×C14911yescharacteristic
676C22⋊C8C23×C14911yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C14911yescharacteristic
683#95C23×C14911yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C14911yescharacteristic
687C24C2×D4×C14911yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C14911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C14911yescharacteristic
718C2×D4C2×D4×C14911yescharacteristic
719C2×D4C2×D4×C14911yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C14911yescharacteristic
736C22×C4C2×D4×C14911yescharacteristic
737C22×C4C2×D4×C14911yescharacteristic
738C22×C4C2×D4×C14911yescharacteristic
739C22×C4C2×D4×C14911yescharacteristic
740C22×C4C2×D4×C14911yescharacteristic
741C22×C4C2×D4×C14911yescharacteristic
742C22×C4C2×D4×C14911yescharacteristic
743C22×C4C24×C14911yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C14911yescharacteristic
770C4⋊C4C2×D4×C14911yescharacteristic
771C4⋊C4C2×D4×C14911yescharacteristic
772C4⋊C4C2×D4×C14911yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
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—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C14911yescharacteristic
826C23#120×C14911yescharacteristic
827C23C22×D4×C14911yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C14911yescharacteristic
892C2×C4#120×C14911yescharacteristic
893C2×C4C22×D4×C14911yescharacteristic
894C2×C4C22×D4×C14911yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C14912yes—
925C22C2×#120×C14911yescharacteristic
926C22#576×C14911yescharacteristic
927C22#577×C14911yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2#3012×C14911yescharacteristic
953C2#3018×C14911yescharacteristic
954C2C2×#458×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. #3094×C149C2semidirect
3. #3091×C149C2semidirect
4. #2498×C149C2semidirect
5. #1618×C149C2semidirect
6. #1616×C149C2semidirect
7. #1615×C149C2semidirect
8. #1613×C149C2semidirect
9. #1612×C149C2semidirect
10. #1610×C149C2semidirect
11. #1609×C149C2semidirect
12. #1607×C149C2semidirect
13. #1504×C149C2semidirect
14. C2×#327×C149C2semidirect
15. #1468×C149C2semidirect
35. C2×#117×C149C22semidirect
37. #484×C149C22semidirect
38. #483×C149C22semidirect
43. #481×C149C22semidirect
44. #481×C149C22semidirect
46. #480×C149C22semidirect
47. #480×C149C22semidirect
52. #407×C149C22semidirect
53. C2×C22⋊C8×C149C22semidirect
54. #400×C149C22semidirect
55. #399×C149C22semidirect
56. #398×C149C22semidirect
57. #397×C149C22semidirect
62. C2×#95×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
477. #18262C149direct (N × H)
478. C149#18262direct (N × H)
480. #3094C2×C149semidirect
481. #3091C2×C149semidirect
482. #2498C2×C149semidirect
483. #1618C2×C149semidirect
484. #1616C2×C149semidirect
485. #1615C2×C149semidirect
486. #1613C2×C149semidirect
487. #1612C2×C149semidirect
488. #1610C2×C149semidirect
489. #1609C2×C149semidirect
490. #1607C2×C149semidirect
491. #1504C2×C149semidirect
492. C2×#327C2×C149semidirect
493. #1468C2×C149semidirect
513. C2×#117C22×C149semidirect
515. #484C22×C149semidirect
516. #483C22×C149semidirect
521. #481C22×C149semidirect
522. #481C22×C149semidirect
524. #480C22×C149semidirect
525. #480C22×C149semidirect
530. #407C22×C149semidirect
531. C2×C22⋊C8C22×C149semidirect
532. #400C22×C149semidirect
533. #399C22×C149semidirect
534. #398C22×C149semidirect
535. #397C22×C149semidirect
540. C2×#95C22×C149semidirect
541. #328C22×C149semidirect
542. #328C22×C149semidirect
545. #327C22×C149semidirect
546. #327C22×C149semidirect
547. #327C22×C149semidirect
548. #327C22×C149semidirect
549. #324C22×C149semidirect
550. #324C22×C149semidirect
551. #323C22×C149semidirect
552. #323C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3534×C1492
#3094×C1492
#3091×C1492
#2498×C1492
#1618×C1492
#1616×C1492
#1615×C1492
#1613×C1492
#1612×C1492
#1610×C1492
#1609×C1492
#1607×C1492
#1504×C1492
C2×#327×C1492
#1468×C1492
#18262149