Finite Group Databasebeta

← C149×#10399 #49189348

Subgroups — C149×#10399 #49189348

Order 38144.

694 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2626×C149C211yesmaximal, characteristic
2#1872×C149C211yesmaximal, characteristic, complemented
3#1852×C149C211yesmaximal, characteristic, complemented
4C2×#328×C149C211yesmaximal, characteristic, complemented
5C2×#323×C149C211yesmaximal, characteristic
6#1439×C149C211yesmaximal, characteristic
7#1294×C149C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C149C2211yescharacteristic
9C22×C4⋊C4×C149C2211yescharacteristic
10C22×C22⋊C4×C149—21no—
11C22×C22⋊C4×C149C2211yescharacteristic
12C2×#107×C149—21no—
13C2×#103×C149—21no—
14C2×C22⋊C8×C149C2211yescharacteristic
15C2×C22⋊C8×C149C2211yescharacteristic
16#399×C149—21no—
17#396×C149—21no—
18#396×C149—21no—
19#393×C149—21no—
20#385×C149—21no—
21#380×C149C2211yescharacteristic
22#379×C149—21no—
23C2×#95×C149—21no—
24C2×#95×C149C2211yescharacteristic
25#340×C149—21no—
26#340×C149—21no—
27#328×C149—22no—
28#323×C149—22no—
29C25×C149D411yescharacteristic
30C22×Q8×C149D411yescharacteristic
31C23×C4×C149—21no—
32C23×C4×C149—21no—
33C23×C4×C149D411yescharacteristic
34C23×C4×C149C2311yescharacteristic
35C22×C8×C149—21no—
36C22×C8×C149—21no—
37C22⋊Q8×C149—21no—
38C22⋊Q8×C149—21no—
39C22⋊Q8×C149—21no—
40C22⋊Q8×C149—21no—
41C2×C4⋊C4×C149—21no—
42C2×C4⋊C4×C149—21no—
43C2×C4⋊C4×C149—21no—
44C2×C4⋊C4×C149—21no—
45C2×C4⋊C4×C149—21no—
46C2×C4⋊C4×C149—42no—
47C2×C4⋊C4×C149D411yescharacteristic
48C2×C4⋊C4×C149D411yescharacteristic
49C2×C4⋊C4×C149D411yescharacteristic
50C2×C22⋊C4×C149—21no—
51C2×C22⋊C4×C149—21no—
52C2×C22⋊C4×C149—21no—
53C2×C22⋊C4×C149—21no—
54C2×C22⋊C4×C149—21no—
55C2×C22⋊C4×C149—21no—
56C2×C22⋊C4×C149—21no—
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—21no—
59C2×C22⋊C4×C149—21no—
60C2×C22⋊C4×C149—21no—
61C2×C22⋊C4×C149—21no—
62C2×C22⋊C4×C149—42no—
63C2×C22⋊C4×C149—42no—
64C2×C22⋊C4×C149—42no—
65#107×C149—42no—
66#103×C149—42no—
67C22⋊C8×C149—21no—
68C22⋊C8×C149—21no—
69C22⋊C8×C149—21no—
70C22⋊C8×C149D412yes—
71#95×C149—21no—
72#95×C149—21no—
73#95×C149—21no—
74#95×C149—21no—
75#95×C149—21no—
76#95×C149—42no—
77C24×C149—21no—
78C24×C149—21no—
79C24×C149—21no—
80C24×C149—21no—
81C24×C149—21no—
82C24×C149—21no—
83C24×C149—41no—
84C24×C149—41no—
85C24×C149—41no—
86C24×C149—41no—
87C24×C149Q1612yes—
88C24×C149C2×D411yescharacteristic
89C2×Q8×C149—21no—
90C2×Q8×C149—21no—
91C2×Q8×C149—41no—
92C2×Q8×C149—41no—
93C22×C4×C149—22no—
94C22×C4×C149—22no—
95C22×C4×C149—21no—
96C22×C4×C149—21no—
97C22×C4×C149—21no—
98C22×C4×C149—21no—
99C22×C4×C149—21no—
100C22×C4×C149—21no—
101C22×C4×C149—21no—
102C22×C4×C149—41no—
103C22×C4×C149—41no—
104C22×C4×C149—41no—
105C22×C4×C149—41no—
106C22×C4×C149—41no—
107C22×C4×C149—41no—
108C22×C4×C149—41no—
109C22×C4×C149—41no—
110C22×C4×C149—41no—
111C22×C4×C149—41no—
112C22×C4×C149—41no—
113C22×C4×C149—41no—
114C22×C4×C149—41no—
115C22×C4×C149—41no—
116C22×C4×C149—41no—
117C22×C4×C149—41no—
118C22×C4×C149C2×D411yescharacteristic
119C22×C4×C149C2×D411yescharacteristic
120C22×C4×C149C2×D411yescharacteristic
121C22×C4×C149#4111yescharacteristic
122C22×C4×C149#4111yescharacteristic
123C22×C4×C149#4111yescharacteristic
124C2×C8×C149—22no—
125C2×C8×C149—41no—
126C2×C8×C149—41no—
127C2×C8×C149—41no—
128C2×C8×C149—41no—
129C2×C8×C149—41no—
130C4⋊C4×C149—22no—
131C4⋊C4×C149—22no—
132C4⋊C4×C149—21no—
133C4⋊C4×C149—21no—
134C4⋊C4×C149—41no—
135C4⋊C4×C149—41no—
136C4⋊C4×C149—41no—
137C4⋊C4×C149—41no—
138C4⋊C4×C149—41no—
139C4⋊C4×C149—41no—
140C4⋊C4×C149—81no—
141C4⋊C4×C149—81no—
142C22⋊C4×C149—48no—
143C22⋊C4×C149—41no—
144C22⋊C4×C149—41no—
145C22⋊C4×C149—41no—
146C22⋊C4×C149—41no—
147C22⋊C4×C149—41no—
148C22⋊C4×C149—41no—
149C22⋊C4×C149—41no—
150C22⋊C4×C149—41no—
151C22⋊C4×C149—81no—
152C22⋊C4×C149—81no—
153C22⋊C4×C149—81no—
154C22⋊C4×C149—81no—
155C23×C149—21no—
156C23×C149—21no—
157C23×C149—21no—
158C23×C149—21no—
159C23×C149—22no—
160C23×C149—22no—
161C23×C149—22no—
162C23×C149—42no—
163C23×C149—42no—
164C23×C149—42no—
165C23×C149—42no—
166C23×C149—42no—
167C23×C149—42no—
168C23×C149—41no—
169C23×C149—41no—
170C23×C149—41no—
171C23×C149—41no—
172C23×C149—41no—
173C23×C149—41no—
174C23×C149—41no—
175C23×C149—41no—
176C23×C149—81no—
177C23×C149—81no—
178C23×C149—81no—
179C23×C149—81no—
180C23×C149—81no—
181C23×C149—81no—
182C23×C149#12011yescharacteristic
183C23×C149#12111yescharacteristic
184C23×C149#12311yescharacteristic
185C23×C149C2×Q1611yescharacteristic
186C23×C149#13511yescharacteristic
187C23×C149AGL(1,ℤ/8)11yescharacteristic
188C23×C149#13711yescharacteristic
189Q8×C149—42no—
190Q8×C149—81no—
191C2×C4×C149—21no—
192C2×C4×C149—21no—
193C2×C4×C149—21no—
194C2×C4×C149—21no—
195C2×C4×C149—41no—
196C2×C4×C149—41no—
197C2×C4×C149—41no—
198C2×C4×C149—41no—
199C2×C4×C149—42no—
200C2×C4×C149—42no—
201C2×C4×C149—42no—
202C2×C4×C149—42no—
203C2×C4×C149—42no—
204C2×C4×C149—42no—
205C2×C4×C149—41no—
206C2×C4×C149—41no—
207C2×C4×C149—41no—
208C2×C4×C149—41no—
209C2×C4×C149—41no—
210C2×C4×C149—41no—
211C2×C4×C149—41no—
212C2×C4×C149—41no—
213C2×C4×C149—41no—
214C2×C4×C149—41no—
215C2×C4×C149—41no—
216C2×C4×C149—41no—
217C2×C4×C149—41no—
218C2×C4×C149—42no—
219C2×C4×C149—41no—
220C2×C4×C149—41no—
221C2×C4×C149—81no—
222C2×C4×C149—81no—
223C2×C4×C149—81no—
224C2×C4×C149—81no—
225C2×C4×C149—81no—
226C2×C4×C149—81no—
227C2×C4×C149—81no—
228C2×C4×C149—81no—
229C2×C4×C149—81no—
230C2×C4×C149#12111yescharacteristic
231C2×C4×C149#12111yescharacteristic
232C2×C4×C149#12311yescharacteristic
233C2×C4×C149#12411yescharacteristic
234C8×C149—42no—
235C8×C149—81no—
236C22×C149—21no—
237C22×C149—21no—
238C22×C149—21no—
239C22×C149—21no—
240C22×C149—21no—
241C22×C149—21no—
242C22×C149—21no—
243C22×C149—21no—
244C22×C149—21no—
245C22×C149—21no—
246C22×C149—21no—
247C22×C149—21no—
248C22×C149—44no—
249C22×C149—42no—
250C22×C149—42no—
251C22×C149—42no—
252C22×C149—82no—
253C22×C149—82no—
254C22×C149—82no—
255C22×C149—81no—
256C22×C149—81no—
257C22×C149—81no—
258C22×C149—81no—
259C22×C149#39411yescharacteristic
260C22×C149#44911yescharacteristic
261C22×C149#45111yescharacteristic
262C22×C149#45311yescharacteristic
263C22×C149#45511yescharacteristic
264C22×C149B(4,𝔽2)11yescharacteristic
265C22×C149#45811yescharacteristic
266C22×C149#46711yescharacteristic
267C22×C149#46811yescharacteristic
268C22×C149#48411yescharacteristic
269C22×C149#48511yescharacteristic
270C4×C149—21no—
271C4×C149—21no—
272C4×C149—21no—
273C4×C149—21no—
274C4×C149—82no—
275C4×C149—81no—
276C4×C149—82no—
277C4×C149—81no—
278C4×C149—81no—
279C4×C149—81no—
280C4×C149—81no—
281C2×C149—21no—
282C2×C149—21no—
283C2×C149—21no—
284C2×C149—21no—
285C2×C149—82no—
286C2×C149#160011yescharacteristic
287C2×C149#160211yescharacteristic
288C2×C149#161211yescharacteristic
289C2×C149#161411yescharacteristic
290C2×C149#203611yescharacteristic
291C2×C149#203711yescharacteristic
292C2×C149#204411yescharacteristic
293#10399C14911yesmaximal, characteristic, direct product factor, Sylow
294C149#1039911yescharacteristic, direct product factor, Sylow
295#2626C2×C14911yescharacteristic
296#1872C2×C14911yescharacteristic, complemented
297#1852C2×C14911yescharacteristic, complemented
298C2×#328C2×C14911yescharacteristic, complemented
299C2×#323C2×C14911yescharacteristic
300#1439C2×C14911yescharacteristic
301#1294C2×C14911yescharacteristic, complemented
302C2×C22⋊Q8C22×C14911yescharacteristic
303C22×C4⋊C4C22×C14911yescharacteristic
304C22×C22⋊C4—21no—
305C22×C22⋊C4C22×C14911yescharacteristic
306C2×#107—21no—
307C2×#103—21no—
308C2×C22⋊C8C22×C14911yescharacteristic
309C2×C22⋊C8C22×C14911yescharacteristic
310#399—21no—
311#396—21no—
312#396—21no—
313#393—21no—
314#385—21no—
315#380C22×C14911yescharacteristic
316#379—21no—
317C2×#95—21no—
318C2×#95C22×C14911yescharacteristic
319#340—21no—
320#340—21no—
321#328—22no—
322#323—22no—
323C25D4×C14911yescharacteristic
324C22×Q8D4×C14911yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4D4×C14911yescharacteristic
328C23×C4C23×C14911yescharacteristic
329C22×C8—21no—
330C22×C8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4D4×C14911yescharacteristic
342C2×C4⋊C4D4×C14911yescharacteristic
343C2×C4⋊C4D4×C14911yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359#107—42no—
360#103—42no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8D4×C14912yes—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—42no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24Q16×C14912yes—
382C24C2×D4×C14911yescharacteristic
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—41no—
386C2×Q8—41no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4C2×D4×C14911yescharacteristic
413C22×C4C2×D4×C14911yescharacteristic
414C22×C4C2×D4×C14911yescharacteristic
415C22×C4#41×C14911yescharacteristic
416C22×C4#41×C14911yescharacteristic
417C22×C4#41×C14911yescharacteristic
418C2×C8—22no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—81no—
435C4⋊C4—81no—
436C22⋊C4—48no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—81no—
446C22⋊C4—81no—
447C22⋊C4—81no—
448C22⋊C4—81no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23#120×C14911yescharacteristic
477C23#121×C14911yescharacteristic
478C23#123×C14911yescharacteristic
479C23C2×Q16×C14911yescharacteristic
480C23#135×C14911yescharacteristic
481C23AGL(1,ℤ/8)×C14911yescharacteristic
482C23#137×C14911yescharacteristic
483Q8—42no—
484Q8—81no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4—81no—
523C2×C4—81no—
524C2×C4#121×C14911yescharacteristic
525C2×C4#121×C14911yescharacteristic
526C2×C4#123×C14911yescharacteristic
527C2×C4#124×C14911yescharacteristic
528C8—42no—
529C8—81no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#394×C14911yescharacteristic
554C22#449×C14911yescharacteristic
555C22#451×C14911yescharacteristic
556C22#453×C14911yescharacteristic
557C22#455×C14911yescharacteristic
558C22B(4,𝔽2)×C14911yescharacteristic
559C22#458×C14911yescharacteristic
560C22#467×C14911yescharacteristic
561C22#468×C14911yescharacteristic
562C22#484×C14911yescharacteristic
563C22#485×C14911yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—82no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—82no—
573C4—81no—
574C4—81no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—82no—
580C2#1600×C14911yescharacteristic
581C2#1602×C14911yescharacteristic
582C2#1612×C14911yescharacteristic
583C2#1614×C14911yescharacteristic
584C2#2036×C14911yescharacteristic
585C2#2037×C14911yescharacteristic
586C2#2044×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#120
commutator, Frattini, cosocleC23×C4C23×C149
prime radicalC25×C149D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1872×C149C2semidirect
3. #1852×C149C2semidirect
4. C2×#328×C149C2semidirect
7. #1294×C149C2semidirect
293. #10399C149direct (N × H)
294. C149#10399direct (N × H)
296. #1872C2×C149semidirect
297. #1852C2×C149semidirect
298. C2×#328C2×C149semidirect
301. #1294C2×C149semidirect

Maximal subgroups

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

subgroupindex
#2626×C1492
#1872×C1492
#1852×C1492
C2×#328×C1492
C2×#323×C1492
#1439×C1492
#1294×C1492
#10399149