Finite Group Databasebeta

← C149×#14421 #49193370

Subgroups — C149×#14421 #49193370

Order 38144.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C149C211yesmaximal, characteristic
2C2×#391×C149C211yesmaximal, characteristic, complemented
3C2×#388×C149C211yesmaximal, characteristic, complemented
4C2×#386×C149C211yesmaximal, characteristic
5C2×#385×C149C211yesmaximal, characteristic, complemented
6#1446×C149C211yesmaximal, characteristic, complemented
7#1440×C149C211yesmaximal, characteristic, complemented
8#1439×C149C211yesmaximal, characteristic, complemented
9#1439×C149C211yesmaximal, characteristic, complemented
10#1439×C149C211yesmaximal, characteristic, complemented
11#1438×C149C211yesmaximal, characteristic
12#1437×C149C211yesmaximal, characteristic, complemented
13C4⋊#95×C149C211yesmaximal, characteristic, complemented
14#1434×C149C211yesmaximal, characteristic, complemented
15C22⋊#95×C149C211yesmaximal, characteristic, complemented
16C23×Q8×C149C2211yescharacteristic
17C23×D4×C149C2211yescharacteristic
18C24×C4×C149C2211yescharacteristic
19C2×#124×C149—24no—
20C2×#124×C149—24no—
21C2×#124×C149C418yescomplemented
22C22×C4⋊C4×C149C2211yescharacteristic
23C22×C4⋊C4×C149C2211yescharacteristic
24C22×C4⋊C4×C149C2211yescharacteristic
25C22×C22⋊C4×C149C2211yescharacteristic
26C22×C22⋊C4×C149C2211yescharacteristic
27C22×C22⋊C4×C149C2211yescharacteristic
28C22×C22⋊C4×C149C2211yescharacteristic
29C22×C22⋊C4×C149C2211yescharacteristic
30C22×C22⋊C4×C149C2211yescharacteristic
31C22×C22⋊C4×C149C2211yescharacteristic
32C22×C22⋊C4×C149C2211yescharacteristic
33C22×C22⋊C4×C149C2211yescharacteristic
34C22×C22⋊C4×C149C2211yescharacteristic
35C22×C22⋊C4×C149C2211yescharacteristic
36C22×C42×C149C2211yescharacteristic
37C22×C42×C149C2211yescharacteristic
38#391×C149—24no—
39#388×C149—24no—
40#386×C149—24no—
41#385×C149—24no—
42C2×#95×C149C2211yescharacteristic
43C2×#95×C149C2211yescharacteristic
44C2×#95×C149C2211yescharacteristic
45C2×#95×C149C2211yescharacteristic
46C2×#95×C149C2211yescharacteristic
47C2×#95×C149C2211yescharacteristic
48C2×#95×C149C2211yescharacteristic
49C2×#95×C149C2211yescharacteristic
50C2×#95×C149C2211yescharacteristic
51C2×#95×C149C2211yescharacteristic
52C2×#95×C149C2211yescharacteristic
53C2×#95×C149C2211yescharacteristic
54C2×#95×C149C2211yescharacteristic
55C2×#95×C149C2211yescharacteristic
56C2×#95×C149C2211yescharacteristic
57C2×#95×C149C2211yescharacteristic
58C25×C149C2311yescharacteristic
59C25×C149C2311yescharacteristic
60C22×Q8×C149—22no—
61C22×Q8×C149—22no—
62C22×Q8×C149—22no—
63C22×Q8×C149—22no—
64C22×Q8×C149—41no—
65C22×Q8×C149—41no—
66C22×Q8×C149C2×C414yescomplemented
67C22×D4×C149—22no—
68C22×D4×C149—22no—
69C22×D4×C149—22no—
70C22×D4×C149—22no—
71C22×D4×C149—41no—
72C22×D4×C149—41no—
73C22×D4×C149C2×C414yes—
74C23×C4×C149—22no—
75C23×C4×C149—22no—
76C23×C4×C149—22no—
77C23×C4×C149—41no—
78C23×C4×C149—41no—
79C23×C4×C149—41no—
80C23×C4×C149—41no—
81C23×C4×C149C2311yescharacteristic
82C23×C4×C149C2311yescharacteristic
83C23×C4×C149C2311yescharacteristic
84C23×C4×C149C2311yescharacteristic
85C23×C4×C149C2311yescharacteristic
86C23×C4×C149C2311yescharacteristic
87C23×C4×C149C2311yescharacteristic
88C23×C4×C149C2311yescharacteristic
89C23×C4×C149C2311yescharacteristic
90C23×C4×C149C2311yescharacteristic
91C23×C4×C149C2311yescharacteristic
92C23×C4×C149C2311yescharacteristic
93C23×C4×C149C2311yescharacteristic
94#124×C149—232no—
95C2×C4⋊C4×C149—22no—
96C2×C4⋊C4×C149—22no—
97C2×C4⋊C4×C149—22no—
98C2×C4⋊C4×C149—22no—
99C2×C4⋊C4×C149—22no—
100C2×C4⋊C4×C149—22no—
101C2×C4⋊C4×C149—41no—
102C2×C4⋊C4×C149—41no—
103C2×C4⋊C4×C149—41no—
104C2×C22⋊C4×C149—22no—
105C2×C22⋊C4×C149—22no—
106C2×C22⋊C4×C149—22no—
107C2×C22⋊C4×C149—22no—
108C2×C22⋊C4×C149—22no—
109C2×C22⋊C4×C149—22no—
110C2×C22⋊C4×C149—22no—
111C2×C22⋊C4×C149—22no—
112C2×C22⋊C4×C149—22no—
113C2×C22⋊C4×C149—22no—
114C2×C22⋊C4×C149—22no—
115C2×C22⋊C4×C149—22no—
116C2×C22⋊C4×C149—22no—
117C2×C22⋊C4×C149—22no—
118C2×C22⋊C4×C149—22no—
119C2×C22⋊C4×C149—41no—
120C2×C22⋊C4×C149—41no—
121C2×C22⋊C4×C149—41no—
122C2×C22⋊C4×C149—41no—
123C2×C22⋊C4×C149—41no—
124C2×C22⋊C4×C149—41no—
125C2×C22⋊C4×C149—41no—
126C2×C22⋊C4×C149—41no—
127C2×C22⋊C4×C149—41no—
128C2×C22⋊C4×C149—41no—
129C2×C22⋊C4×C149—41no—
130C2×C22⋊C4×C149—41no—
131C2×C22⋊C4×C149C2×C414yes—
132C2×C22⋊C4×C149C2×C414yes—
133C2×C22⋊C4×C149C2×C414yescomplemented
134C2×C22⋊C4×C149C2×C414yescomplemented
135C2×C22⋊C4×C149D414yes—
136C2×C22⋊C4×C149D414yes—
137C2×C42×C149—22no—
138C2×C42×C149—22no—
139C2×C42×C149—22no—
140C2×C42×C149—22no—
141C2×C42×C149—41no—
142C2×C42×C149C2×C414yescomplemented
143#95×C149—22no—
144#95×C149—22no—
145#95×C149—22no—
146#95×C149—22no—
147#95×C149—22no—
148#95×C149—22no—
149#95×C149—22no—
150#95×C149—22no—
151#95×C149—22no—
152#95×C149—41no—
153#95×C149—41no—
154#95×C149—41no—
155#95×C149—41no—
156#95×C149—41no—
157#95×C149—41no—
158#95×C149D414yes—
159C24×C149—21no—
160C24×C149—21no—
161C24×C149—21no—
162C24×C149—21no—
163C24×C149—21no—
164C24×C149—21no—
165C24×C149—21no—
166C24×C149—21no—
167C24×C149—21no—
168C24×C149—21no—
169C24×C149—21no—
170C24×C149—21no—
171C24×C149—21no—
172C24×C149—21no—
173C24×C149—21no—
174C24×C149—21no—
175C24×C149—21no—
176C24×C149—21no—
177C24×C149—21no—
178C24×C149—21no—
179C24×C149—21no—
180C24×C149—21no—
181C24×C149—21no—
182C24×C149—21no—
183C24×C149—21no—
184C24×C149—21no—
185C24×C149C22×C412yes—
186C24×C149C22×C412yes—
187C24×C149C2×D412yes—
188C24×C149C2×D412yes—
189C24×C149C2411yescharacteristic
190C2×Q8×C149—28no—
191C2×Q8×C149—28no—
192C2×Q8×C149—44no—
193C2×Q8×C149—44no—
194C2×Q8×C149—44no—
195C2×Q8×C149—44no—
196C2×Q8×C149—44no—
197C2×D4×C149—28no—
198C2×D4×C149—28no—
199C2×D4×C149—44no—
200C2×D4×C149—44no—
201C2×D4×C149—44no—
202C2×D4×C149—44no—
203C2×D4×C149—44no—
204C22×C4×C149—21no—
205C22×C4×C149—21no—
206C22×C4×C149—21no—
207C22×C4×C149—21no—
208C22×C4×C149—21no—
209C22×C4×C149—21no—
210C22×C4×C149—21no—
211C22×C4×C149—21no—
212C22×C4×C149—21no—
213C22×C4×C149—21no—
214C22×C4×C149—21no—
215C22×C4×C149—21no—
216C22×C4×C149—21no—
217C22×C4×C149—21no—
218C22×C4×C149—21no—
219C22×C4×C149—21no—
220C22×C4×C149—21no—
221C22×C4×C149—21no—
222C22×C4×C149—21no—
223C22×C4×C149—21no—
224C22×C4×C149—21no—
225C22×C4×C149—21no—
226C22×C4×C149—21no—
227C22×C4×C149—21no—
228C22×C4×C149—21no—
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—21no—
239C22×C4×C149—21no—
240C22×C4×C149—21no—
241C22×C4×C149—21no—
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—21no—
254C22×C4×C149—21no—
255C22×C4×C149—21no—
256C22×C4×C149—21no—
257C22×C4×C149—21no—
258C22×C4×C149—21no—
259C22×C4×C149—21no—
260C22×C4×C149—21no—
261C22×C4×C149—21no—
262C22×C4×C149—21no—
263C22×C4×C149—21no—
264C22×C4×C149—21no—
265C22×C4×C149—21no—
266C22×C4×C149—21no—
267C22×C4×C149—21no—
268C22×C4×C149—21no—
269C22×C4×C149—21no—
270C22×C4×C149—21no—
271C22×C4×C149—21no—
272C22×C4×C149—21no—
273C22×C4×C149—21no—
274C22×C4×C149—21no—
275C22×C4×C149—21no—
276C22×C4×C149—21no—
277C22×C4×C149—21no—
278C22×C4×C149—21no—
279C22×C4×C149—21no—
280C22×C4×C149—44no—
281C22×C4×C149—44no—
282C22×C4×C149—44no—
283C22×C4×C149—44no—
284C22×C4×C149—44no—
285C22×C4×C149—44no—
286C22×C4×C149—44no—
287C22×C4×C149C22×C412yes—
288C22×C4×C149C22×C412yes—
289C22×C4×C149C22×C412yes—
290C22×C4×C149C22×C412yes—
291C22×C4×C149C22×C412yes—
292C22×C4×C149C2×D412yes—
293C22×C4×C149C2×D412yes—
294C22×C4×C149C2×D412yes—
295C22×C4×C149C2×D412yes—
296C22×C4×C149C2×D412yes—
297C22×C4×C149C2×D412yes—
298C22×C4×C149C2×D412yes—
299C22×C4×C149#4112yes—
300C22×C4×C149#4112yes—
301C22×C4×C149#4112yes—
302C4⋊C4×C149—44no—
303C4⋊C4×C149—44no—
304C4⋊C4×C149—44no—
305C22⋊C4×C149—28no—
306C22⋊C4×C149—28no—
307C22⋊C4×C149—28no—
308C22⋊C4×C149—44no—
309C22⋊C4×C149—44no—
310C22⋊C4×C149—44no—
311C22⋊C4×C149—44no—
312C22⋊C4×C149—44no—
313C22⋊C4×C149—44no—
314C22⋊C4×C149—44no—
315C22⋊C4×C149C22⋊C4116yescomplemented
316C42×C149—28no—
317C42×C149—44no—
318C23×C149—22no—
319C23×C149—22no—
320C23×C149—22no—
321C23×C149—22no—
322C23×C149—22no—
323C23×C149—22no—
324C23×C149—22no—
325C23×C149—22no—
326C23×C149—22no—
327C23×C149—22no—
328C23×C149—22no—
329C23×C149—22no—
330C23×C149—22no—
331C23×C149—22no—
332C23×C149—22no—
333C23×C149—22no—
334C23×C149—22no—
335C23×C149—22no—
336C23×C149—22no—
337C23×C149—22no—
338C23×C149—22no—
339C23×C149—22no—
340C23×C149—22no—
341C23×C149—22no—
342C23×C149—22no—
343C23×C149—41no—
344C23×C149—41no—
345C23×C149—41no—
346C23×C149—41no—
347C23×C149—41no—
348C23×C149—41no—
349C23×C149—41no—
350C23×C149—41no—
351C23×C149—41no—
352C23×C149—41no—
353C23×C149—41no—
354C23×C149—41no—
355C23×C149—41no—
356C23×C149—41no—
357C23×C149—41no—
358C23×C149—41no—
359C23×C149—41no—
360C23×C149—41no—
361C23×C149—41no—
362C23×C149—41no—
363C23×C149—41no—
364C23×C149—41no—
365C23×C149—41no—
366C23×C149—41no—
367C23×C149—41no—
368C23×C149—41no—
369C23×C149—41no—
370C23×C149—41no—
371C23×C149—41no—
372C23×C149—41no—
373C23×C149—41no—
374C23×C149—41no—
375C23×C149—41no—
376C23×C149—41no—
377C23×C149—41no—
378C23×C149—41no—
379C23×C149—41no—
380C23×C149—41no—
381C23×C149—41no—
382C23×C149—41no—
383C23×C149—41no—
384C23×C149—41no—
385C23×C149—41no—
386C23×C149—41no—
387C23×C149C2×C22⋊C414yes—
388C23×C149C23×C411yescharacteristic
389C23×C149C22×D411yescharacteristic
390C23×C149C22×D411yescharacteristic
391C23×C149C22×D411yescharacteristic
392C23×C149C2×#4111yescharacteristic
393C23×C149C2×#4111yescharacteristic
394C23×C149C2×#4111yescharacteristic
395C23×C149H(5,𝔽2)11yescharacteristic
396C23×C149H(5,𝔽2)11yescharacteristic
397C23×C149H(5,𝔽2)11yescharacteristic
398C23×C149H(5,𝔽2)11yescharacteristic
399C23×C149H(5,𝔽2)11yescharacteristic
400C23×C1492−1+411yescharacteristic
401C23×C1492−1+411yescharacteristic
402C23×C1492−1+411yescharacteristic
403Q8×C149—416no—
404D4×C149—416no—
405C2×C4×C149—22no—
406C2×C4×C149—22no—
407C2×C4×C149—22no—
408C2×C4×C149—22no—
409C2×C4×C149—22no—
410C2×C4×C149—22no—
411C2×C4×C149—22no—
412C2×C4×C149—22no—
413C2×C4×C149—22no—
414C2×C4×C149—22no—
415C2×C4×C149—22no—
416C2×C4×C149—22no—
417C2×C4×C149—22no—
418C2×C4×C149—22no—
419C2×C4×C149—22no—
420C2×C4×C149—22no—
421C2×C4×C149—22no—
422C2×C4×C149—22no—
423C2×C4×C149—22no—
424C2×C4×C149—22no—
425C2×C4×C149—22no—
426C2×C4×C149—22no—
427C2×C4×C149—22no—
428C2×C4×C149—22no—
429C2×C4×C149—22no—
430C2×C4×C149—22no—
431C2×C4×C149—22no—
432C2×C4×C149—22no—
433C2×C4×C149—22no—
434C2×C4×C149—22no—
435C2×C4×C149—22no—
436C2×C4×C149—22no—
437C2×C4×C149—22no—
438C2×C4×C149—22no—
439C2×C4×C149—22no—
440C2×C4×C149—22no—
441C2×C4×C149—416no—
442C2×C4×C149—41no—
443C2×C4×C149—41no—
444C2×C4×C149—41no—
445C2×C4×C149—41no—
446C2×C4×C149—41no—
447C2×C4×C149—41no—
448C2×C4×C149—41no—
449C2×C4×C149—41no—
450C2×C4×C149—41no—
451C2×C4×C149—41no—
452C2×C4×C149—41no—
453C2×C4×C149—41no—
454C2×C4×C149—41no—
455C2×C4×C149—41no—
456C2×C4×C149—41no—
457C2×C4×C149—41no—
458C2×C4×C149—41no—
459C2×C4×C149—41no—
460C2×C4×C149—41no—
461C2×C4×C149—41no—
462C2×C4×C149—41no—
463C2×C4×C149—41no—
464C2×C4×C149—41no—
465C2×C4×C149—41no—
466C2×C4×C149—41no—
467C2×C4×C149—41no—
468C2×C4×C149—41no—
469C2×C4×C149—41no—
470C2×C4×C149—41no—
471C2×C4×C149—41no—
472C2×C4×C149—41no—
473C2×C4×C149—41no—
474C2×C4×C149—41no—
475C2×C4×C149—41no—
476C2×C4×C149—41no—
477C2×C4×C149—41no—
478C2×C4×C149—41no—
479C2×C4×C149—41no—
480C2×C4×C149—41no—
481C2×C4×C149—41no—
482C2×C4×C149—41no—
483C2×C4×C149—41no—
484C2×C4×C149—41no—
485C2×C4×C149—41no—
486C2×C4×C149—41no—
487C2×C4×C149—41no—
488C2×C4×C149—41no—
489C2×C4×C149—41no—
490C2×C4×C149—41no—
491C2×C4×C149—41no—
492C2×C4×C149—41no—
493C2×C4×C149—41no—
494C2×C4×C149C2×C22⋊C414yes—
495C2×C4×C149C2×C22⋊C414yes—
496C2×C4×C149C4×D414yes—
497C22×C149—24no—
498C22×C149—24no—
499C22×C149—24no—
500C22×C149—42no—
501C22×C149—42no—
502C22×C149—42no—
503C22×C149—42no—
504C22×C149—42no—
505C22×C149—42no—
506C22×C149—42no—
507C22×C149—42no—
508C22×C149—42no—
509C22×C149—42no—
510C22×C149—42no—
511C22×C149—42no—
512C22×C149—42no—
513C22×C149—42no—
514C22×C149—42no—
515C22×C149—42no—
516C22×C149—42no—
517C22×C149—42no—
518C22×C149—42no—
519C22×C149—81no—
520C22×C149—81no—
521C22×C149—81no—
522C22×C149—81no—
523C22×C149—81no—
524C22×C149—81no—
525C22×C149—81no—
526C22×C149—81no—
527C22×C149C22×C22⋊C411yescharacteristic
528C22×C149C2×C4×D411yescharacteristic
529C22×C149C4×#4111yescharacteristic
530C22×C149#51811yescharacteristic
531C22×C149#52011yescharacteristic
532C22×C149#52011yescharacteristic
533C22×C149#52011yescharacteristic
534C22×C149#53511yescharacteristic
535C22×C149#53511yescharacteristic
536C22×C149#53611yescharacteristic
537C22×C149#53611yescharacteristic
538C22×C149#53711yescharacteristic
539C22×C149#53711yescharacteristic
540C22×C149#53811yescharacteristic
541C22×C149#53811yescharacteristic
542C22×C149#54211yescharacteristic
543C22×C149#54211yescharacteristic
544C22×C149#54211yescharacteristic
545C22×C149#54211yescharacteristic
546C22×C149D4211yescharacteristic
547C22×C149D4211yescharacteristic
548C22×C149#54611yescharacteristic
549C22×C149#54611yescharacteristic
550C22×C149#54611yescharacteristic
551C22×C149#54611yescharacteristic
552C22×C149#54611yescharacteristic
553C22×C149#54711yescharacteristic
554C22×C149#54711yescharacteristic
555C22×C149#54811yescharacteristic
556C22×C149#55611yescharacteristic
557C22×C149#55911yescharacteristic
558C22×C149H(3,𝔽4)11yescharacteristic
559C22×C149#56211yescharacteristic
560C22×C149#56211yescharacteristic
561C22×C149#56311yescharacteristic
562C4×C149—24no—
563C4×C149—24no—
564C4×C149—24no—
565C4×C149—42no—
566C4×C149—42no—
567C4×C149—42no—
568C4×C149—42no—
569C4×C149—42no—
570C4×C149—42no—
571C4×C149—81no—
572C4×C149—81no—
573C4×C149—81no—
574C4×C149—81no—
575C2×C149—44no—
576C2×C149—82no—
577C2×C149#231111yescharacteristic
578C2×C149#232611yescharacteristic
579C2×C149#233711yescharacteristic
580C2×C149D4×C22⋊C411yescharacteristic
581C2×C149#233911yescharacteristic
582C2×C149#236711yescharacteristic
583C2×C149#237911yescharacteristic
584C2×C149#267011yescharacteristic
585C2×C149#267211yescharacteristic
586C2×C149#267411yescharacteristic
587C2×C149#267611yescharacteristic
588C2×C149#270011yescharacteristic
589C2×C149#271011yescharacteristic
590C2×C149#271211yescharacteristic
591C2×C149#271511yescharacteristic
592#14421C14911yesmaximal, characteristic, direct product factor, Sylow
593C149#1442111yescharacteristic, direct product factor, Sylow
594C22×#124C2×C14911yescharacteristic
595C2×#391C2×C14911yescharacteristic, complemented
596C2×#388C2×C14911yescharacteristic, complemented
597C2×#386C2×C14911yescharacteristic
598C2×#385C2×C14911yescharacteristic, complemented
599#1446C2×C14911yescharacteristic, complemented
600#1440C2×C14911yescharacteristic, complemented
601#1439C2×C14911yescharacteristic, complemented
602#1439C2×C14911yescharacteristic, complemented
603#1439C2×C14911yescharacteristic, complemented
604#1438C2×C14911yescharacteristic
605#1437C2×C14911yescharacteristic, complemented
606C4⋊#95C2×C14911yescharacteristic, complemented
607#1434C2×C14911yescharacteristic, complemented
608C22⋊#95C2×C14911yescharacteristic, complemented
609C23×Q8C22×C14911yescharacteristic
610C23×D4C22×C14911yescharacteristic
611C24×C4C22×C14911yescharacteristic
612C2×#124—24no—
613C2×#124—24no—
614C2×#124C4×C14918yescomplemented
615C22×C4⋊C4C22×C14911yescharacteristic
616C22×C4⋊C4C22×C14911yescharacteristic
617C22×C4⋊C4C22×C14911yescharacteristic
618C22×C22⋊C4C22×C14911yescharacteristic
619C22×C22⋊C4C22×C14911yescharacteristic
620C22×C22⋊C4C22×C14911yescharacteristic
621C22×C22⋊C4C22×C14911yescharacteristic
622C22×C22⋊C4C22×C14911yescharacteristic
623C22×C22⋊C4C22×C14911yescharacteristic
624C22×C22⋊C4C22×C14911yescharacteristic
625C22×C22⋊C4C22×C14911yescharacteristic
626C22×C22⋊C4C22×C14911yescharacteristic
627C22×C22⋊C4C22×C14911yescharacteristic
628C22×C22⋊C4C22×C14911yescharacteristic
629C22×C42C22×C14911yescharacteristic
630C22×C42C22×C14911yescharacteristic
631#391—24no—
632#388—24no—
633#386—24no—
634#385—24no—
635C2×#95C22×C14911yescharacteristic
636C2×#95C22×C14911yescharacteristic
637C2×#95C22×C14911yescharacteristic
638C2×#95C22×C14911yescharacteristic
639C2×#95C22×C14911yescharacteristic
640C2×#95C22×C14911yescharacteristic
641C2×#95C22×C14911yescharacteristic
642C2×#95C22×C14911yescharacteristic
643C2×#95C22×C14911yescharacteristic
644C2×#95C22×C14911yescharacteristic
645C2×#95C22×C14911yescharacteristic
646C2×#95C22×C14911yescharacteristic
647C2×#95C22×C14911yescharacteristic
648C2×#95C22×C14911yescharacteristic
649C2×#95C22×C14911yescharacteristic
650C2×#95C22×C14911yescharacteristic
651C25C23×C14911yescharacteristic
652C25C23×C14911yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×C4×C14914yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×C4×C14914yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C14911yescharacteristic
675C23×C4C23×C14911yescharacteristic
676C23×C4C23×C14911yescharacteristic
677C23×C4C23×C14911yescharacteristic
678C23×C4C23×C14911yescharacteristic
679C23×C4C23×C14911yescharacteristic
680C23×C4C23×C14911yescharacteristic
681C23×C4C23×C14911yescharacteristic
682C23×C4C23×C14911yescharacteristic
683C23×C4C23×C14911yescharacteristic
684C23×C4C23×C14911yescharacteristic
685C23×C4C23×C14911yescharacteristic
686C23×C4C23×C14911yescharacteristic
687#124—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4C2×C4×C14914yes—
725C2×C22⋊C4C2×C4×C14914yes—
726C2×C22⋊C4C2×C4×C14914yescomplemented
727C2×C22⋊C4C2×C4×C14914yescomplemented
728C2×C22⋊C4D4×C14914yes—
729C2×C22⋊C4D4×C14914yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—41no—
735C2×C42C2×C4×C14914yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95D4×C14914yes—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×C4×C14912yes—
779C24C22×C4×C14912yes—
780C24C2×D4×C14912yes—
781C24C2×D4×C14912yes—
782C24C24×C14911yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
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—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4C22×C4×C14912yes—
881C22×C4C22×C4×C14912yes—
882C22×C4C22×C4×C14912yes—
883C22×C4C22×C4×C14912yes—
884C22×C4C22×C4×C14912yes—
885C22×C4C2×D4×C14912yes—
886C22×C4C2×D4×C14912yes—
887C22×C4C2×D4×C14912yes—
888C22×C4C2×D4×C14912yes—
889C22×C4C2×D4×C14912yes—
890C22×C4C2×D4×C14912yes—
891C22×C4C2×D4×C14912yes—
892C22×C4#41×C14912yes—
893C22×C4#41×C14912yes—
894C22×C4#41×C14912yes—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4C22⋊C4×C149116yescomplemented
909C42—28no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊C4×C14914yes—
981C23C23×C4×C14911yescharacteristic
982C23C22×D4×C14911yescharacteristic
983C23C22×D4×C14911yescharacteristic
984C23C22×D4×C14911yescharacteristic
985C23C2×#41×C14911yescharacteristic
986C23C2×#41×C14911yescharacteristic
987C23C2×#41×C14911yescharacteristic
988C23H(5,𝔽2)×C14911yescharacteristic
989C23H(5,𝔽2)×C14911yescharacteristic
990C23H(5,𝔽2)×C14911yescharacteristic
991C23H(5,𝔽2)×C14911yescharacteristic
992C23H(5,𝔽2)×C14911yescharacteristic
993C232−1+4×C14911yescharacteristic
994C232−1+4×C14911yescharacteristic
995C232−1+4×C14911yescharacteristic
996Q8—416no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—416no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4C2×C22⋊C4×C14914yes—
1088C2×C4C2×C22⋊C4×C14914yes—
1089C2×C4C4×D4×C14914yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊C4×C14911yescharacteristic
1121C22C2×C4×D4×C14911yescharacteristic
1122C22C4×#41×C14911yescharacteristic
1123C22#518×C14911yescharacteristic
1124C22#520×C14911yescharacteristic
1125C22#520×C14911yescharacteristic
1126C22#520×C14911yescharacteristic
1127C22#535×C14911yescharacteristic
1128C22#535×C14911yescharacteristic
1129C22#536×C14911yescharacteristic
1130C22#536×C14911yescharacteristic
1131C22#537×C14911yescharacteristic
1132C22#537×C14911yescharacteristic
1133C22#538×C14911yescharacteristic
1134C22#538×C14911yescharacteristic
1135C22#542×C14911yescharacteristic
1136C22#542×C14911yescharacteristic
1137C22#542×C14911yescharacteristic
1138C22#542×C14911yescharacteristic
1139C22D42×C14911yescharacteristic
1140C22D42×C14911yescharacteristic
1141C22#546×C14911yescharacteristic
1142C22#546×C14911yescharacteristic
1143C22#546×C14911yescharacteristic
1144C22#546×C14911yescharacteristic
1145C22#546×C14911yescharacteristic
1146C22#547×C14911yescharacteristic
1147C22#547×C14911yescharacteristic
1148C22#548×C14911yescharacteristic
1149C22#556×C14911yescharacteristic
1150C22#559×C14911yescharacteristic
1151C22H(3,𝔽4)×C14911yescharacteristic
1152C22#562×C14911yescharacteristic
1153C22#562×C14911yescharacteristic
1154C22#563×C14911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2#2311×C14911yescharacteristic
1171C2#2326×C14911yescharacteristic
1172C2#2337×C14911yescharacteristic
1173C2D4×C22⋊C4×C14911yescharacteristic
1174C2#2339×C14911yescharacteristic
1175C2#2367×C14911yescharacteristic
1176C2#2379×C14911yescharacteristic
1177C2#2670×C14911yescharacteristic
1178C2#2672×C14911yescharacteristic
1179C2#2674×C14911yescharacteristic
1180C2#2676×C14911yescharacteristic
1181C2#2700×C14911yescharacteristic
1182C2#2710×C14911yescharacteristic
1183C2#2712×C14911yescharacteristic
1184C2#2715×C14911yescharacteristic
subgroupG/H
center, socleC24×C149C24
commutatorC23C23×C4×C149
Frattini, cosocleC24C24×C149
prime radicalC23×D4×C149C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C149C2semidirect
3. C2×#388×C149C2semidirect
5. C2×#385×C149C2semidirect
6. #1446×C149C2semidirect
7. #1440×C149C2semidirect
8. #1439×C149C2semidirect
9. #1439×C149C2semidirect
10. #1439×C149C2semidirect
12. #1437×C149C2semidirect
13. C4⋊#95×C149C2semidirect
14. #1434×C149C2semidirect
15. C22⋊#95×C149C2semidirect
21. C2×#124×C149C4semidirect
66. C22×Q8×C149C2×C4semidirect
133. C2×C22⋊C4×C149C2×C4semidirect
134. C2×C22⋊C4×C149C2×C4semidirect
142. C2×C42×C149C2×C4semidirect
315. C22⋊C4×C149C22⋊C4semidirect
592. #14421C149direct (N × H)
593. C149#14421direct (N × H)
595. C2×#391C2×C149semidirect
596. C2×#388C2×C149semidirect
598. C2×#385C2×C149semidirect
599. #1446C2×C149semidirect
600. #1440C2×C149semidirect
601. #1439C2×C149semidirect
602. #1439C2×C149semidirect
603. #1439C2×C149semidirect
605. #1437C2×C149semidirect
606. C4⋊#95C2×C149semidirect
607. #1434C2×C149semidirect
608. C22⋊#95C2×C149semidirect
614. C2×#124C4×C149semidirect
659. C22×Q8C2×C4×C149semidirect
726. C2×C22⋊C4C2×C4×C149semidirect
727. C2×C22⋊C4C2×C4×C149semidirect
735. C2×C42C2×C4×C149semidirect
908. C22⋊C4C22⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1492
C2×#391×C1492
C2×#388×C1492
C2×#386×C1492
C2×#385×C1492
#1446×C1492
#1440×C1492
#1439×C1492
#1438×C1492
#1437×C1492
C4⋊#95×C1492
#1434×C1492
C22⋊#95×C1492
#14421149