Finite Group Databasebeta

← C149×#11066 #49190015

Subgroups — C149×#11066 #49190015

Order 38144.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#102×C149C211yesmaximal, characteristic
2C22×#102×C149C211yesmaximal, characteristic
3C2×#390×C149C211yesmaximal, characteristic
4C2×#389×C149C211yesmaximal, characteristic, complemented
5C2×#340×C149C211yesmaximal, characteristic, complemented
6C2×#340×C149C211yesmaximal, characteristic, complemented
7C2×#336×C149C211yesmaximal, characteristic, complemented
8C23×D4×C149C2211yescharacteristic
9C23×C8×C149C2211yescharacteristic
10C23×C8×C149C2211yescharacteristic
11C22×C4⋊C4×C149—21no—
12C22×C4⋊C4×C149C2211yescharacteristic
13C22×C4⋊C4×C149C2211yescharacteristic
14C22×C4⋊C4×C149C2211yescharacteristic
15C22×C22⋊C4×C149—21no—
16C22×C22⋊C4×C149—21no—
17C22×C42×C149C2211yescharacteristic
18C2×#102×C149—22no—
19C2×#102×C149—22no—
20C2×#102×C149—22no—
21C2×#102×C149—22no—
22C2×#102×C149—22no—
23C2×#102×C149C414yescomplemented
24#390×C149—22no—
25#390×C149—22no—
26#389×C149—22no—
27#389×C149—22no—
28C2×#95×C149—21no—
29#340×C149—22no—
30#340×C149—22no—
31#336×C149—22no—
32C25×C149—21no—
33C22×D4×C149—21no—
34C22×D4×C149—21no—
35C22×D4×C149—21no—
36C22×D4×C149—21no—
37C22×D4×C149—21no—
38C22×D4×C149—21no—
39C22×D4×C149—21no—
40C22×D4×C149—21no—
41C22×D4×C149—21no—
42C22×D4×C149—21no—
43C22×D4×C149—21no—
44C22×D4×C149C2×C412yes—
45C22×D4×C149D412yes—
46C22×D4×C149Q812yes—
47C23×C4×C149—21no—
48C23×C4×C149—21no—
49C23×C4×C149—21no—
50C23×C4×C149D411yescharacteristic
51C23×C4×C149D411yescharacteristic
52C23×C4×C149C2311yescharacteristic
53C22×C8×C149—21no—
54C22×C8×C149—21no—
55C22×C8×C149—21no—
56C22×C8×C149—21no—
57C22×C8×C149—21no—
58C22×C8×C149—21no—
59C22×C8×C149—21no—
60C22×C8×C149—21no—
61C22×C8×C149—21no—
62C22×C8×C149—21no—
63C22×C8×C149—21no—
64C22×C8×C149—21no—
65C22×C8×C149C2×C412yes—
66C22×C8×C149D412yes—
67C2×C4⋊C4×C149—21no—
68C2×C4⋊C4×C149—21no—
69C2×C4⋊C4×C149—21no—
70C2×C4⋊C4×C149—21no—
71C2×C4⋊C4×C149—21no—
72C2×C4⋊C4×C149—21no—
73C2×C4⋊C4×C149—21no—
74C2×C4⋊C4×C149—21no—
75C2×C4⋊C4×C149—21no—
76C2×C4⋊C4×C149—21no—
77C2×C4⋊C4×C149—21no—
78C2×C4⋊C4×C149—24no—
79C2×C4⋊C4×C149—21no—
80C2×C4⋊C4×C149—21no—
81C2×C4⋊C4×C149—42no—
82C2×C4⋊C4×C149—42no—
83C2×C4⋊C4×C149C2×C412yes—
84C2×C4⋊C4×C149D412yes—
85C2×C4⋊C4×C149D412yes—
86C2×C4⋊C4×C149D412yes—
87C2×C4⋊C4×C149D412yes—
88C2×C22⋊C4×C149—24no—
89C2×C22⋊C4×C149—24no—
90C2×C22⋊C4×C149—42no—
91C2×C22⋊C4×C149—42no—
92C2×C22⋊C4×C149—42no—
93C2×C22⋊C4×C149—42no—
94C2×C42×C149—21no—
95C2×C42×C149—21no—
96C2×C42×C149—21no—
97C2×C42×C149—21no—
98C2×C42×C149—21no—
99C2×C42×C149—21no—
100#102×C149—28no—
101#102×C149—28no—
102#95×C149—24no—
103C24×C149—22no—
104C24×C149—22no—
105C24×C149—22no—
106C24×C149—41no—
107C24×C149—41no—
108C24×C149—41no—
109C24×C149—41no—
110C24×C149—41no—
111C24×C149—41no—
112C24×C149—41no—
113C24×C149—41no—
114C24×C149—41no—
115C24×C149—41no—
116C24×C149—41no—
117C24×C149—41no—
118C24×C149C2×D411yescharacteristic
119C2×D4×C149—22no—
120C2×D4×C149—22no—
121C2×D4×C149—22no—
122C2×D4×C149—22no—
123C2×D4×C149—22no—
124C2×D4×C149—22no—
125C2×D4×C149—22no—
126C2×D4×C149—22no—
127C2×D4×C149—22no—
128C2×D4×C149—22no—
129C2×D4×C149—22no—
130C2×D4×C149—22no—
131C2×D4×C149—22no—
132C2×D4×C149—22no—
133C2×D4×C149—22no—
134C2×D4×C149—41no—
135C2×D4×C149—41no—
136C2×D4×C149—41no—
137C2×D4×C149—41no—
138C2×D4×C149—41no—
139C2×D4×C149—41no—
140C2×D4×C149—41no—
141C2×D4×C149—41no—
142C2×D4×C149—41no—
143C2×D4×C149—41no—
144C2×D4×C149—41no—
145C2×D4×C149—41no—
146C2×D4×C149C4⋊C414yescomplemented
147C22×C4×C149—22no—
148C22×C4×C149—21no—
149C22×C4×C149—22no—
150C22×C4×C149—21no—
151C22×C4×C149—21no—
152C22×C4×C149—21no—
153C22×C4×C149—21no—
154C22×C4×C149—21no—
155C22×C4×C149—22no—
156C22×C4×C149—21no—
157C22×C4×C149—21no—
158C22×C4×C149—21no—
159C22×C4×C149—21no—
160C22×C4×C149—21no—
161C22×C4×C149—21no—
162C22×C4×C149—22no—
163C22×C4×C149—22no—
164C22×C4×C149—41no—
165C22×C4×C149—41no—
166C22×C4×C149—41no—
167C22×C4×C149—41no—
168C22×C4×C149—41no—
169C22×C4×C149—41no—
170C22×C4×C149—41no—
171C22×C4×C149—41no—
172C22×C4×C149—41no—
173C22×C4×C149—41no—
174C22×C4×C149—41no—
175C22×C4×C149—41no—
176C22×C4×C149—41no—
177C22×C4×C149—41no—
178C22×C4×C149—41no—
179C22×C4×C149—41no—
180C22×C4×C149D812yes—
181C22×C4×C149SD1612yes—
182C22×C4×C149C22×C411yescharacteristic
183C22×C4×C149C2×D411yescharacteristic
184C22×C4×C149C2×D411yescharacteristic
185C22×C4×C149C2×D411yescharacteristic
186C22×C4×C149C2×D411yescharacteristic
187C22×C4×C149C2×D411yescharacteristic
188C22×C4×C149C2×D411yescharacteristic
189C22×C4×C149C2×Q811yescharacteristic
190C22×C4×C149#4111yescharacteristic
191C22×C4×C149#4111yescharacteristic
192C22×C4×C149#4111yescharacteristic
193C22×C4×C149#4111yescharacteristic
194C22×C4×C149#4111yescharacteristic
195C22×C4×C149#4111yescharacteristic
196C2×C8×C149—22no—
197C2×C8×C149—22no—
198C2×C8×C149—22no—
199C2×C8×C149—22no—
200C2×C8×C149—22no—
201C2×C8×C149—22no—
202C2×C8×C149—41no—
203C2×C8×C149—41no—
204C2×C8×C149—41no—
205C2×C8×C149—41no—
206C2×C8×C149—41no—
207C2×C8×C149—41no—
208C2×C8×C149—41no—
209C2×C8×C149—41no—
210C4⋊C4×C149—22no—
211C4⋊C4×C149—22no—
212C4⋊C4×C149—22no—
213C4⋊C4×C149—22no—
214C4⋊C4×C149—22no—
215C4⋊C4×C149—22no—
216C4⋊C4×C149—22no—
217C4⋊C4×C149—48no—
218C4⋊C4×C149—41no—
219C4⋊C4×C149—41no—
220C4⋊C4×C149—41no—
221C4⋊C4×C149—41no—
222C4⋊C4×C149C22⋊C414yescomplemented
223C22⋊C4×C149—48no—
224C22⋊C4×C149—48no—
225C42×C149—41no—
226C42×C149—41no—
227C42×C149—41no—
228C42×C149—41no—
229C23×C149—24no—
230C23×C149—42no—
231C23×C149—42no—
232C23×C149—42no—
233C23×C149—42no—
234C23×C149—42no—
235C23×C149—42no—
236C23×C149—42no—
237C23×C149—42no—
238C23×C149—42no—
239C23×C149—42no—
240C23×C149—42no—
241C23×C149—42no—
242C23×C149—42no—
243C23×C149—42no—
244C23×C149—42no—
245C23×C149—42no—
246C23×C149—42no—
247C23×C149—42no—
248C23×C149—81no—
249C23×C149—81no—
250C23×C149—81no—
251C23×C149—81no—
252C23×C149—81no—
253C23×C149—81no—
254C23×C149—81no—
255C23×C149—81no—
256C23×C149—81no—
257C23×C149—81no—
258C23×C149—81no—
259C23×C149—81no—
260C23×C149—81no—
261C23×C149—81no—
262C23×C149—81no—
263C23×C149—81no—
264C23×C149C4×D411yescharacteristic
265C23×C149#12011yescharacteristic
266C23×C149#12011yescharacteristic
267C23×C149#12111yescharacteristic
268C23×C149#12111yescharacteristic
269C23×C149C22⋊Q811yescharacteristic
270C23×C149#12411yescharacteristic
271C23×C149C2×D811yescharacteristic
272C23×C149C2×SD1611yescharacteristic
273C23×C149#13511yescharacteristic
274C23×C149#13511yescharacteristic
275C23×C149AGL(1,ℤ/8)11yescharacteristic
276C23×C149AGL(1,ℤ/8)11yescharacteristic
277C23×C149AGL(1,ℤ/8)11yescharacteristic
278C23×C149#13711yescharacteristic
279D4×C149—24no—
280D4×C149—24no—
281D4×C149—42no—
282D4×C149—42no—
283D4×C149—42no—
284D4×C149—42no—
285D4×C149—42no—
286D4×C149—42no—
287C2×C4×C149—24no—
288C2×C4×C149—22no—
289C2×C4×C149—22no—
290C2×C4×C149—22no—
291C2×C4×C149—22no—
292C2×C4×C149—22no—
293C2×C4×C149—22no—
294C2×C4×C149—41no—
295C2×C4×C149—41no—
296C2×C4×C149—42no—
297C2×C4×C149—42no—
298C2×C4×C149—42no—
299C2×C4×C149—41no—
300C2×C4×C149—41no—
301C2×C4×C149—41no—
302C2×C4×C149—42no—
303C2×C4×C149—41no—
304C2×C4×C149—42no—
305C2×C4×C149—42no—
306C2×C4×C149—41no—
307C2×C4×C149—41no—
308C2×C4×C149—42no—
309C2×C4×C149—42no—
310C2×C4×C149—42no—
311C2×C4×C149—42no—
312C2×C4×C149—42no—
313C2×C4×C149—42no—
314C2×C4×C149—81no—
315C2×C4×C149—81no—
316C2×C4×C149—81no—
317C2×C4×C149—81no—
318C2×C4×C149—81no—
319C2×C4×C149—81no—
320C2×C4×C149—81no—
321C2×C4×C149—81no—
322C2×C4×C149C2×C22⋊C411yescharacteristic
323C2×C4×C149C2×C4⋊C411yescharacteristic
324C2×C4×C149#11711yescharacteristic
325C2×C4×C149C4×D411yescharacteristic
326C2×C4×C149C4×D411yescharacteristic
327C2×C4×C149C4×D411yescharacteristic
328C2×C4×C149#12011yescharacteristic
329C2×C4×C149#12111yescharacteristic
330C2×C4×C149#12111yescharacteristic
331C2×C4×C149#12111yescharacteristic
332C2×C4×C149#12111yescharacteristic
333C2×C4×C149#12111yescharacteristic
334C2×C4×C149#12111yescharacteristic
335C2×C4×C149C22⋊Q811yescharacteristic
336C2×C4×C149C22⋊Q811yescharacteristic
337C2×C4×C149C22⋊Q811yescharacteristic
338C2×C4×C149C22⋊Q811yescharacteristic
339C2×C4×C149C22⋊Q811yescharacteristic
340C2×C4×C149#12311yescharacteristic
341C2×C4×C149#12311yescharacteristic
342C2×C4×C149#12311yescharacteristic
343C2×C4×C149#12311yescharacteristic
344C2×C4×C149#12311yescharacteristic
345C2×C4×C149#12411yescharacteristic
346C2×C4×C149#12411yescharacteristic
347C2×C4×C149#12611yescharacteristic
348C2×C4×C149#12611yescharacteristic
349C2×C4×C149#12711yescharacteristic
350C8×C149—42no—
351C8×C149—42no—
352C22×C149—44no—
353C22×C149—44no—
354C22×C149—44no—
355C22×C149—82no—
356C22×C149—82no—
357C22×C149—82no—
358C22×C149—82no—
359C22×C149—82no—
360C22×C149—82no—
361C22×C149—82no—
362C22×C149—82no—
363C22×C149—82no—
364C22×C149—82no—
365C22×C149—82no—
366C22×C149—82no—
367C22×C149#38511yescharacteristic
368C22×C149#38611yescharacteristic
369C22×C149#38811yescharacteristic
370C22×C149#39211yescharacteristic
371C22×C149#39311yescharacteristic
372C22×C149#39411yescharacteristic
373C22×C149#39611yescharacteristic
374C22×C149C4×D811yescharacteristic
375C22×C149C4×SD1611yescharacteristic
376C22×C149#44011yescharacteristic
377C22×C149#44211yescharacteristic
378C22×C149#44711yescharacteristic
379C22×C149#44711yescharacteristic
380C22×C149#44811yescharacteristic
381C22×C149#44911yescharacteristic
382C22×C149#44911yescharacteristic
383C22×C149#44911yescharacteristic
384C22×C149#45011yescharacteristic
385C22×C149#45211yescharacteristic
386C22×C149#45911yescharacteristic
387C22×C149#46011yescharacteristic
388C22×C149#46311yescharacteristic
389C22×C149#46411yescharacteristic
390C22×C149#46511yescharacteristic
391C22×C149#46611yescharacteristic
392C22×C149#46811yescharacteristic
393C22×C149#46911yescharacteristic
394C22×C149#47411yescharacteristic
395C22×C149#47611yescharacteristic
396C22×C149#47811yescharacteristic
397C22×C149#47811yescharacteristic
398C22×C149#48611yescharacteristic
399C22×C149#48811yescharacteristic
400C22×C149#48911yescharacteristic
401C22×C149#49011yescharacteristic
402C4×C149—44no—
403C4×C149—42no—
404C4×C149—42no—
405C4×C149—82no—
406C4×C149—82no—
407C4×C149#38011yescharacteristic
408C4×C149#38511yescharacteristic
409C4×C149#38811yescharacteristic
410C4×C149#39011yescharacteristic
411C4×C149#39411yescharacteristic
412C4×C149#39611yescharacteristic
413C4×C149#39711yescharacteristic
414C4×C149#39911yescharacteristic
415C2×C149—84no—
416C2×C149#143911yescharacteristic
417C2×C149#186211yescharacteristic
418C2×C149#186411yescharacteristic
419C2×C149#187911yescharacteristic
420C2×C149#188011yescharacteristic
421C2×C149#193411yescharacteristic
422C2×C149#193611yescharacteristic
423C2×C149#199911yescharacteristic
424C2×C149#200011yescharacteristic
425C2×C149#202311yescharacteristic
426C2×C149#202511yescharacteristic
427C2×C149#204111yescharacteristic
428C2×C149#204211yescharacteristic
429C2×C149#206511yescharacteristic
430C2×C149#206711yescharacteristic
431#11066C14911yesmaximal, characteristic, direct product factor, Sylow
432C149#1106611yescharacteristic, direct product factor, Sylow
433C22×#102C2×C14911yescharacteristic
434C22×#102C2×C14911yescharacteristic
435C2×#390C2×C14911yescharacteristic
436C2×#389C2×C14911yescharacteristic, complemented
437C2×#340C2×C14911yescharacteristic, complemented
438C2×#340C2×C14911yescharacteristic, complemented
439C2×#336C2×C14911yescharacteristic, complemented
440C23×D4C22×C14911yescharacteristic
441C23×C8C22×C14911yescharacteristic
442C23×C8C22×C14911yescharacteristic
443C22×C4⋊C4—21no—
444C22×C4⋊C4C22×C14911yescharacteristic
445C22×C4⋊C4C22×C14911yescharacteristic
446C22×C4⋊C4C22×C14911yescharacteristic
447C22×C22⋊C4—21no—
448C22×C22⋊C4—21no—
449C22×C42C22×C14911yescharacteristic
450C2×#102—22no—
451C2×#102—22no—
452C2×#102—22no—
453C2×#102—22no—
454C2×#102—22no—
455C2×#102C4×C14914yescomplemented
456#390—22no—
457#390—22no—
458#389—22no—
459#389—22no—
460C2×#95—21no—
461#340—22no—
462#340—22no—
463#336—22no—
464C25—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4C2×C4×C14912yes—
477C22×D4D4×C14912yes—
478C22×D4Q8×C14912yes—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4D4×C14911yescharacteristic
483C23×C4D4×C14911yescharacteristic
484C23×C4C23×C14911yescharacteristic
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8C2×C4×C14912yes—
498C22×C8D4×C14912yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—42no—
514C2×C4⋊C4—42no—
515C2×C4⋊C4C2×C4×C14912yes—
516C2×C4⋊C4D4×C14912yes—
517C2×C4⋊C4D4×C14912yes—
518C2×C4⋊C4D4×C14912yes—
519C2×C4⋊C4D4×C14912yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532#102—28no—
533#102—28no—
534#95—24no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24—41no—
543C24—41no—
544C24—41no—
545C24—41no—
546C24—41no—
547C24—41no—
548C24—41no—
549C24—41no—
550C24C2×D4×C14911yescharacteristic
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4C4⋊C4×C14914yescomplemented
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4D8×C14912yes—
613C22×C4SD16×C14912yes—
614C22×C4C22×C4×C14911yescharacteristic
615C22×C4C2×D4×C14911yescharacteristic
616C22×C4C2×D4×C14911yescharacteristic
617C22×C4C2×D4×C14911yescharacteristic
618C22×C4C2×D4×C14911yescharacteristic
619C22×C4C2×D4×C14911yescharacteristic
620C22×C4C2×D4×C14911yescharacteristic
621C22×C4C2×Q8×C14911yescharacteristic
622C22×C4#41×C14911yescharacteristic
623C22×C4#41×C14911yescharacteristic
624C22×C4#41×C14911yescharacteristic
625C22×C4#41×C14911yescharacteristic
626C22×C4#41×C14911yescharacteristic
627C22×C4#41×C14911yescharacteristic
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—48no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4C22⋊C4×C14914yescomplemented
655C22⋊C4—48no—
656C22⋊C4—48no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C23—24no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23—81no—
687C23—81no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23—81no—
692C23—81no—
693C23—81no—
694C23—81no—
695C23—81no—
696C23C4×D4×C14911yescharacteristic
697C23#120×C14911yescharacteristic
698C23#120×C14911yescharacteristic
699C23#121×C14911yescharacteristic
700C23#121×C14911yescharacteristic
701C23C22⋊Q8×C14911yescharacteristic
702C23#124×C14911yescharacteristic
703C23C2×D8×C14911yescharacteristic
704C23C2×SD16×C14911yescharacteristic
705C23#135×C14911yescharacteristic
706C23#135×C14911yescharacteristic
707C23AGL(1,ℤ/8)×C14911yescharacteristic
708C23AGL(1,ℤ/8)×C14911yescharacteristic
709C23AGL(1,ℤ/8)×C14911yescharacteristic
710C23#137×C14911yescharacteristic
711D4—24no—
712D4—24no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4C2×C22⋊C4×C14911yescharacteristic
755C2×C4C2×C4⋊C4×C14911yescharacteristic
756C2×C4#117×C14911yescharacteristic
757C2×C4C4×D4×C14911yescharacteristic
758C2×C4C4×D4×C14911yescharacteristic
759C2×C4C4×D4×C14911yescharacteristic
760C2×C4#120×C14911yescharacteristic
761C2×C4#121×C14911yescharacteristic
762C2×C4#121×C14911yescharacteristic
763C2×C4#121×C14911yescharacteristic
764C2×C4#121×C14911yescharacteristic
765C2×C4#121×C14911yescharacteristic
766C2×C4#121×C14911yescharacteristic
767C2×C4C22⋊Q8×C14911yescharacteristic
768C2×C4C22⋊Q8×C14911yescharacteristic
769C2×C4C22⋊Q8×C14911yescharacteristic
770C2×C4C22⋊Q8×C14911yescharacteristic
771C2×C4C22⋊Q8×C14911yescharacteristic
772C2×C4#123×C14911yescharacteristic
773C2×C4#123×C14911yescharacteristic
774C2×C4#123×C14911yescharacteristic
775C2×C4#123×C14911yescharacteristic
776C2×C4#123×C14911yescharacteristic
777C2×C4#124×C14911yescharacteristic
778C2×C4#124×C14911yescharacteristic
779C2×C4#126×C14911yescharacteristic
780C2×C4#126×C14911yescharacteristic
781C2×C4#127×C14911yescharacteristic
782C8—42no—
783C8—42no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22#385×C14911yescharacteristic
800C22#386×C14911yescharacteristic
801C22#388×C14911yescharacteristic
802C22#392×C14911yescharacteristic
803C22#393×C14911yescharacteristic
804C22#394×C14911yescharacteristic
805C22#396×C14911yescharacteristic
806C22C4×D8×C14911yescharacteristic
807C22C4×SD16×C14911yescharacteristic
808C22#440×C14911yescharacteristic
809C22#442×C14911yescharacteristic
810C22#447×C14911yescharacteristic
811C22#447×C14911yescharacteristic
812C22#448×C14911yescharacteristic
813C22#449×C14911yescharacteristic
814C22#449×C14911yescharacteristic
815C22#449×C14911yescharacteristic
816C22#450×C14911yescharacteristic
817C22#452×C14911yescharacteristic
818C22#459×C14911yescharacteristic
819C22#460×C14911yescharacteristic
820C22#463×C14911yescharacteristic
821C22#464×C14911yescharacteristic
822C22#465×C14911yescharacteristic
823C22#466×C14911yescharacteristic
824C22#468×C14911yescharacteristic
825C22#469×C14911yescharacteristic
826C22#474×C14911yescharacteristic
827C22#476×C14911yescharacteristic
828C22#478×C14911yescharacteristic
829C22#478×C14911yescharacteristic
830C22#486×C14911yescharacteristic
831C22#488×C14911yescharacteristic
832C22#489×C14911yescharacteristic
833C22#490×C14911yescharacteristic
834C4—42no—
835C4—42no—
836C4—44no—
837C4—82no—
838C4—82no—
839C4#380×C14911yescharacteristic
840C4#385×C14911yescharacteristic
841C4#388×C14911yescharacteristic
842C4#390×C14911yescharacteristic
843C4#394×C14911yescharacteristic
844C4#396×C14911yescharacteristic
845C4#397×C14911yescharacteristic
846C4#399×C14911yescharacteristic
847C2—84no—
848C2#1439×C14911yescharacteristic
849C2#1862×C14911yescharacteristic
850C2#1864×C14911yescharacteristic
851C2#1879×C14911yescharacteristic
852C2#1880×C14911yescharacteristic
853C2#1934×C14911yescharacteristic
854C2#1936×C14911yescharacteristic
855C2#1999×C14911yescharacteristic
856C2#2000×C14911yescharacteristic
857C2#2023×C14911yescharacteristic
858C2#2025×C14911yescharacteristic
859C2#2041×C14911yescharacteristic
860C2#2042×C14911yescharacteristic
861C2#2065×C14911yescharacteristic
862C2#2067×C14911yescharacteristic
subgroupG/H
center, socleC24×C149C2×D4
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radicalC23×D4×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C149 ◁ C22×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#389×C149C2semidirect
5. C2×#340×C149C2semidirect
6. C2×#340×C149C2semidirect
7. C2×#336×C149C2semidirect
23. C2×#102×C149C4semidirect
146. C2×D4×C149C4⋊C4semidirect
222. C4⋊C4×C149C22⋊C4semidirect
431. #11066C149direct (N × H)
432. C149#11066direct (N × H)
436. C2×#389C2×C149semidirect
437. C2×#340C2×C149semidirect
438. C2×#340C2×C149semidirect
439. C2×#336C2×C149semidirect
455. C2×#102C4×C149semidirect
578. C2×D4C4⋊C4×C149semidirect
654. C4⋊C4C22⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
C22×#102×C1492
C2×#390×C1492
C2×#389×C1492
C2×#340×C1492
C2×#336×C1492
#11066149