Finite Group Databasebeta

← D61⋊#1996 #30616489

Subgroups — D61⋊#1996 #30616489

Order 15616.

1698 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840704C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21462010C214yesmaximal, complemented
4#21462009C212yesmaximal, complemented
5#21462008C212yesmaximal, complemented
6#21461516C214yesmaximal
7C2×C22⋊Q8×D61C211yesmaximal, characteristic
8C22×C4⋊#6923—21no—
9C22×C22⋊#6923C2212yes—
10C22×C22⋊#6923C2212yes—
11C22×C4×#6923—21no—
12#16840704—21no—
13#16840704—21no—
14#16840704C2212yes—
15#16840704C2212yes—
16C4×C22⋊#6923—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C2212yes—
19C4×C22⋊#6923C2212yes—
20C2×(C2×#6923)⋊C4—21no—
21C2×(C2×#6923)⋊C4—21no—
22#16840640C2218yes—
23#16840640C2218yes—
24C22×Q8×D61C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519756C411yescharacteristic, complemented
28C2×#14519755C2212yes—
29C2×#14519754C412yescomplemented
30C2×#14519753C2211yescharacteristic
31C22⋊Q8×D61—21no—
32C22⋊Q8×D61—21no—
33C22⋊Q8×D61—21no—
34C22⋊Q8×D61—21no—
35C22⋊Q8×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61—21no—
38C22⋊Q8×D61—21no—
39C2×C4⋊C4×D61C411yescharacteristic, complemented
40C2×C4⋊C4×D61C412yescomplemented
41C2×C22⋊C4×D61C2212yes—
42C2×C22⋊Q8×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44C23×#6923—22no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—22no—
47C2×C4⋊#6923—44no—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—24no—
50C2×C22⋊#6923—28no—
51C2×C22⋊#6923—22no—
52C2×C22⋊#6923Q818yescomplemented
53C2×C22⋊#6923C2314yes—
54C2×C22⋊#6923C2314yes—
55C2×C4×#6923—22no—
56C2×C4×#6923—22no—
57C2×C4×#6923—44no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60(C2×#6923)⋊C4—22no—
61(C2×#6923)⋊C4—22no—
62C24×D61C2311yescharacteristic
63C22×Dic122C2×C412yescomplemented
64C22×Dic122C2×C411yescharacteristic, complemented
65C2×Q8×D61—21no—
66C2×Q8×D61—21no—
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Q8×D61—44no—
70C23×Dic61C2×C411yescharacteristic
71C22×C4×D61—44no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C412yes—
74C22×C4×D61C2×C412yes—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86#14519757—21no—
87#14519757—21no—
88#14519757—21no—
89#14519757—21no—
90#14519756—21no—
91#14519756—21no—
92#14519756—21no—
93#14519756—21no—
94#14519755—22no—
95#14519755—22no—
96#14519755—22no—
97#14519755—22no—
98#14519754—22no—
99#14519754—22no—
100#14519754—22no—
101#14519754—22no—
102#14519753—21no—
103#14519753—21no—
104#14519753—21no—
105#14519753—21no—
106C2×C4⋊Dic61C2×C411yescharacteristic, complemented
107C2×C4⋊Dic61C2×C412yescomplemented
108C2×#11758196C2×C412yescomplemented
109C2×#11758196C2×C412yescomplemented
110C2×#11758196C2×C412yescomplemented
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—22no—
115C4⋊C4×D61—21no—
116C4⋊C4×D61—21no—
117C4⋊C4×D61—21no—
118C4⋊C4×D61—21no—
119C2×C22⋊Dic61C2×C412yes—
120C2×#11758198C2312yes—
121C2×#11758198C2312yes—
122C22⋊C4×D61—22no—
123C22⋊C4×D61—22no—
124C22⋊C4×D61—22no—
125C22⋊C4×D61—22no—
126C22×Q8×C61C2×C411yescharacteristic, complemented
127C23×C4×C61C2×C411yescharacteristic
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C2×C4⋊C4×C61C2×C412yescomplemented
133C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
134C2×C22⋊C4×C61C2×C412yes—
135C24×C61C22×C411yescharacteristic
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C22×C411yescharacteristic
139C23×D61C2×D411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×Q814yes—
144C23×D61#4114yes—
145C23×D61C2411yescharacteristic
146C22×#6923—28no—
147C22×#6923—24no—
148C22×#6923—24no—
149C22×#6923—44no—
150C22×#6923—44no—
151C22×#6923—44no—
152C22×#6923—44no—
153C22×#6923—44no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C412yes—
164C22×C4×C61C22×C412yes—
165C22×C4×C61C22×C411yescharacteristic
166C22×Dic61—42no—
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C412yes—
173C22×Dic61C22×C412yes—
174C22×Dic61C22×C411yescharacteristic
175Q8×D61—44no—
176Q8×D61—44no—
177Q8×D61—44no—
178Q8×D61—44no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—44no—
196C2×C4×D61—44no—
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22⋊C411yescharacteristic
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—44no—
218C2×Dic122—42no—
219C22⋊#6923—28no—
220C22⋊#6923—24no—
221C22⋊#6923—28no—
222C22⋊#6923—44no—
223C22⋊#6923C2×Q818yescomplemented
224C4⋊#6923—44no—
225C4⋊#6923—44no—
226C4×#6923—44no—
227C4×#6923—44no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244#11758196—22no—
245#11758196—22no—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C2×C22⋊C411yescharacteristic
253C23×C61C2×C22⋊C411yescharacteristic
254C23×C61C4×Q814yes—
255C23×C61C23×C411yescharacteristic
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—48no—
263C22×D61—48no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61C2×C22⋊C411yescharacteristic
271C22×D61C2×C22⋊C411yescharacteristic
272C22×D61C4×Q814yes—
273C22×D61C22⋊Q814yes—
274C22×D61C22⋊Q814yes—
275C22×D61#12412yes—
276C22×D61#12412yes—
277C22×D61C4⋊Q812yes—
278C22×D61C4⋊Q812yes—
279C22×D61C22×D411yescharacteristic
280C22×D61C22×D411yescharacteristic
281C22×D61C22×Q812yes—
282C22×D61C2×#4112yes—
283C2×#6923—28no—
284C2×#6923—44no—
285C2×#6923—44no—
286C2×#6923—416no—
287C2×#6923—44no—
288C2×#6923—44no—
289C2×#6923—44no—
290C2×#6923—88no—
291Q8×C61—42no—
292Q8×C61—42no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C2×C22⋊C411yescharacteristic
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C2×C22⋊C411yescharacteristic
318C2×Dic61C2×C22⋊C411yescharacteristic
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C2×C22⋊C411yescharacteristic
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—44no—
337C4×D61—44no—
338C4×D61—44no—
339C4×D61—44no—
340C4×D61#9914yes—
341Dic122—44no—
342Dic122—42no—
343Dic122—42no—
344Dic122—44no—
345C2×#1996—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—44no—
353C22×C61#39112yes—
354C22×C61#39112yes—
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C2×C4×Q812yes—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—28no—
364C2×D61—24no—
365C2×D61—28no—
366C2×D61—24no—
367C2×D61—44no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61#39112yes—
373C2×D61#39112yes—
374C2×D61C2×#9912yes—
375C2×D61#41012yes—
376C2×D61C2×C22⋊Q812yes—
377C2×D61C2×#12411yescharacteristic
378C2×D61C2×C4⋊Q811yescharacteristic
379#6923—48no—
380#6923—84no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61C2×#9912yes—
387Dic61—21no—
388Dic61—21no—
389Dic61—21no—
390Dic61—42no—
391Dic61—42no—
392Dic61C2×#9912yes—
393C22×C22⋊Q8—611no—
394C2×#380—611no—
395C2×C4×C22⋊C4—611no—
396#1996—612no—
397#1996—612no—
398#1996—614no—
399C2×#342—614no—
400C2×C61—22no—
401C2×C61—22no—
402C2×C61—22no—
403C2×C61C2×#39111yescharacteristic
404C2×C61C22×#9911yescharacteristic
405C2×C61C2×#41011yescharacteristic
406D61—22no—
407D61—21no—
408D61—21no—
409D61—22no—
410D61#199614yescomplemented
411C23×Q8—611no—
412C24×C4—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—612no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—612no—
418C2×C22⋊Q8—1221no—
419C2×C22⋊Q8—1221no—
420C2×C22⋊Q8—1221no—
421C2×C22⋊Q8—1221no—
422C2×C22⋊Q8—1221no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8—1221no—
425C2×C22⋊Q8—1221no—
426C2×C22⋊Q8#692311yescharacteristic, complemented
427C22×C4⋊C4—611no—
428C22×C4⋊C4—612no—
429C22×C4⋊C4—1221no—
430C22×C22⋊C4—612no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4—612no—
433C22×C42—1221no—
434#380—612no—
435#380—612no—
436#380—1221no—
437#380—1221no—
438C4×C22⋊C4—612no—
439C4×C22⋊C4—612no—
440C4×C22⋊C4—1221no—
441C4×C22⋊C4—1221no—
442C2×#95—1221no—
443C2×#95—1221no—
444#342—618no—
445#342—618no—
446C61C2×#199611yescharacteristic, complemented, Sylow
447C25—611no—
448C22×Q8—612no—
449C22×Q8—611no—
450C22×Q8—1221no—
451C22×Q8—1221no—
452C22×Q8—1221no—
453C22×Q8—1221no—
454C22×Q8—2444no—
455C22×Q8C2×#692311yescharacteristic, complemented
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—612no—
470C23×C4—612no—
471C23×C4—1222no—
472C23×C4—1222no—
473C23×C4—2444no—
474C23×C4C2×#692311yescharacteristic
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—1222no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1221no—
488C22⋊Q8—1221no—
489C22⋊Q8—1221no—
490C22⋊Q8—1221no—
491C22⋊Q8—1221no—
492C22⋊Q8—1221no—
493C22⋊Q8—1221no—
494C22⋊Q8—1221no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499C2×C4⋊C4—612no—
500C2×C4⋊C4—612no—
501C2×C4⋊C4—612no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—2444no—
515C2×C4⋊C4C2×#692311yescharacteristic, complemented
516C2×C4⋊C4C2×#692312yescomplemented
517C2×C22⋊C4—618no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—612no—
520C2×C22⋊C4—612no—
521C2×C22⋊C4—612no—
522C2×C22⋊C4—614no—
523C2×C22⋊C4—1222no—
524C2×C22⋊C4—1222no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—1228no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4C2×#692312yes—
532C2×C42—1222no—
533C2×C42—1222no—
534C2×C42—2444no—
535#95—1222no—
536#95—1222no—
537#95—1222no—
538#95—1222no—
539C24—611no—
540C24—611no—
541C24—611no—
542C24—611no—
543C24—611no—
544C24—614no—
545C24—614no—
546C24—611no—
547C24—2442no—
548C24—2442no—
549C24C22×#692311yescharacteristic
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—42no—
553C2×Q8—1222no—
554C2×Q8—1222no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—2442no—
558C2×Q8—2444no—
559C2×Q8—2444no—
560C2×Q8—2444no—
561C2×Q8—2444no—
562C2×Q8—2444no—
563C22×C4—42no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1224no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1224no—
596C22×C4—1228no—
597C22×C4—1224no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2444no—
608C22×C4—2444no—
609C22×C4—2442no—
610C22×C4—2444no—
611C22×C4—2444no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4C22⋊#692311yescharacteristic
616C22×C4C22⋊#692311yescharacteristic
617C22×C4C22⋊#692311yescharacteristic
618C22×C4C22⋊#692311yescharacteristic
619C22×C4C22×#692311yescharacteristic
620C22×C4C22×#692312yes—
621C22×C4C22×#692312yes—
622C22×C4C22×#692311yescharacteristic
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—1222no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—2444no—
638C4⋊C4—2444no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—618no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1228no—
647C22⋊C4—1224no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1228no—
651C22⋊C4—2444no—
652C42—2444no—
653C42—2444no—
654C23—41no—
655C23—41no—
656C23—611no—
657C23—614no—
658C23—612no—
659C23—612no—
660C23—611no—
661C23—611no—
662C23—611no—
663C23—614no—
664C23—614no—
665C23—612no—
666C23—612no—
667C23—612no—
668C23—612no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2448no—
682C23—2448no—
683C23C2×C22⋊#692311yescharacteristic
684C23C2×C22⋊#692311yescharacteristic
685C23Q8×#692314yes—
686C23C23×#692311yescharacteristic
687Q8—42no—
688Q8—42no—
689Q8—2442no—
690Q8—2444no—
691Q8—2444no—
692Q8—2442no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—611no—
704C2×C4—614no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1228no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—4888no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2444no—
731C2×C4—2444no—
732C2×C4—2444no—
733C2×C4—2444no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2444no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4—24416no—
742C2×C4—2444no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4C2×C22⋊#692311yescharacteristic
746C2×C4C2×C22⋊#692311yescharacteristic
747C2×C4C2×C22⋊#692311yescharacteristic
748C2×C4C2×C22⋊#692311yescharacteristic
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—44no—
756C22—612no—
757C22—612no—
758C22—612no—
759C22—612no—
760C22—611no—
761C22—611no—
762C22—612no—
763C22—1224no—
764C22—1228no—
765C22—1224no—
766C22—1228no—
767C22—1221no—
768C22—1221no—
769C22—1221no—
770C22—1221no—
771C22—1221no—
772C22—1221no—
773C22—2442no—
774C22—2444no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22(C2×#6923)⋊Q812yes—
779C22(C2×#6923)⋊Q812yes—
780C22C22×C22⋊#692311yescharacteristic
781C22C2×Q8×#692312yes—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—42no—
786C4—42no—
787C4—612no—
788C4—1221no—
789C4—1221no—
790C4—1221no—
791C4—4884no—
792C4—2448no—
793C4—2442no—
794C4—2442no—
795C4D61⋊#9912yes—
796C2—22no—
797C2—22no—
798C2—22no—
799C2—614no—
800C2—1221no—
801C2—1222no—
802C2—1221no—
803C2—1222no—
804C2C2×(C2×#6923)⋊Q811yescharacteristic
805C2C2×D61⋊#9911yescharacteristic
806C2D61⋊#41011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1996
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21462010C2semidirect
4. #21462009C2semidirect
5. #21462008C2semidirect
24. C22×Q8×D61C4semidirect
27. C2×#14519756C4semidirect
29. C2×#14519754C4semidirect
39. C2×C4⋊C4×D61C4semidirect
40. C2×C4⋊C4×D61C4semidirect
42. C2×C22⋊Q8×C61C4semidirect
52. C2×C22⋊#6923Q8semidirect
63. C22×Dic122C2×C4semidirect
64. C22×Dic122C2×C4semidirect
106. C2×C4⋊Dic61C2×C4semidirect
107. C2×C4⋊Dic61C2×C4semidirect
108. C2×#11758196C2×C4semidirect
109. C2×#11758196C2×C4semidirect
110. C2×#11758196C2×C4semidirect
126. C22×Q8×C61C2×C4semidirect
132. C2×C4⋊C4×C61C2×C4semidirect
133. C2×C4⋊C4×C61C2×C4semidirect
223. C22⋊#6923C2×Q8semidirect
410. D61#1996semidirect
426. C2×C22⋊Q8#6923semidirect
446. C61C2×#1996semidirect
455. C22×Q8C2×#6923semidirect
515. C2×C4⋊C4C2×#6923semidirect
516. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407042
C2×C4×C22⋊#69232
#214620102
#214620092
#214620082
#214615162
C2×C22⋊Q8×D612
C2×#199661