Finite Group Databasebeta

← C2×#21458029 #30556820

Subgroups — C2×#21458029 #30556820

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2#21458029C2116yesmaximal, direct product factor
3C2×#16840119C211yesmaximal, characteristic, complemented
4C2×#16840080C211yesmaximal, characteristic, complemented
5C2×#16840103C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16840010C211yesmaximal, characteristic, complemented
9C2×#16839984C211yesmaximal, characteristic, complemented
10C2×#16839922C211yesmaximal, characteristic, complemented
11C2×#16839912C211yesmaximal, characteristic, complemented
12C2×C4×#11758201C211yesmaximal, characteristic, complemented
13C2×#16839840C211yesmaximal, characteristic, complemented
14C2×#16839761C211yesmaximal, characteristic, complemented
15C2×#16839766C211yesmaximal, characteristic, complemented
16C2×C61×#552C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758201C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23C22×#11758194C2211yescharacteristic, complemented
24#16840408—24no—
25#16840408C2218yes—
26C2×#14519765C2211yescharacteristic
27C2×#14519762—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519751C2211yescharacteristic
30C2×#14519750—21no—
31C2×#14519745—21no—
32C2×C4×D244C2211yescharacteristic
33C2×C22⋊C4×D61—21no—
34#16840119C2218yescomplemented
35#16840103C2218yescomplemented
36#16840080C2218yescomplemented
37#16840059C2218yescomplemented
38#16840018C2218yescomplemented
39#16840010C2218yescomplemented
40#16839984C2218yescomplemented
41#16839922C2218yescomplemented
42#16839912C2218yescomplemented
43C4×#11758201C2218yescomplemented
44#16839840C2218yescomplemented
45C2×#14519710C2211yescharacteristic, complemented
46C2×#14519708C2211yescharacteristic, complemented
47C2×#14519708C2211yescharacteristic, complemented
48C2×C4⋊#92418C2211yescharacteristic, complemented
49#16839766C2218yescomplemented
50#16839761C2218yescomplemented
51C2×#14519701C2211yescharacteristic, complemented
52C2×#14519700C2211yescharacteristic, complemented
53C2×#14519700C2211yescharacteristic, complemented
54C2×#14519700C2211yescharacteristic, complemented
55C2×#14519697C2211yescharacteristic
56C2×#14519697C2211yescharacteristic
57C2×#14519697C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic, complemented
63C2×C4×#92418C2211yescharacteristic, complemented
64C61×#552—24no—
65C61×#552C2218yescomplemented
66C2×#126×C61—21no—
67C2×#125×C61—21no—
68C2×#125×C61C2211yescharacteristic, complemented
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic, complemented
72C2×C4×Q8×C61C2211yescharacteristic, complemented
73C2×C4×D4×C61C2211yescharacteristic
74C2×#117×C61—21no—
75C2×#117×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—24no—
84C22×D244—21no—
85C22×D244—22no—
86C22×D244—42no—
87C22×D244C2311yescharacteristic
88C22×D244C2314yes—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C2×#11758202—42no—
95C2×#11758202C2314yescomplemented
96C2×#11758201—24no—
97C2×#11758201—42no—
98C2×#11758201C2314yes—
99C2×#11758201C2314yes—
100C2×#11758194—42no—
101C2×#11758194—42no—
102C2×#11758194C2314yes—
103C2×#11758194C2314yescomplemented
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108#14519765—22no—
109#14519765C2314yes—
110#14519762—28no—
111#14519756—22no—
112#14519756C2314yes—
113#14519751—22no—
114#14519751C2314yes—
115#14519750—28no—
116#14519745—28no—
117C4×D244—22no—
118C4×D244C2314yes—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×#11758196—21no—
121C2×C22⋊Dic61—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C22⋊C4×D61—28no—
127#14519710C2314yescomplemented
128#14519708C2314yescomplemented
129#14519708C2314yescomplemented
130C4⋊#92418C2314yescomplemented
131#14519701C2314yescomplemented
132#14519700C2314yescomplemented
133#14519700C2314yescomplemented
134#14519700C2314yescomplemented
135#14519697C2314yes—
136#14519697C2314yes—
137#14519697C2314yes—
138#14519697C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141C22⋊#92418C2314yes—
142C22⋊#92418C2314yescomplemented
143C4×#92418C2314yescomplemented
144C22×Q8×C61C2311yescharacteristic
145C22×D4×C61D411yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149#126×C61—28no—
150#125×C61—28no—
151#125×C61—22no—
152#125×C61C2314yescomplemented
153#123×C61—28no—
154C22⋊Q8×C61—22no—
155C22⋊Q8×C61—22no—
156C22⋊Q8×C61C2314yes—
157C22⋊Q8×C61C2314yescomplemented
158C4×Q8×C61—22no—
159C4×Q8×C61C2314yescomplemented
160C4×D4×C61D414yes—
161C4×D4×C61C2314yes—
162#117×C61—22no—
163#117×C61—28no—
164#117×C61C2314yes—
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2314yescomplemented
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61D411yescharacteristic
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C42×C61—21no—
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—24no—
190C23×D61—44no—
191C23×D61—44no—
192C23×D61—82no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61C2412yes—
197C2×D4×C61—42no—
198C2×D4×C61C2×D414yes—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—44no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—82no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224#11758222—28no—
225#11758222—44no—
226#11758222—48no—
227C2×D244—21no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—28no—
232C2×D244—24no—
233C2×D244—21no—
234C2×D244—44no—
235C2×D244—48no—
236C2×D244—44no—
237C2×D244#4114yes—
238C2×D244C2412yes—
239C2×D244C2412yes—
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—44no—
243C2×C4×D61—82no—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122C2412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D414yes—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C4⋊C4×C61C2412yes—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61C2×D414yes—
265C22⋊C4×C61C2×D414yes—
266C42×C61—24no—
267C42×C61—24no—
268C42×C61C2×D412yes—
269C42×C61C2412yes—
270C22⋊Dic61—24no—
271#11758202—44no—
272#11758201—28no—
273#11758201—44no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61C2412yes—
280#11758196—24no—
281#11758194—44no—
282#11758194—44no—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61C22×D412yes—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—24no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—48no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—48no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—84no—
311C22×D61—816no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—42no—
315D4×C61—44no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—24no—
321C2×C4×C61—24no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—48no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D412yes—
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4112yes—
341C2×C4×C61H(5,𝔽2)12yes—
342C2×C4×C61C2511yescharacteristic
343C22⋊D61—48no—
344C22⋊D61—84no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349D244—24no—
350D244—22no—
351D244—22no—
352D244—22no—
353D244—48no—
354D244—42no—
355D244C2×#4114yes—
356C4×D61—48no—
357C4×D61—84no—
358Dic122—22no—
359Dic122—22no—
360Dic122—42no—
361#92418—22no—
362#92418—22no—
363#92418—22no—
364#92418—22no—
365C2×#3323—611nomaximal, Sylow
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—44no—
373C22×C61—44no—
374C22×C61#54612yes—
375C22×C61#57512yes—
376C22×C61#57712yes—
377C22×C61C23×D411yescharacteristic
378C2×D61—24no—
379C2×D61—48no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—816no—
386C2×D61—84no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61#54612yes—
396C4×C61C22×#4111yescharacteristic
397C4×C61C2×H(5,𝔽2)11yescharacteristic
398Dic61—42no—
399Dic61—42no—
400C2×#552D6111yescharacteristic, complemented
401C2×#546—611no—
402#3323—6116no—
403C2×#488—611no—
404C2×#481—611no—
405C2×#485—611no—
406C2×#478—611no—
407C2×#470—611no—
408C2×#468—611no—
409C2×#464—611no—
410C2×#452—611no—
411C2×#450—611no—
412C2×C4×SD16—611no—
413C2×#436—611no—
414C2×#417—611no—
415C2×#418—611no—
416C2×C61—42no—
417C2×C61—42no—
418C2×C61#332314yescomplemented
419C2×C61C2×#54611yescharacteristic
420C2×C61C2×#57511yescharacteristic
421C2×C61C2×#57711yescharacteristic
422D61—44no—
423D61—82no—
424C22×#41—611no—
425C23×D4—611no—
426C22×Q16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×M16—611no—
430C22×M16—611no—
431#552—24no—
432#552C2×D6118yescomplemented
433#546—618no—
434#546—1224no—
435C2×#126—21no—
436C2×#125—21no—
437C2×#125C2×D6111yescharacteristic, complemented
438C2×#124—611no—
439C2×#123—21no—
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8C2×D6111yescharacteristic
443C2×C22⋊Q8C2×D6111yescharacteristic, complemented
444C2×#121—611no—
445C2×#121—1221no—
446C2×#120—1221no—
447C2×C4×Q8C2×D6111yescharacteristic, complemented
448C2×C4×D4—611no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117—21no—
451C2×#117C2×D6111yescharacteristic
452C22×C4⋊C4C2×D6111yescharacteristic, complemented
453C22×C22⋊C4—1221no—
454#488—618no—
455#485—618no—
456#481—618no—
457#478—618no—
458#470—618no—
459#468—618no—
460#464—618no—
461#452—618no—
462#450—618no—
463C4×SD16—618no—
464#436—618no—
465C2×#107—611no—
466C2×#106—611no—
467C2×#106—611no—
468C2×C4⋊C8—611no—
469#418—618no—
470#417—618no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C4×C8—611no—
484C61C2×#332311yescharacteristic, complemented, Sylow
485C25—1221no—
486C2×#41—614no—
487C2×#41—1224no—
488C2×#41—1222no—
489C2×#41—2442no—
490C22×Q8—611no—
491C22×Q8C22×D6111yescharacteristic
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—614no—
495C22×D4—1224no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1222no—
500C22×D4—2442no—
501C22×D4C22⋊D6111yescharacteristic
502C23×C4—21no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×Q16—614no—
508C2×Q16—2442no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—1224no—
512C2×SD16—2442no—
513C2×M16—614no—
514C2×M16—614no—
515C2×M16—2442no—
516C2×M16—2442no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521#126—28no—
522#125—28no—
523#125—22no—
524#125C22×D6114yescomplemented
525#124—614no—
526#124—1222no—
527#123—28no—
528#123—1228no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8C22×D6114yes—
534C22⋊Q8C22×D6114yescomplemented
535#121—614no—
536#121—1222no—
537#121—1228no—
538#120—1228no—
539C4×Q8—22no—
540C4×Q8C22×D6114yescomplemented
541C4×D4—614no—
542C4×D4—1222no—
543C4×D4C22⋊D6114yes—
544C4×D4C22×D6114yes—
545#117—22no—
546#117—28no—
547#117C22×D6114yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4C22⋊D6111yescharacteristic
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C4⋊C4C22×D6114yescomplemented
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1228no—
571C2×C22⋊C4C22⋊D6111yescharacteristic
572C2×C22⋊C4C22⋊D6111yescharacteristic
573C2×C42—21no—
574C2×C42—21no—
575C2×C42C22×D6111yescharacteristic
576#107—614no—
577#106—614no—
578#106—614no—
579C4⋊C8—614no—
580#103—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588#102—614no—
589#102—614no—
590C22⋊C8—614no—
591C22⋊C8—614no—
592C4×C8—614no—
593C24—1221no—
594C24—1224no—
595C24—1221no—
596C24—4882no—
597C24—2444no—
598C24—2444no—
599C24C2×C22⋊D6111yescharacteristic
600C24C2×C22⋊D6111yescharacteristic
601#41—1228no—
602#41—2444no—
603#41—2448no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—612no—
608C2×Q8—1221no—
609C2×Q8—1222no—
610C2×Q8—1222no—
611C2×Q8C23×D6112yes—
612C2×D4—42no—
613C2×D4—614no—
614C2×D4—612no—
615C2×D4—612no—
616C2×D4—1228no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1221no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—4882no—
626C2×D4—2444no—
627C2×D4—2448no—
628C2×D4—2444no—
629C2×D4—2444no—
630C2×D4C2×C22⋊D6114yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—4882no—
646C22×C4—2444no—
647C22×C4C2×C22⋊D6112yes—
648C22×C4C2×C22⋊D6112yes—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657SD16—1228no—
658SD16—2444no—
659M16—2444no—
660M16—2444no—
661C2×C8—612no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—612no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—1222no—
668C2×C8—1222no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—612no—
679C4⋊C4—1221no—
680C4⋊C4—1224no—
681C4⋊C4C2×C22⋊D6114yes—
682C4⋊C4C23×D6112yes—
683C4⋊C4C23×D6112yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4C2×C22⋊D6114yes—
694C22⋊C4C2×C22⋊D6114yes—
695C42—24no—
696C42—24no—
697C42C2×C22⋊D6112yes—
698C42C23×D6112yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—1222no—
706C23—1224no—
707C23—1222no—
708C23—4884no—
709C23—48816no—
710C23—2448no—
711C23—2448no—
712C23—2442no—
713C23—2442no—
714C23—2442no—
715C23—2442no—
716C23—2442no—
717C23C22×C22⋊D6112yes—
718C23C22×C22⋊D6112yes—
719C23C22×C22⋊D6111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1222no—
724Q8—1222no—
725Q8—2442no—
726D4—44no—
727D4—614no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—1224no—
732D4—4884no—
733D4—2448no—
734D4—2448no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—4884no—
758C2×C4—2448no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C22×C22⋊D6112yes—
762C2×C4C22×C22⋊D6112yes—
763C2×C4C22×C22⋊D6112yes—
764C2×C4C22×C22⋊D6112yes—
765C2×C4C22×C22⋊D6111yescharacteristic
766C2×C4#41×D6112yes—
767C2×C4#1451982312yes—
768C2×C4C24×D6111yescharacteristic
769C8—1222no—
770C8—1222no—
771C8—1222no—
772C8—1222no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—1224no—
782C22—48816no—
783C22—4884no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2448no—
790C22#1684040012yes—
791C22#1684056012yes—
792C22#1684057012yes—
793C22C23×C22⋊D6111yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—2442no—
803C4—2442no—
804C4#1684040012yes—
805C4C2×#41×D6111yescharacteristic
806C4C2×#1451982311yescharacteristic
807C2—42no—
808C2—42no—
809C2—4882no—
810C2—2444no—
811C2#2145802914yesdirect product factor
812C2C2×#1684040011yescharacteristic
813C2C2×#1684056011yescharacteristic
814C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#552C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenterC2×#552D61
hypocenterC61C2×#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #21458029C2direct (N × H)
3. C2×#16840119C2semidirect
4. C2×#16840080C2semidirect
5. C2×#16840103C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16840010C2semidirect
9. C2×#16839984C2semidirect
10. C2×#16839922C2semidirect
11. C2×#16839912C2semidirect
12. C2×C4×#11758201C2semidirect
13. C2×#16839840C2semidirect
14. C2×#16839761C2semidirect
15. C2×#16839766C2semidirect
16. C2×C61×#552C2semidirect
19. C22×#11758202C22semidirect
23. C22×#11758194C22semidirect
34. #16840119C22semidirect
35. #16840103C22semidirect
36. #16840080C22semidirect
37. #16840059C22semidirect
38. #16840018C22semidirect
39. #16840010C22semidirect
40. #16839984C22semidirect
41. #16839922C22semidirect
42. #16839912C22semidirect
43. C4×#11758201C22semidirect
44. #16839840C22semidirect
45. C2×#14519710C22semidirect
46. C2×#14519708C22semidirect
47. C2×#14519708C22semidirect
48. C2×C4⋊#92418C22semidirect
49. #16839766C22semidirect
50. #16839761C22semidirect
51. C2×#14519701C22semidirect
52. C2×#14519700C22semidirect
53. C2×#14519700C22semidirect
54. C2×#14519700C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×C4×#92418C22semidirect
65. C61×#552C22semidirect
68. C2×#125×C61C22semidirect
71. C2×C22⋊Q8×C61C22semidirect
72. C2×C4×Q8×C61C22semidirect
76. C22×C4⋊C4×C61C22semidirect
95. C2×#11758202C23semidirect
103. C2×#11758194C23semidirect
127. #14519710C23semidirect
128. #14519708C23semidirect
129. #14519708C23semidirect
130. C4⋊#92418C23semidirect
131. #14519701C23semidirect
132. #14519700C23semidirect
133. #14519700C23semidirect
134. #14519700C23semidirect
142. C22⋊#92418C23semidirect
143. C4×#92418C23semidirect
152. #125×C61C23semidirect
157. C22⋊Q8×C61C23semidirect
159. C4×Q8×C61C23semidirect
176. C2×C4⋊C4×C61C23semidirect
400. C2×#552D61semidirect
418. C2×C61#3323semidirect
432. #552C2×D61semidirect
437. C2×#125C2×D61semidirect
443. C2×C22⋊Q8C2×D61semidirect
447. C2×C4×Q8C2×D61semidirect
452. C22×C4⋊C4C2×D61semidirect
484. C61C2×#3323semidirect
524. #125C22×D61semidirect
534. C22⋊Q8C22×D61semidirect
540. C4×Q8C22×D61semidirect
561. C2×C4⋊C4C22×D61semidirect
811. C2#21458029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404082
#214580292
C2×#168401192
C2×#168400802
C2×#168401032
C2×#168400592
C2×#168400182
C2×#168400102
C2×#168399842
C2×#168399222
C2×#168399122
C2×C4×#117582012
C2×#168398402
C2×#168397612
C2×#168397662
C2×C61×#5522
C2×#332361