Finite Group Databasebeta

← C2×#21457322 #30554987

Subgroups — C2×#21457322 #30554987

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C23×#11758201C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D61C211yesmaximal, characteristic, complemented
4C2×#16840403C211yesmaximal, characteristic
5#21457322C2116yesmaximal, direct product factor
6C2×#16840155C211yesmaximal, characteristic, complemented
7C2×#16840011C211yesmaximal, characteristic, complemented
8C2×#16840001C211yesmaximal, characteristic, complemented
9C2×#16839986C211yesmaximal, characteristic, complemented
10C2×#16839966C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839902C211yesmaximal, characteristic, complemented
13C2×#16839915C211yesmaximal, characteristic, complemented
14C2×#16839865C211yesmaximal, characteristic, complemented
15C2×#16839830C211yesmaximal, characteristic, complemented
16C2×C61×#451C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic, complemented
19C23×D244C2211yescharacteristic
20C2×#14519809—28no—
21C2×#14519809C2218yescomplemented
22C22×#11758202C2211yescharacteristic, complemented
23C22×#11758190C2211yescharacteristic
24C22×#11758190C2211yescharacteristic
25C22×#11758201—28no—
26C22×#11758201C2211yescharacteristic
27C22×#11758201C2211yescharacteristic
28C22×#11758201C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758201C2218yescomplemented
31C22×#11758189C2211yescharacteristic, complemented
32C23×#92418C2211yescharacteristic
33Q8×C22⋊D61—24no—
34Q8×C22⋊D61C2218yescomplemented
35#16840403—24no—
36#16840403C2218yes—
37C2×#14519775—21no—
38C2×#14519775C2211yescharacteristic, complemented
39C2×#14519766C2211yescharacteristic
40C2×#14519762—21no—
41C2×#14519756—21no—
42C2×#14519756C2211yescharacteristic
43C2×#14519753—21no—
44C2×#14519753C2211yescharacteristic, complemented
45C2×#14519752—21no—
46C2×#14519752C2211yescharacteristic
47C2×#14519747—21no—
48C2×Q8×Dic61C2211yescharacteristic, complemented
49C2×#14519739C2211yescharacteristic
50C2×C4×C22⋊D61—21no—
51C2×C4×C22⋊D61C2211yescharacteristic
52C2×C22⋊C4×D61—21no—
53#16840155C2218yescomplemented
54#16840011C2218yescomplemented
55#16840001C2218yescomplemented
56#16839986C2218yescomplemented
57#16839966C2218yescomplemented
58#16839923C2218yescomplemented
59#16839915C2218yescomplemented
60#16839902C2218yescomplemented
61#16839865C2218yescomplemented
62#16839830C2218yescomplemented
63C2×#14519710C2211yescharacteristic, complemented
64C2×#14519706C2211yescharacteristic, complemented
65C2×#14519701C2211yescharacteristic, complemented
66C2×#14519700C2211yescharacteristic, complemented
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#14519689C2211yescharacteristic, complemented
70C2×#14519687C2211yescharacteristic, complemented
71C23×Q8×C61C2211yescharacteristic
72C22×Q16×C61C2211yescharacteristic, complemented
73C22×Q16×C61C2211yescharacteristic, complemented
74C2×C22⋊Q8×C61C2211yescharacteristic
75C61×#451C2218yescomplemented
76C2×#103×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×C22⋊C8×C61C2211yescharacteristic
79C24×D61—21no—
80C2×#11758226—22no—
81C2×#11758226—24no—
82C2×#11758226—42no—
83C2×#11758226C2314yes—
84C22×Dic122—21no—
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—22no—
87C2×Q8×D61—24no—
88C2×Q8×D61—42no—
89C2×Q8×D61C2314yescomplemented
90C22×D244—24no—
91C22×D244—21no—
92C22×D244—21no—
93C22×D244—22no—
94C22×D244—21no—
95C22×D244—42no—
96C22×D244C2311yescharacteristic
97C22×D244C2314yes—
98C22×D244C2311yescharacteristic
99C22×C22⋊D61D411yescharacteristic
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61C2311yescharacteristic
104#14519809—232no—
105C2×#11758202—24no—
106C2×#11758202C2314yescomplemented
107C2×#11758190—24no—
108C2×#11758190—42no—
109C2×#11758190C2314yes—
110C2×#11758190C2314yes—
111C2×#11758201—24no—
112C2×#11758201—24no—
113C2×#11758201—232no—
114C2×#11758201—24no—
115C2×#11758201D418yescomplemented
116C2×#11758201C2314yes—
117C2×#11758201C2314yes—
118C2×#11758201C2314yes—
119C2×#11758201C2314yes—
120C2×#11758189—24no—
121C2×#11758189C2314yescomplemented
122C22×#92418—24no—
123C22×#92418C2311yescharacteristic
124C22×#92418C2314yes—
125C22×#92418C2311yescharacteristic
126#14519775—28no—
127#14519775—22no—
128#14519775C2314yescomplemented
129#14519766—22no—
130#14519766C2314yes—
131#14519762—28no—
132#14519756—22no—
133#14519756—28no—
134#14519756C2314yes—
135#14519753—22no—
136#14519753—28no—
137#14519753C2314yescomplemented
138#14519752—22no—
139#14519752—28no—
140#14519752C2314yes—
141#14519747—28no—
142Q8×Dic61—22no—
143Q8×Dic61C2314yescomplemented
144#14519739—22no—
145#14519739C2314yes—
146C4×C22⋊D61—28no—
147C4×C22⋊D61D414yes—
148C4×C22⋊D61C2314yes—
149C2×C4⋊Dic61—21no—
150C2×C4⋊Dic61C2311yescharacteristic
151C2×#11758196—21no—
152C2×#11758196—21no—
153C2×#11758196—21no—
154C2×#11758196—21no—
155C2×#11758196D411yescharacteristic
156C2×C22⋊Dic61—21no—
157C2×C22⋊Dic61D411yescharacteristic
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198D411yescharacteristic
164C22⋊C4×D61—28no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167#14519710C2314yescomplemented
168#14519706C2314yescomplemented
169#14519701C2314yescomplemented
170#14519700C2314yescomplemented
171#14519699C2314yes—
172#14519699C2314yes—
173#14519689C2314yescomplemented
174#14519687C2314yescomplemented
175C22×Q8×C61—21no—
176C22×Q8×C61—22no—
177C22×Q8×C61—24no—
178C22×Q8×C61—42no—
179C22×Q8×C61C2311yescharacteristic
180C22×Q8×C61C2311yescharacteristic
181C22×Q8×C61C2314yes—
182C22×Q8×C61C2311yescharacteristic
183C23×C4×C61—21no—
184C23×C4×C61C2311yescharacteristic
185C2×Q16×C61—24no—
186C2×Q16×C61—42no—
187C2×Q16×C61C2314yescomplemented
188C2×Q16×C61C2314yescomplemented
189C22×C8×C61C2311yescharacteristic
190C22×C8×C61C2311yescharacteristic
191C22⋊Q8×C61—22no—
192C22⋊Q8×C61C2314yes—
193C2×C4⋊C4×C61—21no—
194C2×C4⋊C4×C61C2311yescharacteristic
195C2×C22⋊C4×C61—21no—
196#103×C61C2314yescomplemented
197#103×C61C2314yescomplemented
198C22⋊C8×C61C2314yes—
199C24×C61C2×D411yescharacteristic
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—24no—
203C23×D61—44no—
204C23×D61—44no—
205C23×D61—82no—
206C23×D61C2×D411yescharacteristic
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—24no—
210C2×Q8×C61—21no—
211C2×Q8×C61—22no—
212C2×Q8×C61—28no—
213C2×Q8×C61—22no—
214C2×Q8×C61—22no—
215C2×Q8×C61—22no—
216C2×Q8×C61—22no—
217C2×Q8×C61—44no—
218C2×Q8×C61—44no—
219C2×Q8×C61—48no—
220C2×Q8×C61C2×D414yes—
221C2×Q8×C61C2412yes—
222C2×Q8×C61C2412yes—
223C2×Q8×C61C2412yes—
224C22×C4×C61—21no—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—24no—
231C22×C4×C61—44no—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2412yes—
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61—24no—
237C2×C22⋊D61C2×D414yes—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758226—28no—
244#11758226—44no—
245#11758226—48no—
246Q8×D61—28no—
247Q8×D61—44no—
248Q8×D61—48no—
249C2×D244—21no—
250C2×D244—22no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—28no—
254C2×D244—24no—
255C2×D244—24no—
256C2×D244—21no—
257C2×D244—24no—
258C2×D244—44no—
259C2×D244—48no—
260C2×D244—44no—
261C2×D244—44no—
262C2×D244—82no—
263C2×D244C2×D414yes—
264C2×D244C2412yes—
265C2×D244C2412yes—
266C2×C4×D61—22no—
267C2×C4×D61—22no—
268C2×C4×D61—24no—
269C2×C4×D61—24no—
270C2×C4×D61—24no—
271C2×C4×D61—44no—
272C2×C4×D61—44no—
273C2×C4×D61—82no—
274C2×C4×D61C2×D412yes—
275C2×C4×D61C2412yes—
276C2×Dic122—22no—
277C2×Dic122—22no—
278C2×Dic122—21no—
279C2×Dic122—24no—
280C2×Dic122—44no—
281C2×Dic122C2412yes—
282Q16×C61—28no—
283Q16×C61—44no—
284C2×C8×C61—22no—
285C2×C8×C61—22no—
286C2×C8×C61C2412yes—
287C2×C8×C61C2412yes—
288C4⋊C4×C61—24no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C2412yes—
291C22⋊C4×C61—24no—
292C22⋊Dic61—24no—
293C22⋊Dic61C2×D414yes—
294#11758202—28no—
295#11758201—28no—
296#11758201—28no—
297#11758201—28no—
298#11758201C2×D4116yescomplemented
299#11758198—24no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198—24no—
304#11758198C2×D414yes—
305C4⋊Dic61—21no—
306C4⋊Dic61—24no—
307C4⋊Dic61C2412yes—
308#11758196—24no—
309#11758196—24no—
310#11758196—24no—
311#11758196—24no—
312#11758196C2×D414yes—
313C4×Dic61—24no—
314C4×Dic61C2×D412yes—
315C4×Dic61C2412yes—
316C2×#92418—22no—
317C2×#92418—28no—
318C2×#92418C2×D414yes—
319C2×#92418C2412yes—
320C2×#92418C2412yes—
321#11758190—28no—
322#11758190—44no—
323#11758189—28no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61#13714yescomplemented
327C23×C61C22×D412yes—
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—24no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—48no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—48no—
341C22×D61—42no—
342C22×D61—84no—
343C22×D61—816no—
344C22×D61C22×D412yes—
345Q8×C61—24no—
346Q8×C61—22no—
347Q8×C61—22no—
348Q8×C61—22no—
349Q8×C61—22no—
350Q8×C61—22no—
351Q8×C61—48no—
352Q8×C61—42no—
353Q8×C61—42no—
354Q8×C61C22×D414yes—
355C2×C4×C61—24no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—24no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—48no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61C22×D412yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D412yes—
371C2×C4×C61H(5,𝔽2)12yes—
372C2×C4×C61C2511yescharacteristic
373C22⋊D61—28no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—42no—
380C2×Dic61—42no—
381C2×Dic61C22×D412yes—
382C2×Dic61C22×D412yes—
383C2×Dic61C22×D412yes—
384D244—24no—
385D244—22no—
386D244—22no—
387D244—22no—
388D244—48no—
389D244—48no—
390D244—42no—
391D244—84no—
392D244C22×D414yes—
393C4×D61—24no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—48no—
397C4×D61—48no—
398C4×D61—84no—
399Dic122—22no—
400Dic122—22no—
401Dic122—48no—
402Dic122—42no—
403C8×C61—22no—
404C8×C61—22no—
405#92418—22no—
406#92418C22×D414yes—
407C2×#3266—611nomaximal, Sylow
408C22×C61—22no—
409C22×C61—28no—
410C22×C61—22no—
411C22×C61D4212yes—
412C22×C61C2×#13712yes—
413C22×C61C2×#13714yescomplemented
414C22×C61#57712yes—
415C22×C61C23×D411yescharacteristic
416C2×D61—22no—
417C2×D61—24no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—44no—
421C2×D61—48no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—816no—
428C2×D61—84no—
429C4×C61—24no—
430C4×C61—22no—
431C4×C61—42no—
432C4×C61—42no—
433C4×C61—42no—
434C4×C61D4212yes—
435C4×C61C23×D411yescharacteristic
436C4×C61C2×H(5,𝔽2)11yescharacteristic
437Dic61—22no—
438Dic61—22no—
439Dic61—22no—
440Dic61—42no—
441Dic61—42no—
442C22×#137—611no—
443C23×SD16—611no—
444C2×D4×Q8—611no—
445C2×#546—611no—
446#3266—6116no—
447C2×#497—611no—
448C2×#468—611no—
449C2×#467—611no—
450C2×#464—611no—
451C2×#461—611no—
452C2×#452—611no—
453C2×#451D6111yescharacteristic, complemented
454C2×#448—611no—
455C2×#450—611no—
456C2×#440—611no—
457C2×#435—611no—
458C2×C61—24no—
459C2×C61#326614yescomplemented
460C2×C61C2×D4211yescharacteristic
461C2×C61C22×#13711yescharacteristic
462C2×C61C2×#57711yescharacteristic
463D61—42no—
464D61—44no—
465D61—82no—
466C22×#41—611no—
467C23×Q8—611no—
468C23×Q8C2×D6111yescharacteristic
469C23×D4—611no—
470C2×#137—618no—
471C2×#137—1228no—
472C22×Q16—611no—
473C22×Q16C2×D6111yescharacteristic, complemented
474C22×Q16C2×D6111yescharacteristic, complemented
475C22×SD16—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—611no—
479C22×SD16—618no—
480C22×SD16—611no—
481C22×SD16—611no—
482C22×SD16—1228no—
483C22×M16—611no—
484C23×C8—611no—
485D4×Q8—618no—
486D4×Q8—1224no—
487#546—618no—
488#546—1224no—
489C2×C4⋊Q8—611no—
490C2×C4⋊Q8—1221no—
491C2×#124—611no—
492C2×#123—1221no—
493C2×C22⋊Q8—611no—
494C2×C22⋊Q8—611no—
495C2×C22⋊Q8—1221no—
496C2×C22⋊Q8—1221no—
497C2×C22⋊Q8C2×D6111yescharacteristic
498C2×#121—611no—
499C2×#121—1221no—
500C2×#120—1221no—
501C2×C4×Q8—611no—
502C2×C4×D4—611no—
503C2×C4×D4—611no—
504C2×C4×D4—1221no—
505C22×C22⋊C4—1221no—
506#497—618no—
507#468—618no—
508#467—618no—
509#464—618no—
510#461—618no—
511#452—618no—
512#451C2×D6118yescomplemented
513#450—618no—
514#448—618no—
515#440—618no—
516#435—618no—
517C2×#107—611no—
518C2×C4⋊C8—611no—
519C2×#103—611no—
520C2×#103—611no—
521C2×#103C2×D6111yescharacteristic, complemented
522C2×#103C2×D6111yescharacteristic, complemented
523C2×#102—611no—
524C2×#102—611no—
525C2×C22⋊C8—611no—
526C2×C22⋊C8C2×D6111yescharacteristic
527C2×#97—611no—
528C61C2×#326611yescharacteristic, complemented, Sylow
529C25—1221no—
530C2×#41—614no—
531C2×#41—1222no—
532C2×#41—1224no—
533C2×#41—2442no—
534C22×Q8—21no—
535C22×Q8—22no—
536C22×Q8—24no—
537C22×Q8—42no—
538C22×Q8—614no—
539C22×Q8—611no—
540C22×Q8—1221no—
541C22×Q8—1222no—
542C22×Q8—1224no—
543C22×Q8—2442no—
544C22×Q8C22×D6111yescharacteristic
545C22×Q8C22×D6111yescharacteristic
546C22×Q8C22×D6114yes—
547C22×Q8C22×D6111yescharacteristic
548C22×D4—611no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—614no—
552C22×D4—1224no—
553C22×D4—1221no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1222no—
557C22×D4—2442no—
558C23×C4—21no—
559C23×C4—611no—
560C23×C4—1221no—
561C23×C4—1221no—
562C23×C4—1221no—
563C23×C4C22×D6111yescharacteristic
564#137—12232no—
565C2×Q16—24no—
566C2×Q16—42no—
567C2×Q16—614no—
568C2×Q16—1224no—
569C2×Q16C22×D6114yescomplemented
570C2×Q16C22×D6114yescomplemented
571C2×SD16—618no—
572C2×SD16—614no—
573C2×SD16—614no—
574C2×SD16—614no—
575C2×SD16—614no—
576C2×SD16—614no—
577C2×SD16—614no—
578C2×SD16—1224no—
579C2×SD16—1224no—
580C2×SD16—12232no—
581C2×SD16—1224no—
582C2×SD16—1224no—
583C2×SD16—2442no—
584C2×M16—614no—
585C2×M16—1224no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—614no—
589C22×C8—1224no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592C4⋊Q8—614no—
593C4⋊Q8—1222no—
594C4⋊Q8—1228no—
595#124—614no—
596#124—1222no—
597#123—1228no—
598C22⋊Q8—22no—
599C22⋊Q8—614no—
600C22⋊Q8—614no—
601C22⋊Q8—1228no—
602C22⋊Q8—1228no—
603C22⋊Q8—1222no—
604C22⋊Q8—1222no—
605C22⋊Q8C22×D6114yes—
606#121—614no—
607#121—1228no—
608#121—1222no—
609#120—1228no—
610C4×Q8—614no—
611C4×Q8—1222no—
612C4×D4—614no—
613C4×D4—614no—
614C4×D4—614no—
615C4×D4—1222no—
616C4×D4—1228no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4C22×D6111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—1228no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—611no—
637C2×C42—1221no—
638#107—614no—
639C4⋊C8—614no—
640#103—614no—
641#103—614no—
642#103C22×D6114yescomplemented
643#103C22×D6114yescomplemented
644#102—614no—
645#102—614no—
646C22⋊C8—614no—
647C22⋊C8C22×D6114yes—
648#97—614no—
649C24—611no—
650C24—1221no—
651C24—1224no—
652C24—1221no—
653C24—4882no—
654C24—2444no—
655C24—2444no—
656C24D4×D6111yescharacteristic
657#41—1228no—
658#41—2444no—
659#41—2448no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—21no—
664C2×Q8—22no—
665C2×Q8—28no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—22no—
669C2×Q8—22no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×Q8—48no—
673C2×Q8—612no—
674C2×Q8—1224no—
675C2×Q8—1221no—
676C2×Q8—1228no—
677C2×Q8—1222no—
678C2×Q8—1222no—
679C2×Q8—2444no—
680C2×Q8—2444no—
681C2×Q8—2448no—
682C2×Q8D4×D6114yes—
683C2×Q8C23×D6112yes—
684C2×Q8C23×D6112yes—
685C2×Q8C23×D6112yes—
686C2×D4—614no—
687C2×D4—614no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4—1228no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1224no—
694C2×D4—1221no—
695C2×D4—1222no—
696C2×D4—1224no—
697C2×D4—1221no—
698C2×D4—1222no—
699C2×D4—1222no—
700C2×D4—4882no—
701C2×D4—2444no—
702C2×D4—2448no—
703C2×D4—2444no—
704C2×D4—2444no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—44no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—1224no—
719C22×C4—1224no—
720C22×C4—1224no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—4882no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4D4×D6112yes—
729C22×C4D4×D6111yescharacteristic
730C22×C4C23×D6112yes—
731C22×C4C23×D6111yescharacteristic
732Q16—28no—
733Q16—44no—
734Q16—1228no—
735SD16—6116no—
736SD16—1228no—
737SD16—1228no—
738SD16—1228no—
739SD16—1228no—
740SD16—2444no—
741M16—1228no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—614no—
745C2×C8—612no—
746C2×C8—612no—
747C2×C8—1228no—
748C2×C8—1222no—
749C2×C8C23×D6112yes—
750C2×C8C23×D6112yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—614no—
754C4⋊C4—612no—
755C4⋊C4—1224no—
756C4⋊C4—1224no—
757C4⋊C4—1224no—
758C4⋊C4—1224no—
759C4⋊C4—1221no—
760C4⋊C4—1224no—
761C4⋊C4C23×D6112yes—
762C22⋊C4—24no—
763C22⋊C4—614no—
764C22⋊C4—614no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4—1224no—
769C22⋊C4—1224no—
770C22⋊C4—1224no—
771C42—612no—
772C42—612no—
773C42—1224no—
774C23—22no—
775C23—22no—
776C23—612no—
777C23—1222no—
778C23—1222no—
779C23—1222no—
780C23—1222no—
781C23—1224no—
782C23—1222no—
783C23—48816no—
784C23—4884no—
785C23—2448no—
786C23—2442no—
787C23—2448no—
788C23—2442no—
789C23—2442no—
790C23—2442no—
791C23—2442no—
792C23#1451980914yescomplemented
793C23C2×D4×D6112yes—
794C23C2×D4×D6111yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—48no—
802Q8—42no—
803Q8—42no—
804Q8—1222no—
805Q8—1222no—
806Q8—2448no—
807Q8—2442no—
808Q8C2×D4×D6114yes—
809D4—614no—
810D4—1228no—
811D4—1222no—
812D4—1222no—
813D4—1222no—
814D4—1224no—
815D4—4884no—
816D4—2448no—
817D4—2448no—
818D4—2442no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—48no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—612no—
833C2×C4—612no—
834C2×C4—612no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1224no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—4884no—
844C2×C4—2448no—
845C2×C4—2448no—
846C2×C4—2442no—
847C2×C4—2442no—
848C2×C4C2×D4×D6112yes—
849C2×C4C2×D4×D6112yes—
850C2×C4C2×D4×D6111yescharacteristic
851C2×C4#1451982212yes—
852C2×C4C24×D6111yescharacteristic
853C8—22no—
854C8—22no—
855C8—614no—
856C8—1222no—
857C22—22no—
858C22—22no—
859C22—28no—
860C22—1222no—
861C22—1224no—
862C22—1222no—
863C22—1222no—
864C22—48816no—
865C22—4884no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22—2444no—
872C22—2448no—
873C22#1684039412yes—
874C22C2×#1451980912yes—
875C22C2×#1451980914yescomplemented
876C22#1684057112yes—
877C22C22×D4×D6111yescharacteristic
878C4—22no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—1222no—
884C4—1222no—
885C4—1222no—
886C4—2442no—
887C4—2442no—
888C4#1684039412yes—
889C4C22×D4×D6111yescharacteristic
890C4C2×#1451982211yescharacteristic
891C2—24no—
892C2—4882no—
893C2—2442no—
894C2—2444no—
895C2#2145732214yesdirect product factor
896C2C2×#1684039411yescharacteristic
897C2C22×#1451980911yescharacteristic
898C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
prime radicalC2×#16840403C2
hypercenterC2×#451D61
hypocenterC61C2×#3266
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
2. C23×#11758201C2semidirect
3. C2×Q8×C22⋊D61C2semidirect
5. #21457322C2direct (N × H)
6. C2×#16840155C2semidirect
7. C2×#16840011C2semidirect
8. C2×#16840001C2semidirect
9. C2×#16839986C2semidirect
10. C2×#16839966C2semidirect
11. C2×#16839923C2semidirect
12. C2×#16839902C2semidirect
13. C2×#16839915C2semidirect
14. C2×#16839865C2semidirect
15. C2×#16839830C2semidirect
16. C2×C61×#451C2semidirect
18. C22×Q8×D61C22semidirect
21. C2×#14519809C22semidirect
22. C22×#11758202C22semidirect
30. C22×#11758201C22semidirect
31. C22×#11758189C22semidirect
34. Q8×C22⋊D61C22semidirect
38. C2×#14519775C22semidirect
44. C2×#14519753C22semidirect
48. C2×Q8×Dic61C22semidirect
53. #16840155C22semidirect
54. #16840011C22semidirect
55. #16840001C22semidirect
56. #16839986C22semidirect
57. #16839966C22semidirect
58. #16839923C22semidirect
59. #16839915C22semidirect
60. #16839902C22semidirect
61. #16839865C22semidirect
62. #16839830C22semidirect
63. C2×#14519710C22semidirect
64. C2×#14519706C22semidirect
65. C2×#14519701C22semidirect
66. C2×#14519700C22semidirect
69. C2×#14519689C22semidirect
70. C2×#14519687C22semidirect
72. C22×Q16×C61C22semidirect
73. C22×Q16×C61C22semidirect
75. C61×#451C22semidirect
76. C2×#103×C61C22semidirect
77. C2×#103×C61C22semidirect
89. C2×Q8×D61C23semidirect
106. C2×#11758202C23semidirect
115. C2×#11758201D4semidirect
121. C2×#11758189C23semidirect
128. #14519775C23semidirect
137. #14519753C23semidirect
143. Q8×Dic61C23semidirect
167. #14519710C23semidirect
168. #14519706C23semidirect
169. #14519701C23semidirect
170. #14519700C23semidirect
173. #14519689C23semidirect
174. #14519687C23semidirect
187. C2×Q16×C61C23semidirect
188. C2×Q16×C61C23semidirect
196. #103×C61C23semidirect
197. #103×C61C23semidirect
298. #11758201C2×D4semidirect
326. C23×C61#137semidirect
413. C22×C61C2×#137semidirect
453. C2×#451D61semidirect
459. C2×C61#3266semidirect
473. C22×Q16C2×D61semidirect
474. C22×Q16C2×D61semidirect
512. #451C2×D61semidirect
521. C2×#103C2×D61semidirect
522. C2×#103C2×D61semidirect
528. C61C2×#3266semidirect
569. C2×Q16C22×D61semidirect
570. C2×Q16C22×D61semidirect
642. #103C22×D61semidirect
643. #103C22×D61semidirect
792. C23#14519809semidirect
875. C22C2×#14519809semidirect
895. C2#21457322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C23×#117582012
C2×Q8×C22⋊D612
C2×#168404032
#214573222
C2×#168401552
C2×#168400112
C2×#168400012
C2×#168399862
C2×#168399662
C2×#168399232
C2×#168399022
C2×#168399152
C2×#168398652
C2×#168398302
C2×C61×#4512
C2×#326661