Finite Group Databasebeta

← C2×#21456729 #30550730

Subgroups — C2×#21456729 #30550730

Order 15616.

2250 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
1C2×#16840343C211yesmaximal, characteristic, complemented
2C2×#16840342C211yesmaximal, characteristic, complemented
3#21456729C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840080C211yesmaximal, characteristic, complemented
6C2×#16840094C211yesmaximal, characteristic, complemented
7C2×#16840019C211yesmaximal, characteristic, complemented
8C2×#16840016C211yesmaximal, characteristic, complemented
9C2×#16839994C211yesmaximal, characteristic, complemented
10C2×#16839992C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839922C211yesmaximal, characteristic, complemented
13C2×#16839910C211yesmaximal, characteristic, complemented
14C2×#16839909C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#483C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758222C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840343—24no—
27#16840343C2218yescomplemented
28#16840342—24no—
29#16840342C2218yescomplemented
30C2×#14519757—21no—
31C2×#14519757C2211yescharacteristic
32C2×#14519757C2211yescharacteristic
33C2×#14519755—21no—
34C2×#14519753C2211yescharacteristic
35C2×#14519752—21no—
36C2×#14519752—21no—
37C2×#14519752C2211yescharacteristic
38C2×#14519752C2211yescharacteristic
39C2×#14519752C2211yescharacteristic
40C2×#14519751—21no—
41C2×#14519751—21no—
42C2×#14519751C2211yescharacteristic
43C2×#14519750—21no—
44C2×#14519750—21no—
45C2×C4⋊C4×D61C2211yescharacteristic
46#16840094C2218yescomplemented
47#16840082C2218yescomplemented
48#16840080C2218yescomplemented
49#16840019C2218yescomplemented
50#16840016C2218yescomplemented
51#16839994C2218yescomplemented
52#16839992C2218yescomplemented
53#16839927C2218yescomplemented
54#16839922C2218yescomplemented
55#16839910C2218yescomplemented
56#16839909C2218yescomplemented
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#483C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C2×#11758222—22no—
82C2×#11758222—42no—
83C2×#11758222—42no—
84C2×#11758222—42no—
85C2×#11758222—42no—
86C2×#11758222D414yes—
87C2×#11758222C2314yes—
88C2×#11758222C2314yes—
89C22×Dic122D411yescharacteristic
90C22×Dic122C2311yescharacteristic
91C22×D244—21no—
92C22×D244—21no—
93C22×D244—21no—
94C22×D244—21no—
95C22×D244D411yescharacteristic
96C22×D244C2311yescharacteristic
97C22×D244C2311yescharacteristic
98C22×C22⋊D61—21no—
99C22×C22⋊D61—21no—
100C22×C22⋊D61D411yescharacteristic
101C22×C22⋊D61D411yescharacteristic
102C22×C4×D61—21no—
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C2×#11758202—42no—
108C2×#11758202C2314yes—
109C2×#11758190—42no—
110C2×#11758190C2314yes—
111C2×#11758201—42no—
112C2×#11758201C2314yes—
113C2×D488—42no—
114C2×D488C2314yes—
115C2×#11758189—42no—
116C2×#11758189C2314yes—
117C22×#92418C2311yescharacteristic
118C22×#92418C2311yescharacteristic
119C2×C8×D61—42no—
120C2×C8×D61C2314yes—
121#14519757—22no—
122#14519757—22no—
123#14519757—28no—
124#14519757C2314yes—
125#14519757C2314yes—
126#14519755—28no—
127#14519753—22no—
128#14519753C2314yes—
129#14519752—28no—
130#14519752—28no—
131#14519752—22no—
132#14519752—22no—
133#14519752—22no—
134#14519752C2314yes—
135#14519752C2314yes—
136#14519752C2314yes—
137#14519751—22no—
138#14519751—28no—
139#14519751—28no—
140#14519751C2314yes—
141#14519750—28no—
142#14519750—28no—
143C2×C4⋊Dic61—21no—
144C2×C4⋊Dic61—21no—
145C2×C4⋊Dic61C2311yescharacteristic
146C2×#11758196—21no—
147C2×#11758196—21no—
148C4⋊C4×D61—22no—
149C4⋊C4×D61C2314yes—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157#14519708C2314yes—
158#14519708C2314yes—
159#14519702C2314yes—
160#14519700C2314yes—
161#14519699C2314yes—
162#14519697C2314yes—
163#14519697C2314yes—
164#14519697C2314yes—
165C22⋊#92418C2314yes—
166#14519689C2314yes—
167#14519689C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22⋊Q8×C61—22no—
174C22⋊Q8×C61C2314yes—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—22no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2314yes—
182C2×C22⋊C4×C61—21no—
183#106×C61C2314yes—
184#106×C61C2314yes—
185#103×C61C2314yes—
186#103×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C23×D61—21no—
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61C2412yes—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—24no—
204C22×C4×C61—82no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—82no—
215C2×C22⋊D61C2×D414yes—
216C2×C22⋊D61C2×D414yes—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758226—44no—
222#11758226—44no—
223#11758226—48no—
224#11758222—44no—
225#11758222—44no—
226#11758222—48no—
227#11758222—44no—
228#11758222—44no—
229#11758222—48no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—24no—
238C2×D244—24no—
239C2×D244—24no—
240C2×D244—42no—
241C2×D244—44no—
242C2×D244—82no—
243C2×D244—82no—
244C2×D244—82no—
245C2×D244C2×D414yes—
246C2×D244C2412yes—
247C2×D244C2412yes—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—24no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
257C2×C4×D61—82no—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2×D412yes—
260C2×C4×D61C2412yes—
261C2×C4×D61C2412yes—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—21no—
265C2×Dic122—42no—
266C2×Dic122C2×D414yes—
267C2×Dic122C2412yes—
268C2×C8×C61—22no—
269C2×C8×C61—22no—
270C2×C8×C61C2412yes—
271C2×C8×C61C2412yes—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—24no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C2412yes—
278C4⋊C4×C61C2412yes—
279C4⋊C4×C61C2412yes—
280C22⋊C4×C61—24no—
281#11758202—44no—
282#11758201—44no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289#11758198—24no—
290C4⋊Dic61—21no—
291C4⋊Dic61—24no—
292C4⋊Dic61—24no—
293C4⋊Dic61C2412yes—
294#11758196—24no—
295#11758196—24no—
296C2×#92418—22no—
297C2×#92418—22no—
298C2×#92418C2412yes—
299C2×#92418C2412yes—
300D488—44no—
301#11758190—44no—
302#11758189—44no—
303C8×D61—44no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61C22×D412yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61C22×D412yes—
324C22×D61C22×D412yes—
325Q8×C61—22no—
326Q8×C61—22no—
327Q8×C61—42no—
328C2×C4×C61—22no—
329C2×C4×C61—24no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61—42no—
340C2×C4×C61—84no—
341C2×C4×C61C22×D412yes—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61H(5,𝔽2)12yes—
344C2×C4×C61H(5,𝔽2)12yes—
345C2×C4×C61C2511yescharacteristic
346C22⋊D61—44no—
347C22⋊D61—44no—
348C22⋊D61—48no—
349C22⋊D61—84no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61C22×D412yes—
357C2×Dic61C22×D412yes—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—22no—
362D244—44no—
363D244—48no—
364D244—42no—
365D244—42no—
366D244—84no—
367D244—84no—
368D244—84no—
369C4×D61—24no—
370C4×D61—24no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—48no—
376C4×D61—48no—
377C4×D61—84no—
378Dic122—22no—
379Dic122—22no—
380Dic122—44no—
381Dic122—42no—
382C8×C61—22no—
383C8×C61—22no—
384#92418—22no—
385#92418—22no—
386C2×#3204—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—44no—
391C22×C61#53412yes—
392C22×C61#57712yes—
393C22×C61#57712yes—
394C22×C61C23×D411yescharacteristic
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—44no—
402C2×D61—44no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—84no—
410C2×D61—84no—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—42no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61#53412yes—
417C4×C61C2×H(5,𝔽2)11yescharacteristic
418C4×C61C2×H(5,𝔽2)11yescharacteristic
419Dic61—22no—
420Dic61—22no—
421Dic61—42no—
422Dic61—42no—
423C2×#537—611no—
424C2×#537—611no—
425#3204—6116no—
426C2×#481—611no—
427C2×#481—611no—
428C2×#483—611no—
429C2×#483D6111yescharacteristic, complemented
430C2×#470—611no—
431C2×#469—611no—
432C2×#465—611no—
433C2×#465—611no—
434C2×#452—611no—
435C2×#452—611no—
436C2×#449—611no—
437C2×#449—611no—
438C2×#408—611no—
439C2×C61—42no—
440C2×C61#320414yescomplemented
441C2×C61C2×#53411yescharacteristic
442C2×C61C2×#57711yescharacteristic
443C2×C61C2×#57711yescharacteristic
444D61—42no—
445D61—42no—
446D61—82no—
447D61—82no—
448C22×#41—611no—
449C22×#41—611no—
450C22×#41—611no—
451C22×Q16—611no—
452C22×SD16—611no—
453C22×SD16—611no—
454C22×D8—611no—
455C22×M16—611no—
456C23×C8—611no—
457#537—618no—
458#537—618no—
459#537—1224no—
460#537—1224no—
461C2×C22⋊Q8—611no—
462C2×C22⋊Q8—611no—
463C2×C22⋊Q8—611no—
464C2×C22⋊Q8—1221no—
465C2×C22⋊Q8—1221no—
466C2×C22⋊Q8C2×D6111yescharacteristic
467C2×#121—611no—
468C2×#121—611no—
469C2×#121—611no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#121—1221no—
473C2×#121—1221no—
474C2×#121—1221no—
475C2×#121—1221no—
476C2×#121—1221no—
477C22×C4⋊C4—611no—
478C22×C4⋊C4C2×D6111yescharacteristic
479#483—618no—
480#483C2×D6118yescomplemented
481#481—618no—
482#481—618no—
483#470—618no—
484#469—618no—
485#465—618no—
486#465—618no—
487#452—618no—
488#452—618no—
489#449—618no—
490#449—618no—
491C2×#106—611no—
492C2×#106—611no—
493C2×#106C2×D6111yescharacteristic
494C2×#106C2×D6111yescharacteristic
495C2×#103—611no—
496C2×#103—611no—
497C2×#103C2×D6111yescharacteristic
498C2×#103C2×D6111yescharacteristic
499C2×#102—611no—
500C2×#102—611no—
501C2×#102—611no—
502C2×#102—611no—
503#408—618no—
504C2×C22⋊C8—611no—
505C2×C22⋊C8—611no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8C2×D6111yescharacteristic
508C61C2×#320411yescharacteristic, complemented, Sylow
509C2×#41—614no—
510C2×#41—614no—
511C2×#41—614no—
512C2×#41—614no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2442no—
516C2×#41—2442no—
517C2×#41—2442no—
518C2×#41—2442no—
519C2×#41—2442no—
520C2×#41—2442no—
521C22×Q8—611no—
522C22×Q8—611no—
523C22×Q8C22×D6111yescharacteristic
524C22×D4—611no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—611no—
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1221no—
535C23×C4—21no—
536C23×C4—611no—
537C23×C4—611no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×Q16—614no—
543C2×Q16—2442no—
544C2×SD16—614no—
545C2×SD16—614no—
546C2×SD16—2442no—
547C2×SD16—2442no—
548C2×D8—614no—
549C2×D8—2442no—
550C2×M16—614no—
551C2×M16—2442no—
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—614no—
555C22×C8—2442no—
556C22×C8C22×D6111yescharacteristic
557C22×C8C22×D6111yescharacteristic
558C22⋊Q8—22no—
559C22⋊Q8—614no—
560C22⋊Q8—614no—
561C22⋊Q8—614no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1228no—
565C22⋊Q8—1228no—
566C22⋊Q8—1222no—
567C22⋊Q8C22×D6114yes—
568#121—614no—
569#121—614no—
570#121—614no—
571#121—614no—
572#121—1228no—
573#121—1228no—
574#121—1222no—
575#121—1222no—
576#121—1222no—
577#121—1228no—
578#121—1228no—
579#121—1228no—
580#121—1228no—
581#121—1222no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—614no—
587C2×C4⋊C4—1222no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4C22×D6111yescharacteristic
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C4⋊C4C22×D6114yes—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604#106—614no—
605#106—614no—
606#106C22×D6114yes—
607#106C22×D6114yes—
608#103—614no—
609#103—614no—
610#103C22×D6114yes—
611#103C22×D6114yes—
612#102—614no—
613#102—614no—
614#102—614no—
615#102—614no—
616C22⋊C8—614no—
617C22⋊C8—614no—
618C22⋊C8—614no—
619C22⋊C8C22×D6114yes—
620C24—611no—
621C24—611no—
622C24—1221no—
623C24—1221no—
624C24D4×D6111yescharacteristic
625#41—2448no—
626#41—2444no—
627#41—2444no—
628#41—2444no—
629#41—2444no—
630#41—2448no—
631#41—2444no—
632#41—2444no—
633#41—2448no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—614no—
638C2×Q8—612no—
639C2×Q8—1221no—
640C2×Q8—1222no—
641C2×Q8—1222no—
642C2×Q8—2442no—
643C2×Q8C23×D6112yes—
644C2×D4—614no—
645C2×D4—614no—
646C2×D4—614no—
647C2×D4—612no—
648C2×D4—612no—
649C2×D4—1224no—
650C2×D4—1224no—
651C2×D4—1224no—
652C2×D4—1224no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4—1222no—
660C2×D4—1222no—
661C2×D4—4882no—
662C2×D4—4882no—
663C2×D4—4882no—
664C2×D4—4882no—
665C2×D4—2442no—
666C2×D4—2444no—
667C2×D4—2442no—
668C2×D4—2442no—
669C2×D4—2444no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—82no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—1224no—
685C22×C4—1224no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1224no—
693C22×C4—4882no—
694C22×C4—2444no—
695C22×C4—2444no—
696C22×C4D4×D6112yes—
697C22×C4D4×D6111yescharacteristic
698C22×C4C23×D6112yes—
699C22×C4C23×D6111yescharacteristic
700Q16—2444no—
701SD16—2444no—
702SD16—2444no—
703D8—2444no—
704M16—2444no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—612no—
708C2×C8—612no—
709C2×C8—1222no—
710C2×C8—1222no—
711C2×C8—2444no—
712C2×C8C23×D6112yes—
713C2×C8C23×D6112yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—24no—
718C4⋊C4—21no—
719C4⋊C4—612no—
720C4⋊C4—1224no—
721C4⋊C4—1224no—
722C4⋊C4—1224no—
723C4⋊C4—1224no—
724C4⋊C4—1221no—
725C4⋊C4C23×D6112yes—
726C4⋊C4C23×D6112yes—
727C4⋊C4C23×D6112yes—
728C22⋊C4—24no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—612no—
740C23—612no—
741C23—1222no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23—1222no—
748C23—1222no—
749C23—2442no—
750C23—2442no—
751C23—2442no—
752C23—2442no—
753C23—2442no—
754C23—2442no—
755C23C2×D4×D6112yes—
756C23C2×D4×D6111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—42no—
760Q8—1222no—
761Q8—1222no—
762Q8—2444no—
763Q8—2442no—
764D4—1222no—
765D4—1222no—
766D4—1222no—
767D4—1222no—
768D4—4884no—
769D4—4884no—
770D4—4884no—
771D4—4884no—
772D4—2444no—
773D4—2448no—
774D4—2444no—
775D4—2444no—
776D4—2448no—
777D4—2442no—
778D4—2442no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—84no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1224no—
797C2×C4—1224no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—4884no—
805C2×C4—2448no—
806C2×C4—2448no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4C2×D4×D6112yes—
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4#1451982312yes—
812C2×C4#1451982312yes—
813C2×C4C24×D6111yescharacteristic
814C8—22no—
815C8—22no—
816C8—1222no—
817C8—1222no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—44no—
822C22—1222no—
823C22—1222no—
824C22—1222no—
825C22—1222no—
826C22—1222no—
827C22—1222no—
828C22—4884no—
829C22—4884no—
830C22—2442no—
831C22—2442no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22—2444no—
837C22—2444no—
838C22#1684032312yes—
839C22#1684056812yes—
840C22#1684057112yes—
841C22C22×D4×D6111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—1222no—
848C4—1222no—
849C4—2442no—
850C4—2442no—
851C4#1684032312yes—
852C4C2×#1451982311yescharacteristic
853C4C2×#1451982311yescharacteristic
854C2—42no—
855C2—4882no—
856C2—4882no—
857C2—2442no—
858C2—2442no—
859C2#2145672914yesdirect product factor
860C2C2×#1684032311yescharacteristic
861C2C2×#1684056811yescharacteristic
862C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#483C2
socleC23×C61C22×D4
hypercenterC2×#483D61
hypocenterC61C2×#3204
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#16840343C2semidirect
2. C2×#16840342C2semidirect
3. #21456729C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840080C2semidirect
6. C2×#16840094C2semidirect
7. C2×#16840019C2semidirect
8. C2×#16840016C2semidirect
9. C2×#16839994C2semidirect
10. C2×#16839992C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839922C2semidirect
13. C2×#16839910C2semidirect
14. C2×#16839909C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#483C2semidirect
27. #16840343C22semidirect
29. #16840342C22semidirect
46. #16840094C22semidirect
47. #16840082C22semidirect
48. #16840080C22semidirect
49. #16840019C22semidirect
50. #16840016C22semidirect
51. #16839994C22semidirect
52. #16839992C22semidirect
53. #16839927C22semidirect
54. #16839922C22semidirect
55. #16839910C22semidirect
56. #16839909C22semidirect
65. #16839727C22semidirect
71. C61×#483C22semidirect
429. C2×#483D61semidirect
440. C2×C61#3204semidirect
480. #483C2×D61semidirect
508. C61C2×#3204semidirect
859. C2#21456729direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403432
C2×#168403422
#214567292
C2×#168400822
C2×#168400802
C2×#168400942
C2×#168400192
C2×#168400162
C2×#168399942
C2×#168399922
C2×#168399272
C2×#168399222
C2×#168399102
C2×#168399092
C2×#168397272
C2×C61×#4832
C2×#320461