Finite Group Databasebeta

← C2×#21456713 #30550712

Subgroups — C2×#21456713 #30550712

Order 15616.

2122 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×#16840338C211yesmaximal, characteristic
2C2×#16840335C211yesmaximal, characteristic
3#21456713C2116yesmaximal, direct product factor
4C2×#16840106C211yesmaximal, characteristic, complemented
5C2×#16840105C211yesmaximal, characteristic, complemented
6C2×#16840103C211yesmaximal, characteristic, complemented
7C2×#16840021C211yesmaximal, characteristic, complemented
8C2×#16840019C211yesmaximal, characteristic, complemented
9C2×#16840004C211yesmaximal, characteristic, complemented
10C2×#16840002C211yesmaximal, characteristic, complemented
11C2×#16839920C211yesmaximal, characteristic, complemented
12C2×#16839919C211yesmaximal, characteristic, complemented
13C2×#16839919C211yesmaximal, characteristic, complemented
14C2×#16839917C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic
16C2×C61×#485C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×Dic244C2211yescharacteristic
22C22×#11758202C2211yescharacteristic
23C22×#11758202C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840338—24no—
27#16840338C2218yes—
28#16840335—24no—
29#16840335C2218yes—
30C2×#14519777—21no—
31C2×#14519776—21no—
32C2×#14519765—21no—
33C2×#14519763—21no—
34C2×#14519762—21no—
35C2×#14519761—21no—
36C2×#14519761—21no—
37C2×#14519759—21no—
38C2×#14519757C2211yescharacteristic
39C2×#14519757C2211yescharacteristic
40C2×#14519757C2211yescharacteristic
41C2×#14519757C2211yescharacteristic
42C2×#14519757C2211yescharacteristic
43C2×#14519756C2211yescharacteristic
44C2×#14519753C2211yescharacteristic
45C2×#14519735C2211yescharacteristic
46#16840106C2218yescomplemented
47#16840105C2218yescomplemented
48#16840103C2218yescomplemented
49#16840021C2218yescomplemented
50#16840019C2218yescomplemented
51#16840004C2218yescomplemented
52#16840002C2218yescomplemented
53#16839920C2218yescomplemented
54#16839919C2218yescomplemented
55#16839919C2218yescomplemented
56#16839917C2218yescomplemented
57C2×#14519710C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65#16839727C2218yes—
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#485C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—42no—
78C2×#11758222—42no—
79C2×#11758222D414yes—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122—22no—
83C22×Dic122—21no—
84C22×Dic122—42no—
85C22×Dic122—42no—
86C22×Dic122D411yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2311yescharacteristic
89C22×Dic122C2311yescharacteristic
90C22×Dic122C2314yes—
91C2×Q8×D61—22no—
92C2×Q8×D61—42no—
93C2×Q8×D61—42no—
94C2×Q8×D61C2314yes—
95C22×D244D411yescharacteristic
96C22×C22⋊D61D411yescharacteristic
97C22×C22⋊D61D411yescharacteristic
98C23×Dic61—21no—
99C22×C4×D61—21no—
100C22×C4×D61C2311yescharacteristic
101C22×C4×D61C2311yescharacteristic
102C2×Dic244—42no—
103C2×Dic244—42no—
104C2×Dic244C2314yes—
105C2×Dic244C2314yes—
106C2×#11758202—42no—
107C2×#11758202—42no—
108C2×#11758202C2314yes—
109C2×#11758202C2314yes—
110C2×#11758189—42no—
111C2×#11758189C2314yes—
112C22×#92418C2311yescharacteristic
113C22×#92418C2311yescharacteristic
114C2×C8×D61—42no—
115C2×C8×D61C2314yes—
116#14519777—28no—
117#14519776—28no—
118#14519765—28no—
119#14519763—28no—
120#14519762—28no—
121#14519761—28no—
122#14519761—28no—
123#14519759—28no—
124#14519757—22no—
125#14519757—22no—
126#14519757—22no—
127#14519757—22no—
128#14519757—22no—
129#14519757C2314yes—
130#14519757C2314yes—
131#14519757C2314yes—
132#14519757C2314yes—
133#14519757C2314yes—
134#14519756—22no—
135#14519756C2314yes—
136#14519753—22no—
137#14519753C2314yes—
138#14519735—22no—
139#14519735C2314yes—
140C2×C4⋊Dic61—21no—
141C2×C4⋊Dic61—21no—
142C2×C4⋊Dic61—21no—
143C2×C4⋊Dic61—21no—
144C2×C4⋊Dic61—21no—
145C2×C4⋊Dic61C2311yescharacteristic
146C2×#11758196—21no—
147C2×#11758196—21no—
148C2×C22⋊Dic61—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×C4×Dic61—21no—
157#14519710C2314yes—
158#14519708C2314yes—
159#14519702C2314yes—
160#14519702C2314yes—
161#14519700C2314yes—
162#14519700C2314yes—
163#14519700C2314yes—
164#14519700C2314yes—
165C22⋊#92418C2314yes—
166#14519689C2314yes—
167#14519689C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22⋊Q8×C61—22no—
173C22⋊Q8×C61C2314yes—
174#117×C61—22no—
175#117×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C42×C61—21no—
183#107×C61C2314yes—
184#106×C61C2314yes—
185#103×C61C2314yes—
186#103×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61C2×D411yescharacteristic
189C23×D61C2×D411yescharacteristic
190C23×D61C2×D411yescharacteristic
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61C2×D414yes—
208C2×C22⋊D61C2×D414yes—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—21no—
214C22×Dic61—44no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217Q8×D61—44no—
218Q8×D61—44no—
219Q8×D61—48no—
220#11758222—48no—
221#11758222—44no—
222#11758222—44no—
223C2×D244—42no—
224C2×D244C2×D414yes—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—24no—
230C2×C4×D61—44no—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2412yes—
234C2×C4×D61C2412yes—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—24no—
245C2×Dic122—24no—
246C2×Dic122—44no—
247C2×Dic122—44no—
248C2×Dic122—42no—
249C2×Dic122—44no—
250C2×Dic122—44no—
251C2×Dic122—48no—
252C2×Dic122C2×D414yes—
253C2×Dic122C2412yes—
254C2×Dic122C2412yes—
255C2×Dic122C2412yes—
256C2×C8×C61—22no—
257C2×C8×C61—22no—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C4⋊C4×C61C2412yes—
267C22⋊C4×C61—24no—
268C22⋊C4×C61—24no—
269C42×C61—24no—
270C22⋊Dic61—24no—
271#11758202—44no—
272#11758202—44no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280C4⋊Dic61—21no—
281C4⋊Dic61—24no—
282C4⋊Dic61—24no—
283C4⋊Dic61—24no—
284C4⋊Dic61—24no—
285C4⋊Dic61—24no—
286C4⋊Dic61C2412yes—
287#11758196—24no—
288#11758196—24no—
289C4×Dic61—24no—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294Dic244—44no—
295Dic244—44no—
296#11758189—44no—
297C8×D61—44no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61C22×D412yes—
310C22×D61C22×D412yes—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61H(5,𝔽2)12yes—
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—44no—
332C22⋊D61—44no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—48no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61C22×D412yes—
345C2×Dic61C22×D412yes—
346D244—44no—
347C4×D61—24no—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—48no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—22no—
360Dic122—44no—
361Dic122—48no—
362Dic122—48no—
363Dic122—42no—
364Dic122—42no—
365Dic122—42no—
366C8×C61—22no—
367C8×C61—22no—
368#92418—22no—
369#92418—22no—
370C2×#3202—611nomaximal, Sylow
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—44no—
375C22×C61#53412yes—
376C22×C61#57812yes—
377C22×C61#57812yes—
378C22×C61C23×D411yescharacteristic
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—44no—
386C2×D61—44no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#53412yes—
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—22no—
396Dic61—22no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401C2×#536—611no—
402C2×#536—611no—
403#3202—6116no—
404C2×#485—611no—
405C2×#485—611no—
406C2×#485—611no—
407C2×#485D6111yescharacteristic, complemented
408C2×#470—611no—
409C2×#470—611no—
410C2×#467—611no—
411C2×#467—611no—
412C2×#451—611no—
413C2×#451—611no—
414C2×#451—611no—
415C2×#451—611no—
416C2×#408—611no—
417C2×C61—42no—
418C2×C61#320214yescomplemented
419C2×C61C2×#53411yescharacteristic
420C2×C61C2×#57811yescharacteristic
421C2×C61C2×#57811yescharacteristic
422D61—42no—
423D61—42no—
424C22×#41—611no—
425C23×Q8—611no—
426C23×Q8—611no—
427C22×Q16—611no—
428C22×Q16—611no—
429C22×Q16—611no—
430C22×Q16—611no—
431C22×M16—611no—
432C23×C8—611no—
433#536—618no—
434#536—618no—
435#536—1224no—
436#536—1224no—
437C2×C4⋊Q8—1221no—
438C2×C4⋊Q8—1221no—
439C2×#124—1221no—
440C2×#124—1221no—
441C2×#123—1221no—
442C2×#123—1221no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×C22⋊Q8—611no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—611no—
448C2×C22⋊Q8—611no—
449C2×C22⋊Q8—611no—
450C2×C22⋊Q8—611no—
451C2×C22⋊Q8—611no—
452C2×C22⋊Q8C2×D6111yescharacteristic
453C2×#117—611no—
454C2×#117C2×D6111yescharacteristic
455#485—618no—
456#485—618no—
457#485—618no—
458#485C2×D6118yescomplemented
459#470—618no—
460#470—618no—
461#467—618no—
462#467—618no—
463#451—618no—
464#451—618no—
465#451—618no—
466#451—618no—
467C2×#107—611no—
468C2×#107C2×D6111yescharacteristic
469C2×#106—611no—
470C2×#106C2×D6111yescharacteristic
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103C2×D6111yescharacteristic
478C2×#103C2×D6111yescharacteristic
479#408—618no—
480C2×C22⋊C8—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C22⋊C8C2×D6111yescharacteristic
484C61C2×#320211yescharacteristic, complemented, Sylow
485C2×#41—614no—
486C2×#41—614no—
487C2×#41—2442no—
488C2×#41—2442no—
489C22×Q8—611no—
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—611no—
493C22×Q8—611no—
494C22×Q8—614no—
495C22×Q8—1221no—
496C22×Q8—1222no—
497C22×Q8—1221no—
498C22×Q8—1222no—
499C22×Q8—2442no—
500C22×Q8—2442no—
501C22×Q8—2442no—
502C22×Q8—2442no—
503C22×Q8C22×D6111yescharacteristic
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4C22×D6111yescharacteristic
512C2×Q16—614no—
513C2×Q16—614no—
514C2×Q16—614no—
515C2×Q16—614no—
516C2×Q16—2442no—
517C2×Q16—2442no—
518C2×Q16—2442no—
519C2×Q16—2442no—
520C2×M16—614no—
521C2×M16—2442no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—614no—
525C22×C8—2442no—
526C22×C8C22×D6111yescharacteristic
527C22×C8C22×D6111yescharacteristic
528C4⋊Q8—1228no—
529C4⋊Q8—1228no—
530#124—1228no—
531#124—1228no—
532#123—1228no—
533#123—1228no—
534#123—1228no—
535#123—1228no—
536C22⋊Q8—22no—
537C22⋊Q8—614no—
538C22⋊Q8—614no—
539C22⋊Q8—614no—
540C22⋊Q8—614no—
541C22⋊Q8—614no—
542C22⋊Q8—614no—
543C22⋊Q8—614no—
544C22⋊Q8—1222no—
545C22⋊Q8—1222no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8C22×D6114yes—
552#117—22no—
553#117—614no—
554#117—1222no—
555#117C22×D6114yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C42—21no—
579C2×C42—1221no—
580#107—614no—
581#107C22×D6114yes—
582#106—614no—
583#106C22×D6114yes—
584#103—614no—
585#103—614no—
586#103—614no—
587#103—614no—
588#103—614no—
589#103—614no—
590#103C22×D6114yes—
591#103C22×D6114yes—
592C22⋊C8—614no—
593C22⋊C8—614no—
594C22⋊C8—614no—
595C22⋊C8C22×D6114yes—
596C24—611no—
597C24—611no—
598C24D4×D6111yescharacteristic
599#41—2448no—
600#41—2444no—
601#41—2444no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—614no—
606C2×Q8—612no—
607C2×Q8—612no—
608C2×Q8—612no—
609C2×Q8—1224no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—1224no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—1222no—
617C2×Q8—1222no—
618C2×Q8—1222no—
619C2×Q8—1222no—
620C2×Q8—2442no—
621C2×Q8—2444no—
622C2×Q8—2444no—
623C2×Q8—2444no—
624C2×Q8—2448no—
625C2×Q8—2444no—
626C2×Q8—2444no—
627C2×Q8—2444no—
628C2×Q8—2448no—
629C2×Q8C23×D6112yes—
630C2×D4—614no—
631C2×D4—614no—
632C2×D4—614no—
633C2×D4—2442no—
634C2×D4—2442no—
635C2×D4—2442no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—1224no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1224no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—2444no—
659C22×C4—2444no—
660C22×C4D4×D6112yes—
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664Q16—2444no—
665Q16—2444no—
666Q16—2444no—
667Q16—2444no—
668M16—2444no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—612no—
672C2×C8—612no—
673C2×C8—1222no—
674C2×C8—1222no—
675C2×C8—2444no—
676C2×C8C23×D6112yes—
677C2×C8C23×D6112yes—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—612no—
683C4⋊C4—1224no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1221no—
690C4⋊C4—1224no—
691C4⋊C4C23×D6112yes—
692C4⋊C4C23×D6112yes—
693C4⋊C4C23×D6112yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—1224no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C42—24no—
705C42—1224no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—612no—
710C23—612no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23C2×D4×D6112yes—
718C23C2×D4×D6111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—42no—
722Q8—1222no—
723Q8—1222no—
724Q8—1222no—
725Q8—1222no—
726Q8—1222no—
727Q8—1222no—
728Q8—2444no—
729Q8—2448no—
730Q8—2448no—
731Q8—2442no—
732Q8—2442no—
733Q8—2442no—
734D4—2444no—
735D4—2444no—
736D4—2444no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—2448no—
764C2×C4—2448no—
765C2×C4—2442no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4C2×D4×D6112yes—
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4#1451982312yes—
772C2×C4#1451982312yes—
773C2×C4C24×D6111yescharacteristic
774C8—22no—
775C8—22no—
776C8—1222no—
777C8—1222no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—2444no—
789C22—2444no—
790C22#1684032312yes—
791C22#1684057612yes—
792C22#1684057812yes—
793C22C22×D4×D6111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1222no—
800C4—1222no—
801C4—2442no—
802C4—2442no—
803C4—2442no—
804C4—2442no—
805C4#1684032312yes—
806C4C2×#1451982311yescharacteristic
807C4C2×#1451982311yescharacteristic
808C2—42no—
809C2—2442no—
810C2—2442no—
811C2#2145671314yesdirect product factor
812C2C2×#1684032311yescharacteristic
813C2C2×#1684057611yescharacteristic
814C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#485C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#485D61
hypocenterC61C2×#3202
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #21456713C2direct (N × H)
4. C2×#16840106C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840103C2semidirect
7. C2×#16840021C2semidirect
8. C2×#16840019C2semidirect
9. C2×#16840004C2semidirect
10. C2×#16840002C2semidirect
11. C2×#16839920C2semidirect
12. C2×#16839919C2semidirect
13. C2×#16839919C2semidirect
14. C2×#16839917C2semidirect
16. C2×C61×#485C2semidirect
46. #16840106C22semidirect
47. #16840105C22semidirect
48. #16840103C22semidirect
49. #16840021C22semidirect
50. #16840019C22semidirect
51. #16840004C22semidirect
52. #16840002C22semidirect
53. #16839920C22semidirect
54. #16839919C22semidirect
55. #16839919C22semidirect
56. #16839917C22semidirect
71. C61×#485C22semidirect
407. C2×#485D61semidirect
418. C2×C61#3202semidirect
458. #485C2×D61semidirect
484. C61C2×#3202semidirect
811. C2#21456713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403382
C2×#168403352
#214567132
C2×#168401062
C2×#168401052
C2×#168401032
C2×#168400212
C2×#168400192
C2×#168400042
C2×#168400022
C2×#168399202
C2×#168399192
C2×#168399172
C2×#168397272
C2×C61×#4852
C2×#320261