Finite Group Databasebeta

← C2×#21457247 #30552941

Subgroups — C2×#21457247 #30552941

Order 15616.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840383C211yesmaximal, characteristic
2C2×#16840374C211yesmaximal, characteristic, complemented
3#21457247C2116yesmaximal, direct product factor
4C2×#16840070C211yesmaximal, characteristic, complemented
5C2×#16840058C211yesmaximal, characteristic, complemented
6C2×#16840048C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16840020C211yesmaximal, characteristic, complemented
9C2×#16840008C211yesmaximal, characteristic
10C2×#16840003C211yesmaximal, characteristic, complemented
11C2×#16839991C211yesmaximal, characteristic
12C2×#16839985C211yesmaximal, characteristic, complemented
13C2×#16839985C211yesmaximal, characteristic, complemented
14C2×#16839973C211yesmaximal, characteristic, complemented
15C2×#16839968C211yesmaximal, characteristic, complemented
16C2×C61×#424C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21#16840383—24no—
22#16840383C2218yes—
23#16840374—24no—
24#16840374C2218yescomplemented
25C2×#14519777C2211yescharacteristic
26C2×#14519777C2211yescharacteristic
27C2×#14519772—21no—
28C2×#14519770—21no—
29C2×#14519770—21no—
30C2×#14519769C2211yescharacteristic
31C2×#14519767—21no—
32C2×#14519767—21no—
33C2×#14519765C2211yescharacteristic
34C2×#14519763—21no—
35C2×#14519759—21no—
36C2×#14519756C2211yescharacteristic
37C2×#14519756C2211yescharacteristic
38C2×#14519756C2211yescharacteristic
39C2×#14519755—21no—
40C2×#14519751C2211yescharacteristic
41C2×C4×Dic122C2211yescharacteristic
42C2×C4×Dic122C2211yescharacteristic
43C2×C4×Dic122C2211yescharacteristic
44C2×C4×D244C2211yescharacteristic
45#16840070C2218yescomplemented
46#16840063C2218yescomplemented
47#16840058C2218yescomplemented
48#16840048C2218yescomplemented
49#16840020C2218yescomplemented
50#16840008C2218yes—
51#16840003C2218yescomplemented
52#16839991C2218yes—
53#16839985C2218yescomplemented
54#16839985C2218yescomplemented
55#16839973C2218yescomplemented
56#16839968C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#424C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×C4⋊C8×C61C2211yescharacteristic
76C2×C4⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C4×D61—21no—
84C2×Dic244—42no—
85C2×Dic244—42no—
86C2×Dic244C2314yes—
87C2×Dic244C2314yes—
88C2×#11758190—42no—
89C2×#11758190—42no—
90C2×#11758190C2314yes—
91C2×#11758190C2314yes—
92#14519777—22no—
93#14519777—22no—
94#14519777C2314yes—
95#14519777C2314yes—
96#14519772—28no—
97#14519770—28no—
98#14519770—28no—
99#14519769—22no—
100#14519769C2314yes—
101#14519767—28no—
102#14519767—28no—
103#14519765—22no—
104#14519765C2314yes—
105#14519763—28no—
106#14519759—28no—
107#14519756—22no—
108#14519756—22no—
109#14519756—22no—
110#14519756C2314yes—
111#14519756C2314yes—
112#14519756C2314yes—
113#14519755—28no—
114#14519751—22no—
115#14519751C2314yes—
116C4×Dic122—22no—
117C4×Dic122—22no—
118C4×Dic122—22no—
119C4×Dic122C2314yes—
120C4×Dic122C2314yes—
121C4×Dic122C2314yes—
122C4×D244—22no—
123C4×D244C2314yes—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61—21no—
149#14519711C2314yes—
150#14519711C2314yes—
151#14519709C2314yes—
152#14519709C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161C23×C4×C61C2311yescharacteristic
162C2×M16×C61—42no—
163C2×M16×C61C2314yes—
164C22×C8×C61—42no—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2314yes—
170#117×C61D414yes—
171#117×C61C2314yes—
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C22⋊C4×C61D411yescharacteristic
175C2×C22⋊C4×C61D411yescharacteristic
176C2×C42×C61C2311yescharacteristic
177C2×C42×C61C2311yescharacteristic
178C4⋊C8×C61C2314yes—
179C4⋊C8×C61C2314yes—
180C4⋊C8×C61C2314yes—
181C4⋊C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—82no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—21no—
206C2×D244C2412yes—
207C2×C4×D61—24no—
208C2×C4×D61—82no—
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—24no—
219C2×Dic122—82no—
220C2×Dic122C2412yes—
221C2×Dic122C2412yes—
222C2×Dic122C2412yes—
223M16×C61—44no—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—44no—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C4⋊C4×C61C2×D414yes—
234C4⋊C4×C61C2×D414yes—
235C22⋊C4×C61C2×D414yes—
236C22⋊C4×C61C2×D414yes—
237C42×C61C2×D412yes—
238C42×C61C2×D412yes—
239C42×C61C2412yes—
240C42×C61C2412yes—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270Dic244—44no—
271Dic244—44no—
272#11758190—44no—
273#11758190—44no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61C22×D412yes—
278C23×C61C22×D411yescharacteristic
279C22×D61—22no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—24no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61C22×D412yes—
292C2×C4×C61C22×D412yes—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61H(5,𝔽2)12yes—
298C2×C4×C612−1+412yes—
299C2×C4×C61C2511yescharacteristic
300C22⋊D61—84no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315D244—22no—
316D244—22no—
317D244—42no—
318C4×D61—84no—
319Dic122—22no—
320Dic122—22no—
321Dic122—22no—
322Dic122—22no—
323Dic122—22no—
324Dic122—22no—
325Dic122—42no—
326Dic122—42no—
327Dic122—42no—
328Dic122—84no—
329C8×C61—22no—
330C8×C61—22no—
331C8×C61—22no—
332C8×C61—22no—
333C2×#3258—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—44no—
338C22×C61#53712yes—
339C22×C61#57712yes—
340C22×C61#57812yes—
341C22×C61C23×D411yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—84no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61#53712yes—
352C4×C61C2×H(5,𝔽2)11yescharacteristic
353C4×C61C2×2−1+411yescharacteristic
354Dic61—42no—
355Dic61—42no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#542—611no—
362C2×#541—611no—
363#3258—6116no—
364C2×#479—611no—
365C2×#477—611no—
366C2×#475—611no—
367C2×#478—611no—
368C2×#470—611no—
369C2×#468—611no—
370C2×#467—611no—
371C2×#465—611no—
372C2×#464—611no—
373C2×#464—611no—
374C2×#462—611no—
375C2×#461—611no—
376C2×#424D6111yescharacteristic, complemented
377C2×C61—42no—
378C2×C61#325814yescomplemented
379C2×C61C2×#53711yescharacteristic
380C2×C61C2×#57711yescharacteristic
381C2×C61C2×#57811yescharacteristic
382D61—82no—
383C22×Q16—611no—
384C22×Q16—611no—
385C22×SD16—611no—
386C22×SD16—611no—
387C22×M16C2×D6111yescharacteristic
388C23×C8C2×D6111yescharacteristic
389#542—618no—
390#542—1224no—
391#541—618no—
392#541—1224no—
393C2×C4⋊Q8—611no—
394C2×C4⋊Q8—611no—
395C2×#126—1221no—
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#125—611no—
399C2×#125—1221no—
400C2×#125—1221no—
401C2×#124—611no—
402C2×#124—1221no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—1221no—
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×D4—611no—
413C2×#117C2×D6111yescharacteristic
414#479—618no—
415#478—618no—
416#477—618no—
417#475—618no—
418#470—618no—
419#468—618no—
420#467—618no—
421#465—618no—
422#464—618no—
423#464—618no—
424#462—618no—
425#461—618no—
426C2×#107—611no—
427C2×#107—611no—
428C2×#106—611no—
429C2×#106—611no—
430#424C2×D6118yescomplemented
431C2×C4⋊C8C2×D6111yescharacteristic
432C2×C4⋊C8C2×D6111yescharacteristic
433C2×C4⋊C8C2×D6111yescharacteristic
434C2×C4⋊C8C2×D6111yescharacteristic
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#102—611no—
442C2×#102—611no—
443C61C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—611no—
445C22×Q8—611no—
446C22×Q8—611no—
447C22×Q8—1221no—
448C22×D4—611no—
449C22×D4—1221no—
450C23×C4—1221no—
451C23×C4C22×D6111yescharacteristic
452C2×Q16—614no—
453C2×Q16—614no—
454C2×Q16—2442no—
455C2×Q16—2442no—
456C2×SD16—614no—
457C2×SD16—614no—
458C2×SD16—2442no—
459C2×SD16—2442no—
460C2×M16—42no—
461C2×M16C22×D6114yes—
462C22×C8—42no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6114yes—
468C4⋊Q8—614no—
469C4⋊Q8—614no—
470C4⋊Q8—1222no—
471C4⋊Q8—1222no—
472#126—1228no—
473#126—1228no—
474#126—1228no—
475#125—614no—
476#125—1228no—
477#125—1228no—
478#125—1222no—
479#124—614no—
480#124—1228no—
481#124—1222no—
482#123—1228no—
483C22⋊Q8—614no—
484C22⋊Q8—614no—
485C22⋊Q8—614no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1228no—
490#121—614no—
491#121—1222no—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1222no—
498C4×D4—614no—
499C4×D4—1222no—
500#117D24414yes—
501#117C22×D6114yes—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4D24411yescharacteristic
518C2×C4⋊C4D24411yescharacteristic
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4D24411yescharacteristic
527C2×C22⋊C4D24411yescharacteristic
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533#107—614no—
534#107—614no—
535#106—614no—
536#106—614no—
537C4⋊C8C22×D6114yes—
538C4⋊C8C22×D6114yes—
539C4⋊C8C22×D6114yes—
540C4⋊C8C22×D6114yes—
541#103—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#102—614no—
548#102—614no—
549C24—1221no—
550C24C2×D24411yescharacteristic
551C2×Q8—612no—
552C2×Q8—612no—
553C2×Q8—612no—
554C2×Q8—1224no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1222no—
559C2×Q8—1222no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1222no—
563C2×Q8—1222no—
564C2×Q8—4882no—
565C2×D4—612no—
566C2×D4—1224no—
567C2×D4—1221no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—4882no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1224no—
581C22×C4—4882no—
582C22×C4C2×D24412yes—
583C22×C4C2×D24411yescharacteristic
584C22×C4C2×D24411yescharacteristic
585C22×C4C2×D24411yescharacteristic
586C22×C4C2×D24411yescharacteristic
587C22×C4C2×D24411yescharacteristic
588C22×C4C23×D6112yes—
589C22×C4C23×D6111yescharacteristic
590Q16—2444no—
591Q16—2444no—
592SD16—2444no—
593SD16—2444no—
594M16—44no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—44no—
600C2×C8C23×D6112yes—
601C2×C8C23×D6112yes—
602C2×C8C23×D6112yes—
603C2×C8C23×D6112yes—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—612no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4C2×D24414yes—
624C4⋊C4C2×D24414yes—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4C2×D24414yes—
633C22⋊C4C2×D24414yes—
634C42—1224no—
635C42—1224no—
636C42—1224no—
637C42C2×D24412yes—
638C42C2×D24412yes—
639C42C23×D6112yes—
640C42C23×D6112yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23C22×D24412yes—
649C23C22×D24411yescharacteristic
650Q8—1222no—
651Q8—1222no—
652Q8—1222no—
653Q8—1222no—
654Q8—1222no—
655Q8—1222no—
656Q8—4884no—
657Q8—2442no—
658Q8—2442no—
659Q8—2442no—
660D4—1222no—
661D4—1222no—
662D4—4884no—
663D4—2442no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—4884no—
680C2×C4—2442no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4C22×D24412yes—
688C2×C4C22×D24412yes—
689C2×C4C22×D24412yes—
690C2×C4C22×D24412yes—
691C2×C4C22×D24412yes—
692C2×C4C22×D24411yescharacteristic
693C2×C4#1451982212yes—
694C2×C4#1451982512yes—
695C2×C4C24×D6111yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—4884no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22#1684034312yes—
709C22#1684057412yes—
710C22#1684057912yes—
711C22C23×D24411yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—2442no—
718C4—2442no—
719C4—2442no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4#1684034312yes—
725C4C2×#1451982211yescharacteristic
726C4C2×#1451982511yescharacteristic
727C2—42no—
728C2—4882no—
729C2#2145724714yesdirect product factor
730C2C2×#1684034311yescharacteristic
731C2C2×#1684057411yescharacteristic
732C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#424C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#424D61
hypocenterC61C2×#3258
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#16840374C2semidirect
3. #21457247C2direct (N × H)
4. C2×#16840070C2semidirect
5. C2×#16840058C2semidirect
6. C2×#16840048C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16840020C2semidirect
10. C2×#16840003C2semidirect
12. C2×#16839985C2semidirect
13. C2×#16839985C2semidirect
14. C2×#16839973C2semidirect
15. C2×#16839968C2semidirect
16. C2×C61×#424C2semidirect
24. #16840374C22semidirect
45. #16840070C22semidirect
46. #16840063C22semidirect
47. #16840058C22semidirect
48. #16840048C22semidirect
49. #16840020C22semidirect
51. #16840003C22semidirect
53. #16839985C22semidirect
54. #16839985C22semidirect
55. #16839973C22semidirect
56. #16839968C22semidirect
72. C61×#424C22semidirect
376. C2×#424D61semidirect
378. C2×C61#3258semidirect
430. #424C2×D61semidirect
443. C61C2×#3258semidirect
729. C2#21457247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
C2×#168403742
#214572472
C2×#168400702
C2×#168400582
C2×#168400482
C2×#168400632
C2×#168400202
C2×#168400082
C2×#168400032
C2×#168399912
C2×#168399852
C2×#168399732
C2×#168399682
C2×C61×#4242
C2×#325861