Finite Group Databasebeta

← C2×#21458306 #30558594

Subgroups — C2×#21458306 #30558594

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840469C211yesmaximal, characteristic, complemented
2C2×#16840458C211yesmaximal, characteristic
3#21458306C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840098C211yesmaximal, characteristic, complemented
6C2×#16840081C211yesmaximal, characteristic, complemented
7C2×#16840104C211yesmaximal, characteristic, complemented
8C2×#16840076C211yesmaximal, characteristic, complemented
9C2×#16840070C211yesmaximal, characteristic, complemented
10C2×#16840043C211yesmaximal, characteristic, complemented
11C2×#16840008C211yesmaximal, characteristic, complemented
12C2×#16839991C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×#16839804C211yesmaximal, characteristic, complemented
15C22×#14519711C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18#16840469—24no—
19#16840469C2218yescomplemented
20#16840458—24no—
21#16840458C2218yes—
22C2×#14519777C2211yescharacteristic
23C2×#14519772—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519768—21no—
26C2×#14519759—21no—
27C2×#14519756C2211yescharacteristic
28C2×#14519756C2211yescharacteristic
29C2×#14519754—21no—
30C2×#14519754—21no—
31C2×#14519751C2211yescharacteristic
32C2×#14519751C2211yescharacteristic
33C2×#14519749—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×D4×Dic61—21no—
37C2×#14519737—21no—
38C2×#14519736C2211yescharacteristic
39C22×C4⋊Dic61C2211yescharacteristic
40C22×C4⋊Dic61C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840104C2218yescomplemented
44#16840098C2218yescomplemented
45#16840081C2218yescomplemented
46#16840076C2218yescomplemented
47#16840070C2218yescomplemented
48#16840043C2218yescomplemented
49#16840008C2218yescomplemented
50#16839991C2218yescomplemented
51#16839864C2218yescomplemented
52#16839804C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519711C2211yescharacteristic
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519711C2218yescomplemented
60C2×#14519709C2211yescharacteristic
61C2×#14519709C2211yescharacteristic
62C2×#14519709C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#435C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758190—24no—
87C2×#11758190C2314yes—
88#14519777—22no—
89#14519777C2314yes—
90#14519772—28no—
91#14519769—22no—
92#14519769C2314yes—
93#14519768—28no—
94#14519759—28no—
95#14519756—22no—
96#14519756—22no—
97#14519756C2314yes—
98#14519756C2314yes—
99#14519754—28no—
100#14519754—28no—
101#14519751—22no—
102#14519751—22no—
103#14519751C2314yes—
104#14519751C2314yes—
105#14519749—28no—
106C4×Dic122—22no—
107C4×Dic122C2314yes—
108C4×D244—22no—
109C4×D244C2314yes—
110D4×Dic61—28no—
111#14519737—28no—
112#14519736—22no—
113#14519736C2314yes—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—22no—
116C2×C4⋊Dic61—22no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2314yes—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2314yes—
124C2×C4⋊Dic61C2314yes—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143#14519711C2314yes—
144#14519711C2314yes—
145#14519711C2314yes—
146#14519711C2314yes—
147#14519711C2314yes—
148#14519711C2314yes—
149#14519709C2314yes—
150#14519709C2314yes—
151#14519709C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519699C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158C22×D4×C61D411yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C2×M16×C61—24no—
162C2×M16×C61C2314yes—
163C22×C8×C61—24no—
164C22×C8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×D4×C61D414yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C4⋊C8×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C22⋊C8×C61C2314yes—
178#97×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C2×D4×C61—24no—
183C2×D4×C61C2×D414yes—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—44no—
200C2×C22⋊D61—82no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—24no—
210C22×Dic61—24no—
211C22×Dic61—82no—
212C22×Dic61—82no—
213C22×Dic61—82no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—21no—
217C2×D244C2412yes—
218C2×C4×D61—24no—
219C2×C4×D61—82no—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—21no—
223C2×Dic122—24no—
224C2×Dic122—82no—
225C2×Dic122C2412yes—
226M16×C61—28no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61—28no—
231C2×C8×C61#4114yes—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C2×C8×C61C2412yes—
235C2×C8×C61C2412yes—
236C4⋊C4×C61C2×D414yes—
237C22⋊C4×C61C2×D414yes—
238C22⋊C4×C61C2×D414yes—
239C42×C61C2×D412yes—
240C42×C61C2412yes—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270#11758190—28no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61#13714yes—
277C23×C61C22×D412yes—
278C23×C61C22×D412yes—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284D4×C61—28no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4112yes—
301C2×C4×C612−1+412yes—
302C2×C4×C61C2511yescharacteristic
303C22⋊D61—48no—
304C22⋊D61—84no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—84no—
320C2×Dic61—84no—
321C2×Dic61—84no—
322D244—22no—
323D244—22no—
324D244—42no—
325C4×D61—84no—
326Dic122—22no—
327Dic122—22no—
328Dic122—42no—
329Dic122—84no—
330C8×C61—22no—
331C8×C61—22no—
332C8×C61—22no—
333C8×C61C2×#4114yes—
334C2×#3346—611nomaximal, Sylow
335C22×C61—28no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—44no—
342C22×C61#54712yes—
343C22×C61C2×#13714yes—
344C22×C61C2×#13712yes—
345C22×C61#57612yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—84no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61#54712yes—
356C4×C61C22×#4111yescharacteristic
357C4×C61C2×2−1+411yescharacteristic
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365C2×#554—611no—
366C2×#553—611no—
367#3346—6116no—
368C2×#501—611no—
369C2×#484—611no—
370C2×#481—611no—
371C2×#485—611no—
372C2×#480—611no—
373C2×#479—611no—
374C2×#474—611no—
375C2×#468—611no—
376C2×#465—611no—
377C2×#440—611no—
378C2×#435D6111yescharacteristic, complemented
379C2×#428—611no—
380C22×#107—611no—
381C2×C61—24no—
382C2×C61—42no—
383C2×C61#334614yescomplemented
384C2×C61C2×#54711yescharacteristic
385C2×C61C22×#13711yescharacteristic
386C2×C61C2×#57611yescharacteristic
387D61—82no—
388C22×SD16—611no—
389C22×M16C2×D6111yescharacteristic
390C23×C8C2×D6111yescharacteristic
391#554—618no—
392#554—1224no—
393#553—618no—
394#553—1224no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#125—611no—
398C2×#125—1221no—
399C2×#123—1221no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—611no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8—1221no—
404C2×#121—611no—
405C2×#121—611no—
406C2×#121—1221no—
407C2×C4×Q8—611no—
408C2×C4×D4—611no—
409C2×C4×D4—1221no—
410C2×C4×D4—1221no—
411C2×C4×D4C2×D6111yescharacteristic
412C2×#117—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416#501—618no—
417#485—618no—
418#484—618no—
419#481—618no—
420#480—618no—
421#479—618no—
422#474—618no—
423#468—618no—
424#465—618no—
425#440—618no—
426#435C2×D6118yescomplemented
427#428—618no—
428C2×#107—611no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#107—618no—
433C2×#107—611no—
434C2×#107—611no—
435C2×#106—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×C4⋊C8C2×D6111yescharacteristic
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×C22⋊C8C2×D6111yescharacteristic
447C2×#97C2×D6111yescharacteristic
448C61C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×Q8—1221no—
451C22×D4—611no—
452C22×D4—1221no—
453C22×D4—1221no—
454C22×D4D24411yescharacteristic
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4C22×D6111yescharacteristic
460C23×C4C22×D6111yescharacteristic
461C2×SD16—614no—
462C2×SD16—1224no—
463C2×M16—24no—
464C2×M16C22×D6114yes—
465C22×C8—24no—
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6114yes—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C4⋊Q8—614no—
472C4⋊Q8—1222no—
473#126—1228no—
474#125—614no—
475#125—1228no—
476#125—1222no—
477#123—1228no—
478C22⋊Q8—614no—
479C22⋊Q8—614no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—1228no—
483C22⋊Q8—1228no—
484#121—614no—
485#121—614no—
486#121—1228no—
487#121—1222no—
488#121—1222no—
489C4×Q8—614no—
490C4×Q8—1222no—
491C4×D4—614no—
492C4×D4—1228no—
493C4×D4—1228no—
494C4×D4—1222no—
495C4×D4D24414yes—
496C4×D4C22×D6114yes—
497#117—614no—
498#117—1222no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4D24411yescharacteristic
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4D24411yescharacteristic
528C2×C22⋊C4D24411yescharacteristic
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42C22×D6111yescharacteristic
532#107—614no—
533#107—614no—
534#107—614no—
535#107—614no—
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540#106—614no—
541C4⋊C8C22×D6114yes—
542#103—614no—
543#103—614no—
544#103—614no—
545#102—614no—
546#102—614no—
547#102—614no—
548C22⋊C8C22×D6114yes—
549C22⋊C8C22×D6114yes—
550#97C22×D6114yes—
551C24—1221no—
552C24C2×D24411yescharacteristic
553C24C2×D24411yescharacteristic
554C2×Q8—612no—
555C2×Q8—1224no—
556C2×Q8—1221no—
557C2×Q8—1222no—
558C2×Q8—1222no—
559C2×Q8—4882no—
560C2×D4—24no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1224no—
564C2×D4—1221no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—4882no—
568C2×D4—2444no—
569C2×D4C2×D24414yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1224no—
585C22×C4—4882no—
586C22×C4—4882no—
587C22×C4—4882no—
588C22×C4—4882no—
589C22×C4C2×D24412yes—
590C22×C4C2×D24412yes—
591C22×C4C2×D24411yescharacteristic
592C22×C4C2×D24411yescharacteristic
593C22×C4C2×D24411yescharacteristic
594C22×C4C2×D24411yescharacteristic
595C22×C4C23×D6112yes—
596C22×C4C23×D6112yes—
597C22×C4C23×D6111yescharacteristic
598SD16—1228no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#1175822414yes—
605C2×C8C23×D6112yes—
606C2×C8C23×D6112yes—
607C2×C8C23×D6112yes—
608C2×C8C23×D6112yes—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—612no—
614C4⋊C4—612no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1224no—
623C4⋊C4—1221no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4C2×D24414yes—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4C2×D24414yes—
638C22⋊C4C2×D24414yes—
639C42—1224no—
640C42—1224no—
641C42C2×D24412yes—
642C42C23×D6112yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—1222no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23#1451981014yes—
653C23C22×D24412yes—
654C23C22×D24412yes—
655C23C22×D24411yescharacteristic
656Q8—1222no—
657Q8—1222no—
658Q8—4884no—
659Q8—2442no—
660D4—28no—
661D4—1222no—
662D4—1222no—
663D4—4884no—
664D4—2448no—
665D4—2442no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—4884no—
686C2×C4—4884no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4C22×D24412yes—
695C2×C4C22×D24412yes—
696C2×C4C22×D24412yes—
697C2×C4C22×D24412yes—
698C2×C4C22×D24411yescharacteristic
699C2×C4C2×#1175822412yes—
700C2×C4#1451982412yes—
701C2×C4C24×D6111yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#1175822414yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—4884no—
714C22—2442no—
715C22—2442no—
716C22—2442no—
717C22#1684041612yes—
718C22C2×#1451981014yes—
719C22C2×#1451981012yes—
720C22#1684056712yes—
721C22C23×D24411yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—2442no—
727C4—2442no—
728C4—2442no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4#1684041612yes—
734C4C22×#1175822411yescharacteristic
735C4C2×#1451982411yescharacteristic
736C2—24no—
737C2—42no—
738C2—4882no—
739C2#2145830614yesdirect product factor
740C2C2×#1684041611yescharacteristic
741C2C22×#1451981011yescharacteristic
742C2C2×#1684056711yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840458C2
hypercenterC2×#435D61
hypocenterC61C2×#3346
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16840469C2semidirect
3. #21458306C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840098C2semidirect
6. C2×#16840081C2semidirect
7. C2×#16840104C2semidirect
8. C2×#16840076C2semidirect
9. C2×#16840070C2semidirect
10. C2×#16840043C2semidirect
11. C2×#16840008C2semidirect
12. C2×#16839991C2semidirect
13. C2×#16839864C2semidirect
14. C2×#16839804C2semidirect
15. C22×#14519711C2semidirect
16. C2×C61×#435C2semidirect
19. #16840469C22semidirect
42. #16840171C22semidirect
43. #16840104C22semidirect
44. #16840098C22semidirect
45. #16840081C22semidirect
46. #16840076C22semidirect
47. #16840070C22semidirect
48. #16840043C22semidirect
49. #16840008C22semidirect
50. #16839991C22semidirect
51. #16839864C22semidirect
52. #16839804C22semidirect
59. C2×#14519711C22semidirect
72. C61×#435C22semidirect
378. C2×#435D61semidirect
383. C2×C61#3346semidirect
426. #435C2×D61semidirect
448. C61C2×#3346semidirect
739. C2#21458306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404692
C2×#168404582
#214583062
C2×#168401712
C2×#168400982
C2×#168400812
C2×#168401042
C2×#168400762
C2×#168400702
C2×#168400432
C2×#168400082
C2×#168399912
C2×#168398642
C2×#168398042
C22×#145197112
C2×C61×#4352
C2×#334661