Finite Group Databasebeta

← C2×#21458172 #30558432

Subgroups — C2×#21458172 #30558432

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic, complemented
2C2×#16840413C211yesmaximal, characteristic
3#21458172C2116yesmaximal, direct product factor
4C2×#16840159C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840080C211yesmaximal, characteristic, complemented
7C2×#16840094C211yesmaximal, characteristic, complemented
8C2×#16840092C211yesmaximal, characteristic, complemented
9C2×#16840046C211yesmaximal, characteristic, complemented
10C2×#16840051C211yesmaximal, characteristic, complemented
11C2×#16839992C211yesmaximal, characteristic, complemented
12C2×#16839991C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C2×#106×D61C211yesmaximal, characteristic, complemented
16C22×#106×C61C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758190C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840467—24no—
21#16840467C2218yescomplemented
22#16840413—24no—
23#16840413C2218yes—
24C2×#14519776C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519762—21no—
28C2×#14519760—21no—
29C2×#14519757C2211yescharacteristic
30C2×#14519756—21no—
31C2×#14519756C2211yescharacteristic
32C2×#14519755—21no—
33C2×#14519755—21no—
34C2×#14519752C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519742C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840159C2218yescomplemented
43#16840094C2218yescomplemented
44#16840092C2218yescomplemented
45#16840082C2218yescomplemented
46#16840080C2218yescomplemented
47#16840051C2218yescomplemented
48#16840046C2218yescomplemented
49#16839992C2218yescomplemented
50#16839991C2218yescomplemented
51#16839849C2218yescomplemented
52C8×C22⋊D61C2218yescomplemented
53C2×#14519709C2211yescharacteristic
54C2×#14519708C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58#106×D61C2218yescomplemented
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C23×C8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#106×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2218yescomplemented
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122C2311yescharacteristic
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61D411yescharacteristic
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×#11758190—24no—
91C2×#11758190C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C2×C8×D61—24no—
95C2×C8×D61C2314yes—
96#14519776—22no—
97#14519776—22no—
98#14519776C2314yes—
99#14519776C2314yes—
100#14519767—28no—
101#14519762—28no—
102#14519760—28no—
103#14519757—22no—
104#14519757C2314yes—
105#14519756—22no—
106#14519756—28no—
107#14519756C2314yes—
108#14519755—28no—
109#14519755—28no—
110#14519752—22no—
111#14519752C2314yes—
112#14519751—22no—
113#14519751C2314yes—
114#14519742—22no—
115#14519742C2314yes—
116#14519739—22no—
117#14519739C2314yes—
118C4×C22⋊D61—28no—
119C4×C22⋊D61D414yes—
120C4×C22⋊D61C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61C2314yes—
134C4⋊C4×D61C2314yes—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61D411yescharacteristic
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198D411yescharacteristic
142C2×C4×Dic61—21no—
143C2×C4×Dic61C2311yescharacteristic
144#14519709C2314yes—
145#14519708C2314yes—
146#14519708C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519702C2314yes—
151#14519700C2314yes—
152#14519700C2314yes—
153#14519699C2314yes—
154#14519697C2314yes—
155#14519697C2314yes—
156C22⋊#92418C2314yes—
157#14519689C2314yes—
158C8×Dic61C2314yes—
159C23×C4×C61—21no—
160C23×C4×C61—21no—
161C23×C4×C61C2311yescharacteristic
162C22×C8×C61—24no—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—22no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2314yes—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2314yes—
176#106×C61C2314yes—
177#106×C61C2314yes—
178#106×C61C2314yes—
179#106×C61C2314yes—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C23×D61C2×D411yescharacteristic
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—24no—
190C22×C4×C61—24no—
191C22×C4×C61—44no—
192C22×C4×C61—82no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—44no—
199C2×C22⋊D61SD1618yescomplemented
200C2×C22⋊D61C2×D414yes—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207#11758222—432no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—24no—
211C2×D244—21no—
212C2×D244—44no—
213C2×D244C2412yes—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—44no—
220C2×C4×D61—44no—
221C2×C4×D61—82no—
222C2×C4×D61C2×D412yes—
223C2×C4×D61C2412yes—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122—24no—
228C2×Dic122—24no—
229C2×Dic122—44no—
230C2×Dic122—82no—
231C2×Dic122C2412yes—
232C2×C8×C61—22no—
233C2×C8×C61—28no—
234C2×C8×C61#4114yescomplemented
235C2×C8×C61C2412yes—
236C2×C8×C61C2412yes—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2412yes—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C22⋊Dic61—24no—
248C22⋊Dic61C2×D414yes—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253#11758198C2×D414yes—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—24no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196C2×D414yes—
266C4×Dic61—24no—
267C4×Dic61C2×D412yes—
268C4×Dic61C2412yes—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418C2412yes—
272C2×#92418C2412yes—
273#11758190—28no—
274C8×D61—28no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61C2×SD1614yes—
278C23×C61C22×D412yes—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61C2×SD1614yes—
287C22×D61C22×D412yes—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—48no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—84no—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4112yes—
305C2×C4×C612−1+412yes—
306C2×C4×C61C2511yescharacteristic
307C22⋊D61—48no—
308C22⋊D61C2×SD16116yescomplemented
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C2×SD1614yes—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321D244—22no—
322D244—22no—
323D244—48no—
324D244—42no—
325C4×D61—24no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—48no—
329C4×D61—48no—
330C4×D61—84no—
331Dic122—22no—
332Dic122—22no—
333Dic122—42no—
334Dic122—48no—
335Dic122—84no—
336C8×C61—22no—
337C8×C61C2×#4114yescomplemented
338#92418—22no—
339#92418—22no—
340C2×#3335—611nomaximal, Sylow
341C22×C61—28no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61#54712yes—
345C22×C61C22×SD1614yes—
346C22×C61C22×SD1612yes—
347C22×C61#57712yes—
348C22×C61C23×D411yescharacteristic
349C2×D61—28no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—84no—
356C2×D61C22×SD1614yes—
357C4×C61—22no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61#54712yes—
363C4×C61C22×#4111yescharacteristic
364C4×C61C2×2−1+411yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—42no—
368Dic61—42no—
369Dic61—42no—
370Dic61C22×SD1614yes—
371C2×#554—611no—
372C2×#547—611no—
373#3335—6116no—
374C2×#498—611no—
375C2×#481—611no—
376C2×#481—611no—
377C2×#483—611no—
378C2×#483—611no—
379C2×#475—611no—
380C2×#476—611no—
381C2×#465—611no—
382C2×#465—611no—
383C2×C4×SD16—611no—
384C2×C8×D4—611no—
385C22×#106—611no—
386C22×#106D6111yescharacteristic, complemented
387C2×C61—24no—
388C2×C61#333514yescomplemented
389C2×C61C2×#54711yescharacteristic
390C2×C61C23×SD1611yescharacteristic
391C2×C61C2×#57711yescharacteristic
392D61—24no—
393D61—82no—
394C22×#41—1221no—
395C22×SD16—611no—
396C23×C8—611no—
397C23×C8C2×D6111yescharacteristic
398#554—618no—
399#554—1224no—
400#547—618no—
401#547—1224no—
402C2×C4⋊Q8—611no—
403C2×C4⋊Q8—611no—
404C2×#125—1221no—
405C2×#123—1221no—
406C2×#123—1221no—
407C2×C22⋊Q8—611no—
408C2×C22⋊Q8—611no—
409C2×C22⋊Q8—1221no—
410C2×C22⋊Q8—1221no—
411C2×C22⋊Q8—1221no—
412C2×#121—611no—
413C2×#121—611no—
414C2×C4×Q8—611no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—1221no—
418C22×C4⋊C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4C2×D6111yescharacteristic
421C22×C4⋊C4C2×D6111yescharacteristic
422#498—618no—
423#483—618no—
424#483—618no—
425#481—618no—
426#481—618no—
427#476—618no—
428#475—618no—
429#465—618no—
430#465—618no—
431C4×SD16—618no—
432C8×D4—618no—
433C2×#106—611no—
434C2×#106—611no—
435C2×#106—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×#106—618no—
439C2×#106C2×D6111yescharacteristic
440C2×#106C2×D6111yescharacteristic
441C2×#106C2×D6111yescharacteristic
442C2×#106C2×D6111yescharacteristic
443C2×#106C2×D6118yescomplemented
444C2×C4⋊C8—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8—611no—
453C2×C4×C8—611no—
454C61C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—1228no—
456C2×#41—2448no—
457C22×Q8—611no—
458C22×Q8—1221no—
459C22×Q8—1221no—
460C22×D4—611no—
461C22×D4—611no—
462C22×D4—1221no—
463C22×D4—1221no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—611no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471C2×SD16—614no—
472C2×SD16—1224no—
473C22×C8—24no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—614no—
477C22×C8—1224no—
478C22×C8C22×D6111yescharacteristic
479C22×C8C22×D6114yes—
480C22×C8C22×D6111yescharacteristic
481C4⋊Q8—614no—
482C4⋊Q8—614no—
483C4⋊Q8—1222no—
484C4⋊Q8—1222no—
485#125—1228no—
486#123—1228no—
487#123—1228no—
488C22⋊Q8—614no—
489C22⋊Q8—614no—
490C22⋊Q8—1228no—
491C22⋊Q8—1228no—
492C22⋊Q8—1228no—
493C22⋊Q8—1222no—
494C22⋊Q8—1222no—
495#121—614no—
496#121—614no—
497#121—1222no—
498#121—1222no—
499C4×Q8—614no—
500C4×Q8—1222no—
501C4×D4—614no—
502C4×D4—614no—
503C4×D4—614no—
504C4×D4—1222no—
505C4×D4—1228no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6114yes—
529C2×C4⋊C4C22×D6114yes—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—611no—
538C2×C42—1221no—
539#106—614no—
540#106—614no—
541#106—614no—
542#106—614no—
543#106—614no—
544#106C22×D6114yes—
545#106C22×D6114yes—
546#106C22×D6114yes—
547#106C22×D6114yes—
548C4⋊C8—614no—
549#103—614no—
550#103—614no—
551#103—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555C22⋊C8—614no—
556C22⋊C8—614no—
557C4×C8—614no—
558C24—611no—
559C24—1221no—
560C24D4×D6111yescharacteristic
561#41—24432no—
562C2×Q8—612no—
563C2×Q8—1224no—
564C2×Q8—1224no—
565C2×Q8—1221no—
566C2×Q8—1222no—
567C2×Q8—1222no—
568C2×Q8—4882no—
569C2×Q8—2444no—
570C2×D4—614no—
571C2×D4—618no—
572C2×D4—612no—
573C2×D4—1224no—
574C2×D4—1224no—
575C2×D4—1221no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—2444no—
579C2×D4—2444no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1224no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—4882no—
604C22×C4—2444no—
605C22×C4—2444no—
606C22×C4D4×D6112yes—
607C22×C4D4×D6111yescharacteristic
608C22×C4C23×D6112yes—
609C22×C4C23×D6111yescharacteristic
610SD16—1228no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—612no—
614C2×C8—612no—
615C2×C8—1222no—
616C2×C8—1222no—
617C2×C8—1228no—
618C2×C8#1175822214yescomplemented
619C2×C8C23×D6112yes—
620C2×C8C23×D6112yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—614no—
628C4⋊C4—612no—
629C4⋊C4—612no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1224no—
639C4⋊C4C23×D6112yes—
640C4⋊C4C23×D6112yes—
641C4⋊C4C23×D6112yes—
642C4⋊C4C23×D6112yes—
643C22⋊C4—614no—
644C22⋊C4—614no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C42—612no—
651C42—612no—
652C42—1224no—
653C23—22no—
654C23—22no—
655C23—614no—
656C23—612no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—2442no—
661C23—2442no—
662C23—2442no—
663C23SD16×D6114yes—
664C23C2×D4×D6112yes—
665C23C2×D4×D6111yescharacteristic
666Q8—1222no—
667Q8—1222no—
668Q8—4884no—
669Q8—2448no—
670Q8—2442no—
671D4—6116no—
672D4—1222no—
673D4—1222no—
674D4—2448no—
675D4—2448no—
676D4—2442no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—614no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1224no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—4884no—
704C2×C4—2448no—
705C2×C4—2448no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4C2×#1175822212yes—
712C2×C4#1451982512yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—1222no—
716C8—1222no—
717C8C2×#1175822214yescomplemented
718C22—22no—
719C22—22no—
720C22—28no—
721C22—614no—
722C22—1222no—
723C22—1222no—
724C22—1228no—
725C22—4884no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22#1684041312yes—
730C22C2×SD16×D6114yes—
731C22C2×SD16×D6112yes—
732C22#1684056812yes—
733C22C22×D4×D6111yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—614no—
740C4—1222no—
741C4—1222no—
742C4—2442no—
743C4—2442no—
744C4—2442no—
745C4#1684041312yes—
746C4C22×#1175822211yescharacteristic
747C4C2×#1451982511yescharacteristic
748C2—24no—
749C2—1224no—
750C2—4882no—
751C2#2145817214yesdirect product factor
752C2C2×#1684041311yescharacteristic
753C2C22×SD16×D6111yescharacteristic
754C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#106×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840413C2
hypercenterC22×#106D61
hypocenterC61C2×#3335
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#16840467C2semidirect
3. #21458172C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840080C2semidirect
7. C2×#16840094C2semidirect
8. C2×#16840092C2semidirect
9. C2×#16840046C2semidirect
10. C2×#16840051C2semidirect
11. C2×#16839992C2semidirect
12. C2×#16839991C2semidirect
13. C2×#16839849C2semidirect
14. C2×C8×C22⋊D61C2semidirect
15. C2×#106×D61C2semidirect
16. C22×#106×C61C2semidirect
21. #16840467C22semidirect
42. #16840159C22semidirect
43. #16840094C22semidirect
44. #16840092C22semidirect
45. #16840082C22semidirect
46. #16840080C22semidirect
47. #16840051C22semidirect
48. #16840046C22semidirect
49. #16839992C22semidirect
50. #16839991C22semidirect
51. #16839849C22semidirect
52. C8×C22⋊D61C22semidirect
58. #106×D61C22semidirect
76. C2×#106×C61C22semidirect
199. C2×C22⋊D61SD16semidirect
234. C2×C8×C61#41semidirect
308. C22⋊D61C2×SD16semidirect
337. C8×C61C2×#41semidirect
386. C22×#106D61semidirect
388. C2×C61#3335semidirect
443. C2×#106C2×D61semidirect
454. C61C2×#3335semidirect
618. C2×C8#11758222semidirect
717. C8C2×#11758222semidirect
751. C2#21458172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168404132
#214581722
C2×#168401592
C2×#168400822
C2×#168400802
C2×#168400942
C2×#168400922
C2×#168400462
C2×#168400512
C2×#168399922
C2×#168399912
C2×#168398492
C2×C8×C22⋊D612
C2×#106×D612
C22×#106×C612
C2×#333561