Finite Group Databasebeta

← C2×#21461818 #30615650

Subgroups — C2×#21461818 #30615650

Order 15616.

1802 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic
2C2×D61⋊#104C211yesmaximal, characteristic
3C2×#16840755C211yesmaximal, characteristic, complemented
4C2×(C2×#6923)⋊Q8C211yesmaximal, characteristic, complemented
5#21461818C218yesmaximal, direct product factor
6C2×#16840641C211yesmaximal, characteristic, complemented
7C2×#16840634C211yesmaximal, characteristic, complemented
8C2×#137×D61C211yesmaximal, characteristic
9C2×D61⋊M16C2211yescharacteristic
10#16840831—22no—
11#16840831—22no—
12#16840831—22no—
13#16840831C2214yes—
14C2×Q8×#6923—21no—
15C2×D4×#6923—22no—
16C2×D4×#6923—21no—
17C2×#14519856—21no—
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923—21no—
20C22×C4⋊#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C2×#14519842—21no—
23D61⋊#104—22no—
24D61⋊#104C2214yes—
25C2×#14519841—21no—
26#16840755—22no—
27#16840755C2214yescomplemented
28C2×#14519840—21no—
29C2×#14519840—21no—
30(C2×#6923)⋊Q8—22no—
31(C2×#6923)⋊Q8C2214yescomplemented
32C2×(C2×#6923)⋊C4—22no—
33#16840641C2214yescomplemented
34#16840634C2214yescomplemented
35C2×#41×D61C2211yescharacteristic
36C22×Q8×D61C2211yescharacteristic
37C2×#14519810C411yescharacteristic, complemented
38C2×#14519809—21no—
39C2×#14519808C411yescharacteristic, complemented
40C2×#14519807C411yescharacteristic, complemented
41C2×#14519806—21no—
42#137×D61—22no—
43#137×D61—22no—
44#137×D61C414yescomplemented
45#137×D61C2214yes—
46C2×Q16×D61—21no—
47C2×SD16×D61—21no—
48C2×M16×D61C2211yescharacteristic
49C2×#137×C61C411yescharacteristic, complemented
50C23×#6923—21no—
51C23×#6923—22no—
52C23×#6923D412yes—
53C2×#11758213—21no—
54D61⋊M16—21no—
55D61⋊M16—21no—
56D61⋊M16—21no—
57D61⋊M16C2312yes—
58C2×#11758217—21no—
59C2×D61⋊C8—21no—
60Q8×#6923—24no—
61Q8×#6923—24no—
62D4×#6923—28no—
63D4×#6923—24no—
64D4×#6923—28no—
65D4×#6923—24no—
66#14519856—24no—
67#14519856—21no—
68#14519856—21no—
69#14519856—24no—
70#14519856D412yes—
71#14519856C2312yes—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—24no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—24no—
79C2×C4⋊#6923D412yes—
80C2×C4⋊#6923D411yescharacteristic
81C2×C4⋊#6923D411yescharacteristic
82C2×C4⋊#6923C2312yes—
83C2×C22⋊#6923—22no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—22no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923C2312yes—
93#14519842—24no—
94#14519841—24no—
95#14519840—24no—
96#14519840—24no—
97(C2×#6923)⋊C4—28no—
98C2×#11758226D411yescharacteristic
99C2×#11758222—21no—
100C2×#11758222C2×C411yescharacteristic
101C2×#11758224—21no—
102C2×#11758224D411yescharacteristic
103#41×D61—21no—
104#41×D61—21no—
105#41×D61—21no—
106#41×D61—21no—
107#41×D61C2×C412yes—
108#41×D61D412yes—
109#41×D61D412yes—
110#41×D61C2312yes—
111C22×Dic122—21no—
112C22×Dic122C2×C411yescharacteristic, complemented
113C2×Q8×D61—21no—
114C2×Q8×D61—21no—
115C2×Q8×D61—21no—
116C2×Q8×D61—21no—
117C2×Q8×D61—21no—
118C2×Q8×D61—21no—
119C2×Q8×D61—21no—
120C2×Q8×D61—21no—
121C2×Q8×D61—21no—
122C2×Q8×D61—21no—
123C2×Q8×D61C2×C412yescomplemented
124C2×Q8×D61D411yescharacteristic
125C2×Q8×D61C2312yes—
126C2×D4×D61—21no—
127C2×D4×D61D411yescharacteristic
128C22×C4×D61—21no—
129C22×C4×D61—21no—
130C22×C4×D61C2311yescharacteristic
131#14519810—22no—
132#14519810C2×C414yescomplemented
133#14519809—24no—
134#14519809—24no—
135#14519808—22no—
136#14519808C2×C414yescomplemented
137#14519807—22no—
138#14519807C2×C414yescomplemented
139#14519806—24no—
140#14519806—24no—
141C2×Dic244—21no—
142C2×#11758202—21no—
143C2×#11758202—21no—
144Q16×D61—24no—
145Q16×D61—24no—
146C2×#11758190—21no—
147C2×#11758200—21no—
148C2×#11758201—21no—
149SD16×D61—24no—
150SD16×D61—24no—
151C2×#11758194C2×C411yescharacteristic, complemented
152C2×#11758189—21no—
153M16×D61—21no—
154M16×D61—21no—
155M16×D61C2×C412yescomplemented
156M16×D61C2312yes—
157C2×C8×D61—21no—
158C2×#41×C61C2×C411yescharacteristic
159C22×Q8×C61C2×C411yescharacteristic, complemented
160#137×C61—22no—
161#137×C61C2×C414yescomplemented
162C2×Q16×C61—21no—
163C2×SD16×C61—21no—
164C2×M16×C61C2×C411yescharacteristic, complemented
165C23×D61—21no—
166C23×D61C2×D411yescharacteristic
167C22×#6923—24no—
168C22×#6923—21no—
169C22×#6923—22no—
170C22×#6923—21no—
171C22×#6923—22no—
172C22×#6923—28no—
173C22×#6923—22no—
174C22×#6923—42no—
175C22×#6923—41no—
176C22×#6923—41no—
177C22×#6923—44no—
178C22×#6923—84no—
179C22×#6923C2×D414yes—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61C22⋊C412yes—
183#41×C61C22×C412yes—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61C22⋊C411yescharacteristic
190C2×Q8×C61C22×C412yescomplemented
191C2×D4×C61—21no—
192C2×D4×C61C22⋊C411yescharacteristic
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C22×C411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61#4111yescharacteristic
202#11758226—21no—
203#11758226—21no—
204#11758226C22⋊C412yes—
205#11758226C2×D412yes—
206Q8×D61—21no—
207Q8×D61—21no—
208Q8×D61—22no—
209Q8×D61—22no—
210Q8×D61—22no—
211Q8×D61—22no—
212Q8×D61—22no—
213Q8×D61—22no—
214Q8×D61—22no—
215Q8×D61—22no—
216Q8×D61—41no—
217Q8×D61—41no—
218Q8×D61—41no—
219Q8×D61—41no—
220Q8×D61—41no—
221Q8×D61—41no—
222Q8×D61—41no—
223Q8×D61—41no—
224Q8×D61C22⋊C412yes—
225Q8×D61C2×D412yes—
226#11758224—22no—
227#11758224—22no—
228#11758224—22no—
229#11758224—22no—
230#11758224—21no—
231#11758224—21no—
232#11758224C22⋊C412yes—
233#11758224C2×D412yes—
234D4×D61—22no—
235D4×D61—22no—
236D4×D61—22no—
237D4×D61—22no—
238D4×D61—21no—
239D4×D61—21no—
240D4×D61C22⋊C412yes—
241D4×D61C2×D412yes—
242#11758222—21no—
243#11758222—21no—
244#11758222—22no—
245#11758222—22no—
246#11758222—22no—
247#11758222—22no—
248#11758222C22⋊C412yes—
249#11758222C22×C412yes—
250C2×D244—21no—
251C2×D244C22⋊C411yescharacteristic
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—41no—
262C2×C4×D61—41no—
263C2×C4×D61—41no—
264C2×C4×D61—41no—
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61#4111yescharacteristic
274C2×C4×D61#4111yescharacteristic
275C2×C4×D61#4111yescharacteristic
276C2×C4×D61C2411yescharacteristic
277C2×Dic122—21no—
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122—21no—
282C2×Dic122—21no—
283C2×Dic122—22no—
284C2×Dic122—22no—
285C2×Dic122—41no—
286C2×Dic122—41no—
287C2×Dic122—41no—
288C2×Dic122—41no—
289C2×Dic122C22⋊C411yescharacteristic
290C2×Dic122C22×C412yescomplemented
291C22⋊#6923—28no—
292C22⋊#6923—22no—
293C22⋊#6923—22no—
294#11758217—22no—
295#11758217—41no—
296C2×#92420—41no—
297C4⋊#6923—28no—
298C4⋊#6923—22no—
299C4⋊#6923—21no—
300C4⋊#6923—22no—
301C4⋊#6923—21no—
302C4⋊#6923—22no—
303C4⋊#6923—22no—
304C4⋊#6923C2×D412yes—
305C4⋊#6923C2×D412yes—
306C4×#6923—28no—
307C4×#6923—22no—
308C4×#6923—22no—
309C4×#6923—22no—
310C4×#6923—22no—
311C4×#6923—41no—
312C4×#6923—41no—
313#11758213—22no—
314#11758213—41no—
315D61⋊C8—22no—
316D61⋊C8—41no—
317Q16×C61—24no—
318SD16×C61—24no—
319M16×C61—21no—
320M16×C61C22×C412yescomplemented
321C2×C8×C61—21no—
322#11758202—24no—
323#11758202—24no—
324#11758201—24no—
325#11758200—24no—
326#11758194—21no—
327#11758194C22×C412yescomplemented
328C2×#92418—21no—
329Dic244—24no—
330#11758190—24no—
331#11758189—22no—
332#11758189—22no—
333C8×D61—22no—
334C8×D61—22no—
335C23×C61—21no—
336C23×C61C4×D411yescharacteristic
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—21no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61C4×D411yescharacteristic
345C22×D61#12011yescharacteristic
346C22×D61#12011yescharacteristic
347C22×D61#12111yescharacteristic
348C22×D61#12111yescharacteristic
349C22×D61C22×D411yescharacteristic
350C2×#6923—24no—
351C2×#6923—22no—
352C2×#6923—24no—
353C2×#6923—22no—
354C2×#6923—44no—
355C2×#6923—44no—
356C2×#6923—42no—
357C2×#6923—42no—
358C2×#6923—44no—
359C2×#6923—42no—
360C2×#6923—42no—
361C2×#6923—44no—
362C2×#6923—82no—
363C2×#6923—88no—
364Q8×C61—21no—
365Q8×C61—22no—
366Q8×C61—22no—
367Q8×C61—41no—
368Q8×C61—41no—
369Q8×C61C2×C22⋊C412yes—
370D4×C61—22no—
371D4×C61—22no—
372D4×C61—21no—
373D4×C61C2×C22⋊C412yes—
374C2×C4×C61—21no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C4×D411yescharacteristic
383C2×C4×C61C4×D411yescharacteristic
384C2×C4×C61C4×D411yescharacteristic
385C2×C4×C61C23×C411yescharacteristic
386C22⋊D61—22no—
387C22⋊D61—22no—
388C22⋊D61—22no—
389C22⋊D61—22no—
390C22⋊D61—22no—
391C22⋊D61—22no—
392C2×Dic61—21no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61C4×D411yescharacteristic
399C2×Dic61#12111yescharacteristic
400C2×Dic61#12111yescharacteristic
401C2×Dic61#12311yescharacteristic
402C2×Dic61#12311yescharacteristic
403C2×Dic61C2×#4111yescharacteristic
404D244—22no—
405D244—22no—
406D244—21no—
407D244C2×C22⋊C412yes—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—42no—
415C4×D61—42no—
416C4×D61—42no—
417C4×D61—42no—
418C4×D61C2×C22⋊C411yescharacteristic
419C4×D61C2×C22⋊C411yescharacteristic
420C4×D61C4×D411yescharacteristic
421C4×D61C4×D411yescharacteristic
422C4×D61#12011yescharacteristic
423C4×D61#12011yescharacteristic
424C4×D61#12111yescharacteristic
425C4×D61#12111yescharacteristic
426C4×D61#12111yescharacteristic
427C4×D61#12111yescharacteristic
428C4×D61#12311yescharacteristic
429C4×D61#12311yescharacteristic
430C4×D61C22×D411yescharacteristic
431C4×D61C22×D411yescharacteristic
432C4×D61C22×D411yescharacteristic
433C4×D61C2×#4111yescharacteristic
434Dic122—21no—
435Dic122—22no—
436Dic122—22no—
437Dic122—22no—
438Dic122—22no—
439Dic122—41no—
440Dic122—41no—
441Dic122—42no—
442Dic122—42no—
443Dic122—42no—
444Dic122—42no—
445Dic122C2×C22⋊C412yes—
446#92420—42no—
447C8×C61—22no—
448#92418—22no—
449C2×#1882—611nomaximal, Sylow
450C22×C61—22no—
451C22×C61—22no—
452C22×C61—42no—
453C22×C61#38611yescharacteristic
454C22×C61#38611yescharacteristic
455C22×C61C2×C4×D411yescharacteristic
456C2×D61—22no—
457C2×D61—22no—
458C2×D61—22no—
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—22no—
464C2×D61—42no—
465C2×D61—44no—
466C2×D61—42no—
467C2×D61—42no—
468C2×D61#38611yescharacteristic
469C2×D61#38611yescharacteristic
470C2×D61#45512yes—
471C2×D61#45612yes—
472C2×D61C2×#12011yescharacteristic
473C2×D61C2×#12111yescharacteristic
474#6923—44no—
475#6923—44no—
476#6923—42no—
477#6923—42no—
478C4×C61—22no—
479C4×C61—42no—
480C4×C61#38611yescharacteristic
481C4×C61#38611yescharacteristic
482C4×C61C22×C22⋊C411yescharacteristic
483C4×C61C2×C4×D411yescharacteristic
484Dic61—22no—
485Dic61—42no—
486Dic61#38611yescharacteristic
487Dic61#38611yescharacteristic
488Dic61C2×#12111yescharacteristic
489Dic61C2×#12311yescharacteristic
490C22×#137—611no—
491C2×#520—611no—
492C22×#104—611no—
493C2×#419—611no—
494C2×#391—611no—
495#1882—618no—
496C2×#343—611no—
497C2×#339—611no—
498C2×C61—21no—
499C2×C61—21no—
500C2×C61—42no—
501C2×C61#188212yescomplemented
502C2×C61C2×#38611yescharacteristic
503D61—21no—
504D61—21no—
505D61—42no—
506D61#188212yescomplemented
507D61C2×#45511yescharacteristic
508D61C2×#45611yescharacteristic
509C22×#41—611no—
510C23×Q8—611no—
511C2×#137—611no—
512C2×#137—611no—
513C2×#137—614no—
514C2×#137—614no—
515C2×#137—611no—
516C2×#137—1221no—
517C2×#137—1221no—
518C2×#137—1222no—
519C2×#137—1222no—
520C2×#137#692311yescharacteristic, complemented
521C22×Q16—1221no—
522C22×SD16—1221no—
523C22×M16—611no—
524C22×M16—611no—
525#520—614no—
526#520—1222no—
527#520—1222no—
528#520—1222no—
529C2×C4×Q8—1221no—
530C2×C4×D4—1222no—
531C2×C4×D4—1221no—
532C2×#117—611no—
533C2×#117—1221no—
534C22×C4⋊C4—611no—
535C22×C4⋊C4—1221no—
536C22×C42—611no—
537C2×#104—614no—
538C2×#104—1221no—
539C2×#104—1222no—
540C2×#104—1221no—
541#419—614no—
542#419—1222no—
543C2×#103—1221no—
544C2×#103—1221no—
545#391—614no—
546#391—1222no—
547C2×#95—1222no—
548#343—614no—
549#339—614no—
550C61C2×#188211yescharacteristic, complemented, Sylow
551C2×#41—612no—
552C2×#41—612no—
553C2×#41—612no—
554C2×#41—612no—
555C2×#41—611no—
556C2×#41—611no—
557C2×#41—611no—
558C2×#41—1221no—
559C2×#41—1221no—
560C2×#41—1221no—
561C2×#41—1221no—
562C2×#41—1221no—
563C2×#41—1221no—
564C2×#41C2×#692311yescharacteristic
565C22×Q8—611no—
566C22×Q8—612no—
567C22×Q8—612no—
568C22×Q8—611no—
569C22×Q8—1221no—
570C22×Q8—1221no—
571C22×Q8—1221no—
572C22×Q8—1221no—
573C22×Q8—1221no—
574C22×Q8—1221no—
575C22×Q8—1221no—
576C22×Q8—1221no—
577C22×Q8—1221no—
578C22×Q8—1221no—
579C22×Q8—1221no—
580C22×Q8C2×#692311yescharacteristic, complemented
581C22×D4—611no—
582C22×D4—1221no—
583C23×C4—611no—
584C23×C4—612no—
585C23×C4—1221no—
586C23×C4—1221no—
587C23×C4—1222no—
588C23×C4—1221no—
589#137—22no—
590#137—614no—
591#137—614no—
592#137—614no—
593#137—1222no—
594#137—1224no—
595#137—1224no—
596#137—1224no—
597#137—1224no—
598#137—1222no—
599#137—1222no—
600#137C2×#692314yescomplemented
601C2×Q16—21no—
602C2×Q16—1221no—
603C2×Q16—1224no—
604C2×Q16—1224no—
605C2×Q16—1221no—
606C2×Q16—1221no—
607C2×SD16—21no—
608C2×SD16—1221no—
609C2×SD16—1224no—
610C2×SD16—1224no—
611C2×SD16—1221no—
612C2×SD16—1221no—
613C2×M16—611no—
614C2×M16—612no—
615C2×M16—612no—
616C2×M16—612no—
617C2×M16—1221no—
618C2×M16—1221no—
619C2×M16—1221no—
620C2×M16—1221no—
621C2×M16—1221no—
622C2×M16—1221no—
623C2×M16—1221no—
624C2×M16—1221no—
625C2×M16C2×#692311yescharacteristic, complemented
626C22×C8—1221no—
627C22×C8—1221no—
628C4×Q8—1224no—
629C4×Q8—1224no—
630C4×D4—1228no—
631C4×D4—1224no—
632C4×D4—1224no—
633C4×D4—1228no—
634#117—612no—
635#117—612no—
636#117—1224no—
637#117—1221no—
638#117—1221no—
639#117—1224no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—612no—
643C2×C4⋊C4—612no—
644C2×C4⋊C4—1224no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4—1221no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1222no—
650C2×C4⋊C4—1224no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1222no—
653C2×C42—612no—
654C2×C42—1221no—
655C2×C42—1222no—
656C2×C42—1221no—
657C2×C42—1221no—
658C2×C42—1221no—
659C2×C42—1221no—
660C2×C42—1221no—
661#104—1224no—
662#104—1224no—
663#103—1224no—
664#103—1224no—
665#95—1228no—
666C24—611no—
667C24—1221no—
668#41—21no—
669#41—21no—
670#41—612no—
671#41—612no—
672#41—612no—
673#41—612no—
674#41—612no—
675#41—612no—
676#41—1222no—
677#41—1222no—
678#41—1222no—
679#41—1222no—
680#41—1222no—
681#41—1222no—
682#41—1222no—
683#41—1222no—
684#41—1221no—
685#41—1221no—
686#41—1221no—
687#41—1221no—
688#41—1221no—
689#41—1221no—
690#41C22⋊#692312yes—
691#41C22×#692312yes—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—612no—
698C2×Q8—612no—
699C2×Q8—611no—
700C2×Q8—612no—
701C2×Q8—1221no—
702C2×Q8—1222no—
703C2×Q8—1222no—
704C2×Q8—1221no—
705C2×Q8—1221no—
706C2×Q8—1222no—
707C2×Q8—1222no—
708C2×Q8—1222no—
709C2×Q8—1222no—
710C2×Q8—1222no—
711C2×Q8—1222no—
712C2×Q8—1222no—
713C2×Q8—1222no—
714C2×Q8—1221no—
715C2×Q8—1221no—
716C2×Q8—1221no—
717C2×Q8—1221no—
718C2×Q8—1221no—
719C2×Q8—2441no—
720C2×Q8—2441no—
721C2×Q8—2441no—
722C2×Q8—2441no—
723C2×Q8—2441no—
724C2×Q8—2441no—
725C2×Q8—2441no—
726C2×Q8—2441no—
727C2×Q8—2441no—
728C2×Q8—2441no—
729C2×Q8—2441no—
730C2×Q8—2441no—
731C2×Q8C22⋊#692311yescharacteristic
732C2×Q8C22×#692312yescomplemented
733C2×D4—21no—
734C2×D4—612no—
735C2×D4—612no—
736C2×D4—611no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1222no—
742C2×D4—1222no—
743C2×D4—1222no—
744C2×D4—1222no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4C22⋊#692311yescharacteristic
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—614no—
764C22×C4—1222no—
765C22×C4—1222no—
766C22×C4—1221no—
767C22×C4—1222no—
768C22×C4—1222no—
769C22×C4—1221no—
770C22×C4—1222no—
771C22×C4—1222no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1222no—
775C22×C4—1228no—
776C22×C4—1222no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1222no—
780C22×C4—1224no—
781C22×C4—1221no—
782C22×C4—4884no—
783C22×C4—2441no—
784C22×C4—2441no—
785C22×C4—2441no—
786C22×C4—2441no—
787C22×C4—2444no—
788C22×C4—2441no—
789C22×C4—2441no—
790C22×C4—2442no—
791C22×C4C22×#692311yescharacteristic
792Q16—24no—
793Q16—1224no—
794Q16—1224no—
795Q16—1224no—
796SD16—24no—
797SD16—1224no—
798SD16—1224no—
799SD16—1224no—
800M16—21no—
801M16—612no—
802M16—1222no—
803M16—1222no—
804M16—1221no—
805M16—1222no—
806M16—1222no—
807M16—2441no—
808M16—2441no—
809M16C22×#692312yescomplemented
810C2×C8—21no—
811C2×C8—1222no—
812C2×C8—1222no—
813C2×C8—1221no—
814C2×C8—1222no—
815C2×C8—2441no—
816C2×C8—2441no—
817C4⋊C4—612no—
818C4⋊C4—612no—
819C4⋊C4—1221no—
820C4⋊C4—1222no—
821C4⋊C4—1222no—
822C4⋊C4—1222no—
823C4⋊C4—1222no—
824C4⋊C4—1221no—
825C4⋊C4—1228no—
826C22⋊C4—1222no—
827C22⋊C4—1222no—
828C22⋊C4—1228no—
829C42—1222no—
830C42—1222no—
831C42—1222no—
832C42—1222no—
833C42—1228no—
834C42—2441no—
835C42—2441no—
836C23—21no—
837C23—611no—
838C23—611no—
839C23—611no—
840C23—611no—
841C23—611no—
842C23—611no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1222no—
847C23—1221no—
848C23—2442no—
849C23—2442no—
850C23D4×#692311yescharacteristic
851Q8—21no—
852Q8—22no—
853Q8—22no—
854Q8—41no—
855Q8—41no—
856Q8—612no—
857Q8—1222no—
858Q8—1222no—
859Q8—1221no—
860Q8—1222no—
861Q8—1222no—
862Q8—2442no—
863Q8—2442no—
864Q8—2442no—
865Q8—2442no—
866Q8—2441no—
867Q8—2441no—
868Q8C2×C22⋊#692312yes—
869D4—22no—
870D4—22no—
871D4—21no—
872D4—612no—
873D4—1222no—
874D4—1222no—
875D4—1222no—
876D4—1222no—
877D4—1222no—
878D4—1222no—
879D4—1222no—
880D4—1222no—
881D4—1221no—
882D4C2×C22⋊#692312yes—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—611no—
892C2×C4—611no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—611no—
896C2×C4—611no—
897C2×C4—611no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—611no—
902C2×C4—611no—
903C2×C4—611no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1221no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1224no—
923C2×C4—1224no—
924C2×C4—1222no—
925C2×C4—4882no—
926C2×C4—4888no—
927C2×C4—2442no—
928C2×C4—2442no—
929C2×C4—2442no—
930C2×C4—2442no—
931C2×C4—2442no—
932C2×C4—2442no—
933C2×C4—2442no—
934C2×C4—2444no—
935C2×C4—2442no—
936C2×C4—2444no—
937C2×C4—2444no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2444no—
941C2×C4C2×C22⋊#692311yescharacteristic
942C2×C4C2×C22⋊#692311yescharacteristic
943C2×C4D4×#692311yescharacteristic
944C2×C4D4×#692311yescharacteristic
945C2×C4D4×#692311yescharacteristic
946C2×C4C23×#692311yescharacteristic
947C8—22no—
948C8—1222no—
949C8—2442no—
950C22—22no—
951C22—22no—
952C22—42no—
953C22—612no—
954C22—612no—
955C22—611no—
956C22—611no—
957C22—611no—
958C22—611no—
959C22—1221no—
960C22—1221no—
961C22—1221no—
962C22—1222no—
963C22—1221no—
964C22—1222no—
965C22—1222no—
966C22—1222no—
967C22—2442no—
968C22—2442no—
969C22—2444no—
970C22—2442no—
971C22#1684071011yescharacteristic
972C22#1684071011yescharacteristic
973C22C2×D4×#692311yescharacteristic
974C4—22no—
975C4—42no—
976C4—611no—
977C4—611no—
978C4—611no—
979C4—611no—
980C4—1222no—
981C4—2442no—
982C4—2444no—
983C4—2442no—
984C4—2444no—
985C4—2442no—
986C4#1684071011yescharacteristic
987C4#1684071011yescharacteristic
988C4C22×C22⋊#692311yescharacteristic
989C4C2×D4×#692311yescharacteristic
990C2—21no—
991C2—21no—
992C2—42no—
993C2—611no—
994C2—611no—
995C2—612no—
996C2—1221no—
997C2—1221no—
998C2—2442no—
999C2#2146181812yesdirect product factor
1000C2C2×#1684071011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#137×C61C4
socleC22×C61#386
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC2×#137#6923
hypocenterC61C2×#1882
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
3. C2×#16840755C2semidirect
4. C2×(C2×#6923)⋊Q8C2semidirect
5. #21461818C2direct (N × H)
6. C2×#16840641C2semidirect
7. C2×#16840634C2semidirect
27. #16840755C22semidirect
31. (C2×#6923)⋊Q8C22semidirect
33. #16840641C22semidirect
34. #16840634C22semidirect
37. C2×#14519810C4semidirect
39. C2×#14519808C4semidirect
40. C2×#14519807C4semidirect
44. #137×D61C4semidirect
49. C2×#137×C61C4semidirect
112. C22×Dic122C2×C4semidirect
123. C2×Q8×D61C2×C4semidirect
132. #14519810C2×C4semidirect
136. #14519808C2×C4semidirect
138. #14519807C2×C4semidirect
151. C2×#11758194C2×C4semidirect
155. M16×D61C2×C4semidirect
159. C22×Q8×C61C2×C4semidirect
161. #137×C61C2×C4semidirect
164. C2×M16×C61C2×C4semidirect
190. C2×Q8×C61C22×C4semidirect
290. C2×Dic122C22×C4semidirect
320. M16×C61C22×C4semidirect
327. #11758194C22×C4semidirect
501. C2×C61#1882semidirect
506. D61#1882semidirect
520. C2×#137#6923semidirect
550. C61C2×#1882semidirect
580. C22×Q8C2×#6923semidirect
600. #137C2×#6923semidirect
625. C2×M16C2×#6923semidirect
732. C2×Q8C22×#6923semidirect
809. M16C22×#6923semidirect
999. C2#21461818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×D61⋊#1042
C2×#168407552
C2×(C2×#6923)⋊Q82
#214618182
C2×#168406412
C2×#168406342
C2×#137×D612
C2×#188261