Finite Group Databasebeta

← #34030818

Subgroups — #34030818

Order 18688.

2912 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989655C211yesmaximal, characteristic, complemented
2C22×Q8×#64408C211yesmaximal, characteristic, complemented
3#22626460C213yesmaximal, complemented
4#22626457C213yesmaximal, complemented
5#22626455C213yesmaximal, complemented
6#22626447C213yesmaximal
7#22626446C211yesmaximal, characteristic, complemented
8Q8×C22⋊#64408C211yesmaximal, characteristic, complemented
9Q8×C22⋊#64408C211yesmaximal, characteristic, complemented
10#22626422C213yesmaximal, complemented
11#22626418C213yesmaximal, complemented
12C22⋊Q8×#64408C213yesmaximal, complemented
13#22626385C213yesmaximal
14#22626371C211yesmaximal, characteristic, complemented
15D4×Q8×D73C211yesmaximal, characteristic
16#17989655—28no—
17C2×Q8×#64408—28no—
18C2×Q8×#64408C2211yescharacteristic
19C2×Q8×#64408C2213yes—
20C2×Q8×#64408C2211yescharacteristic
21C2×Q8×#64408C2213yes—
22C2×Q8×#64408C2213yes—
23C2×Q8×#64408C2211yescharacteristic
24C2×Q8×#64408C2213yes—
25C2×Q8×#64408C2211yescharacteristic
26C2×#14556670C2213yes—
27C2×#14556670C2213yes—
28C22×C4⋊#64408C2213yes—
29C22×C4×#64408C2213yes—
30(C2×#64408)⋊Q8C2213yes—
31(C2×#64408)⋊Q8C2213yes—
32(C2×#64408)⋊Q8C2213yes—
33(C2×#64408)⋊Q8C2213yes—
34#17989538C2213yes—
35#17989538C2213yes—
36#17989538C2216yes—
37#17989537C2213yes—
38#17989537C2213yes—
39#17989537C2216yes—
40#17989536C2213yes—
41#17989536C2213yes—
42#17989536C2216yes—
43#17989536C2216yes—
44#17989536C2216yes—
45#17989535C2211yescharacteristic
46#17989535C2213yes—
47#17989534C2213yes—
48#17989534C2213yes—
49#17989531C2213yes—
50#17989529C2213yes—
51#17989529C2213yes—
52C4⋊C4×#64408C2213yes—
53C4⋊C4×#64408C2213yes—
54C4⋊C4×#64408C2216yes—
55C4×C4⋊#64408C2213yes—
56C4×C4⋊#64408C2213yes—
57C22⋊C4×#64408C2216yes—
58C4×C22⋊#64408C2213yes—
59C4×C22⋊#64408C2213yes—
60#17989523C2213yes—
61C22×Q8×D73C2211yescharacteristic
62C22×Q8×D73C2211yescharacteristic
63Q8×D292C411yescharacteristic, complemented
64D4×Dic146C413yescomplemented
65#17989252C413yescomplemented
66Q8×C22⋊D73C411yescharacteristic, complemented
67Q8×C22⋊D73C411yescharacteristic, complemented
68#17989250C413yescomplemented
69#17989250C413yescomplemented
70C4⋊Q8×D73C2213yes—
71C22⋊Q8×D73C2213yes—
72C22⋊Q8×D73C2213yes—
73C4×Q8×D73C2211yescharacteristic
74C4×D4×D73C2213yes—
75D4×Q8×C73C411yescharacteristic, complemented
76C23×#64408C2311yescharacteristic
77C23×#64408C2313yes—
78Q8×#64408—212no—
79Q8×#64408—212no—
80Q8×#64408—212no—
81Q8×#64408—212no—
82Q8×#64408—24no—
83Q8×#64408—24no—
84Q8×#64408—24no—
85Q8×#64408D418yescomplemented
86#14556670—212no—
87#14556670—212no—
88C2×C4⋊#64408—212no—
89C2×C4⋊#64408C2313yes—
90C2×C4⋊#64408C2316yes—
91C2×C4⋊#64408C2313yes—
92C2×C4⋊#64408C2313yes—
93C2×C4⋊#64408C2313yes—
94C2×C4⋊#64408C2313yes—
95C2×C4⋊#64408C2313yes—
96C2×C4⋊#64408C2313yes—
97C2×C4⋊#64408C2313yes—
98C2×C22⋊#64408C2313yes—
99C2×C22⋊#64408C2311yescharacteristic
100C2×C22⋊#64408C2311yescharacteristic
101C2×C22⋊#64408C2311yescharacteristic
102C2×C22⋊#64408C2313yes—
103C2×C22⋊#64408C2313yes—
104C2×C4×#64408—212no—
105C2×C4×#64408C2313yes—
106C2×C4×#64408C2313yes—
107C2×C4×#64408C2313yes—
108C2×C4×#64408C2313yes—
109C2×C4×#64408C2316yes—
110C2×C4×#64408C2313yes—
111C2×C4×#64408C2316yes—
112C2×C4×#64408C2313yes—
113(C2×#64408)⋊C4C2311yescharacteristic
114(C2×#64408)⋊C4C2313yes—
115(C2×#64408)⋊C4C2313yes—
116(C2×#64408)⋊C4C2313yes—
117(C2×#64408)⋊C4C2313yes—
118(C2×#64408)⋊C4C2313yes—
119(C2×#64408)⋊C4C2313yes—
120(C2×#64408)⋊C4C2313yes—
121(C2×#64408)⋊C4C2316yes—
122(C2×#64408)⋊C4C2316yes—
123(C2×#64408)⋊C4C2311yescharacteristic
124(C2×#64408)⋊C4C2313yes—
125(C2×#64408)⋊C4C2316yes—
126C22×Dic146C2×C413yes—
127C22×Dic146C2×C413yescomplemented
128C2×Q8×D73—24no—
129C2×Q8×D73—24no—
130C2×Q8×D73—24no—
131C2×Q8×D73—24no—
132C2×Q8×D73C2×C413yes—
133C2×Q8×D73C2×C411yescharacteristic
134C2×Q8×D73C2×C413yescomplemented
135C2×Q8×D73C2×C411yescharacteristic, complemented
136C2×Q8×D73C2313yes—
137C2×Q8×D73C2313yes—
138C2×Q8×D73C2311yescharacteristic
139C2×D4×D73C2311yescharacteristic
140C22×C4×D73C2313yes—
141C22×C4×D73C2313yes—
142#14556591C2×C413yescomplemented
143#14556590C2×C416yescomplemented
144#14556590C2×C416yescomplemented
145#14556589C2×C413yescomplemented
146#14556589C2×C413yescomplemented
147#14556571C2×C413yes—
148#14556571C2×C413yescomplemented
149#14556570C2×C413yes—
150#14556570C2×C413yescomplemented
151#14556569C2×C416yes—
152#14556569C2×C416yescomplemented
153#14556568C2×C416yes—
154#14556568C2×C416yescomplemented
155#14556567C2×C413yes—
156#14556567C2×C413yescomplemented
157Q8×Dic73C2×C411yescharacteristic, complemented
158C4×Dic146C2×C413yescomplemented
159#14556556C2×C413yescomplemented
160C4×D292C2×C413yes—
161D4×Dic73C2×C413yes—
162#14556553C2×C413yes—
163C4×C22⋊D73C2×C413yes—
164C4×C22⋊D73C2×C413yes—
165#14556551C2×C413yes—
166#14556551C2×C413yes—
167C4⋊C4×D73C2313yes—
168C4⋊C4×D73C2316yes—
169C4⋊C4×D73C2313yes—
170C22⋊C4×D73C2313yes—
171C22⋊C4×D73C2313yes—
172C42×D73C2313yes—
173C22×Q8×C73C2×C411yescharacteristic
174C22×Q8×C73C2×C411yescharacteristic, complemented
175C4⋊Q8×C73C2×C413yescomplemented
176C22⋊Q8×C73C2×C413yes—
177C22⋊Q8×C73C2×C413yescomplemented
178C4×Q8×C73C2×C411yescharacteristic, complemented
179C4×D4×C73C2×C413yes—
180C22×#64408—22no—
181C22×#64408—22no—
182C22×#64408—22no—
183C22×#64408—26no—
184C22×#64408—26no—
185C22×#64408—43no—
186C22×#64408C2413yes—
187C22×#64408C2411yescharacteristic
188C22×#64408C2413yes—
189C22×#64408C2413yes—
190C22×#64408C2411yescharacteristic
191C22×#64408C2411yescharacteristic
192C22×#64408C2413yes—
193C22×#64408C2411yescharacteristic
194C4⋊#64408—212no—
195C4⋊#64408—26no—
196C4⋊#64408—26no—
197C4⋊#64408—26no—
198C4⋊#64408—26no—
199C4⋊#64408—26no—
200C4⋊#64408—26no—
201C4⋊#64408—43no—
202C4⋊#64408C2×D4112yes—
203C22⋊#64408—26no—
204C22⋊#64408—22no—
205C22⋊#64408—22no—
206C22⋊#64408—26no—
207C22⋊#64408—22no—
208C22⋊#64408—43no—
209C4×#64408—26no—
210C4×#64408—26no—
211C4×#64408—212no—
212C4×#64408—26no—
213C4×#64408—26no—
214C4×#64408—26no—
215C4×#64408—46no—
216C4×#64408C2×D4112yes—
217C23×D73C2411yescharacteristic
218C23×D73C2411yescharacteristic
219C2×Dic146—212no—
220C2×Dic146—212no—
221C2×Dic146C22×C416yes—
222C2×Dic146C22×C416yes—
223C2×Dic146C22×C413yes—
224C2×Dic146C22×C413yes—
225C2×Dic146C22×C413yes—
226Q8×D73—24no—
227Q8×D73—24no—
228Q8×D73—26no—
229Q8×D73—26no—
230Q8×D73—26no—
231Q8×D73—26no—
232Q8×D73—212no—
233Q8×D73—212no—
234Q8×D73C2×D414yes—
235Q8×D73#4114yes—
236C2×D292C22×C411yescharacteristic
237C2×C22⋊D73C22×C411yescharacteristic
238C2×C22⋊D73C22×C411yescharacteristic
239D4×D73—22no—
240D4×D73—22no—
241C22×Dic73C22×C413yes—
242C22×Dic73C22×C413yes—
243C2×C4×D73—26no—
244C2×C4×D73—26no—
245C2×C4×D73—26no—
246C2×C4×D73—26no—
247C2×C4×D73C22×C413yes—
248C2×C4×D73C22×C413yes—
249C2×C4×D73C22×C413yes—
250C2×C4×D73C22×C413yes—
251C2×C4×D73C2411yescharacteristic
252C2×C4×D73C2413yes—
253C2×C4×D73C2413yes—
254C2×C4×D73C2413yes—
255C2×C4×D73C2413yes—
256C4⋊Dic73C22×C413yes—
257C4⋊Dic73C22×C413yes—
258C4⋊Dic73C22×C416yes—
259#11924007C22×C413yes—
260#11924007C22×C413yes—
261#11924007C22×C416yes—
262#11924007C22×C416yes—
263#11924007C22×C416yes—
264C22⋊Dic73C22×C413yes—
265C22⋊Dic73C22×C413yes—
266#11924005C22×C413yes—
267#11924005C22×C413yes—
268#11924005C22×C413yes—
269#11924005C22×C413yes—
270C4×Dic73C22×C413yes—
271C4×Dic73C22×C413yes—
272C4×Dic73C22×C413yes—
273C2×Q8×C73—24no—
274C2×Q8×C73—24no—
275C2×Q8×C73C22×C413yes—
276C2×Q8×C73C22×C413yes—
277C2×Q8×C73C22×C411yescharacteristic
278C2×D4×C73C22×C411yescharacteristic
279C22×C4×C73C22×C413yes—
280C22×C4×C73C22×C413yes—
281C4⋊C4×C73C22×C413yes—
282C4⋊C4×C73C22×C413yes—
283C4⋊C4×C73C22×C416yes—
284C22⋊C4×C73C22×C413yes—
285C22⋊C4×C73C22×C413yes—
286C42×C73C22×C413yes—
287C23×C73C23×C411yescharacteristic
288C23×C73C23×C411yescharacteristic
289C22×D73—21no—
290C22×D73—21no—
291C22×D73—21no—
292C22×D73—21no—
293C22×D73—21no—
294C22×D73—21no—
295C22×D73—21no—
296C22×D73—21no—
297C22×D73—21no—
298C22×D73—21no—
299C22×D73C23×C411yescharacteristic
300C22×D73C23×C411yescharacteristic
301C22×D732−1+412yes—
302C22×D732−1+412yes—
303C22×D73C2511yescharacteristic
304C2×#64408—28no—
305C2×#64408—21no—
306C2×#64408—21no—
307C2×#64408—21no—
308C2×#64408—21no—
309C2×#64408—23no—
310C2×#64408—23no—
311C2×#64408—23no—
312C2×#64408—21no—
313C2×#64408—23no—
314C2×#64408—21no—
315C2×#64408—23no—
316C2×#64408—23no—
317C2×#64408—21no—
318C2×#64408—23no—
319C2×#64408—21no—
320C2×#64408—21no—
321C2×#64408—23no—
322C2×#64408—23no—
323C2×#64408—23no—
324C2×#64408—23no—
325C2×#64408—21no—
326C2×#64408—412no—
327C2×#64408C22×D412yes—
328C2×#64408C22×D416yes—
329C2×#644082−1+412yes—
330Q8×C73—26no—
331Q8×C73—26no—
332Q8×C73C4×D414yes—
333D4×C73—22no—
334C2×C4×C73—26no—
335C2×C4×C73—26no—
336C2×C4×C73C23×C411yescharacteristic
337C2×C4×C73C23×C413yes—
338C2×C4×C73C23×C413yes—
339C2×C4×C73C23×C413yes—
340C2×C4×C73C23×C413yes—
341C22⋊D73—22no—
342C22⋊D73—22no—
343C2×Dic73—26no—
344C2×Dic73—26no—
345C2×Dic73C23×C411yescharacteristic
346C2×Dic73C23×C413yes—
347C2×Dic73C23×C413yes—
348C2×Dic73C23×C413yes—
349C2×Dic73C23×C413yes—
350D292—22no—
351C4×D73—23no—
352C4×D73—23no—
353C4×D73—23no—
354C4×D73—23no—
355C4×D73—21no—
356C4×D73—21no—
357C4×D73—23no—
358C4×D73—23no—
359C4×D73—26no—
360C4×D73—26no—
361C4×D73—26no—
362C4×D73—26no—
363C4×D73C22×D416yes—
364C4×D73C2×#4116yes—
365Dic146—26no—
366Dic146—26no—
367Dic146—212no—
368Dic146—212no—
369Dic146C4×D4112yes—
370C22×C73—21no—
371C22×C73—21no—
372C22×C73—21no—
373C22×C73—21no—
374C22×C73—21no—
375C22×C73#51912yescomplemented
376C22×C73C24×C411yescharacteristic
377C2×D73—21no—
378C2×D73—21no—
379C2×D73—22no—
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—22no—
383C2×D73—21no—
384C2×D73—21no—
385C2×D73—21no—
386C2×D73—41no—
387C2×D73—41no—
388C2×D73—41no—
389C2×D73—41no—
390C2×D73#51912yescomplemented
391C2×D73C23×D411yescharacteristic
392C2×D73C22×#4111yescharacteristic
393C2×D73C2×2−1+411yescharacteristic
394C2×D73C2×2−1+411yescharacteristic
395C2×D73C2×2−1+411yescharacteristic
396C2×D73#58511yescharacteristic
397#64408—22no—
398#64408—22no—
399#64408—26no—
400#64408—43no—
401#64408—41no—
402#64408—43no—
403#64408—43no—
404#64408—41no—
405C4×C73—23no—
406C4×C73—23no—
407C4×C73—21no—
408C4×C73—23no—
409C4×C73C2×C4×D416yes—
410Dic73—23no—
411Dic73—23no—
412Dic73—21no—
413Dic73—23no—
414Dic73C2×C4×D416yes—
415#34291—731nomaximal, Sylow
416C2×C73—22no—
417C2×C73—41no—
418C2×C73C22×C4×D411yescharacteristic
419C2×C73C2×#51911yescharacteristic
420C2×C73C4×2−1+411yescharacteristic
421D73—22no—
422D73—41no—
423D73#348611yescharacteristic
424D73#348911yescharacteristic
425D73#351611yescharacteristic
426D73#352311yescharacteristic
427C2×D4×Q8—731no—
428C2×#519—731no—
429C22×C4×Q8—731no—
430#2365—733no—
431#2362—733no—
432#2360—733no—
433#2352—733no—
434#2351—731no—
435Q8×C22⋊C4—731no—
436Q8×C22⋊C4—731no—
437#2327—733no—
438#2323—733no—
439C4×C22⋊Q8—733no—
440#2290—733no—
441#2276—731no—
442C73#3429111yescharacteristic, complemented, Sylow
443C23×Q8—731no—
444C23×Q8—731no—
445D4×Q8—731no—
446D4×Q8—731no—
447D4×Q8—733no—
448D4×Q8—733no—
449D4×Q8—733no—
450D4×Q8—731no—
451D4×Q8—733no—
452D4×Q8#6440811yescharacteristic, complemented
453C2×C4⋊Q8—733no—
454C2×C22⋊Q8—733no—
455C2×C22⋊Q8—733no—
456#519—1468no—
457C2×C4×Q8—731no—
458C2×C4×Q8—731no—
459C2×C4×Q8—733no—
460C2×C4×Q8—733no—
461C2×C4×Q8—731no—
462C2×C4×Q8—731no—
463C2×C4×Q8—731no—
464C2×C4×Q8—733no—
465C2×C4×Q8—733no—
466C2×C4×Q8—1468no—
467C2×C4×D4—733no—
468C2×#117—733no—
469C2×#117—733no—
470C22×C4⋊C4—733no—
471C22×C42—733no—
472#391—733no—
473#391—733no—
474#391—733no—
475#391—733no—
476#389—733no—
477#389—736no—
478#389—733no—
479#388—733no—
480#388—736no—
481#388—733no—
482#387—736no—
483#387—733no—
484#387—736no—
485#387—736no—
486#387—733no—
487#386—733no—
488#386—731no—
489#385—733no—
490#385—733no—
491#382—733no—
492#380—733no—
493#380—733no—
494C4×C4⋊C4—733no—
495C4×C4⋊C4—733no—
496C4×C4⋊C4—733no—
497C4×C4⋊C4—733no—
498C4×C4⋊C4—736no—
499C4×C22⋊C4—733no—
500C4×C22⋊C4—733no—
501C4×C22⋊C4—736no—
502#376—733no—
503C22×Q8—731no—
504C22×Q8—733no—
505C22×Q8—733no—
506C22×Q8—733no—
507C22×Q8—731no—
508C22×Q8—733no—
509C22×Q8—731no—
510C22×Q8—733no—
511C22×Q8—733no—
512C22×Q8—1464no—
513C22×Q8—1464no—
514C22×Q8—1464no—
515C22×Q8—1464no—
516C22×Q8C2×#6440811yescharacteristic
517C22×Q8C2×#6440811yescharacteristic, complemented
518C22×D4—731no—
519C23×C4—733no—
520C23×C4—733no—
521C23×C4—733no—
522C23×C4—731no—
523C4⋊Q8—733no—
524C4⋊Q8—733no—
525C4⋊Q8—736no—
526C4⋊Q8—736no—
527C4⋊Q8—733no—
528C4⋊Q8C2×#6440813yescomplemented
529C22⋊Q8—733no—
530C22⋊Q8—733no—
531C22⋊Q8—733no—
532C22⋊Q8—733no—
533C22⋊Q8—736no—
534C22⋊Q8—736no—
535C22⋊Q8—733no—
536C22⋊Q8—733no—
537C22⋊Q8—736no—
538C22⋊Q8—736no—
539C22⋊Q8C2×#6440813yes—
540C22⋊Q8C2×#6440813yescomplemented
541C4×Q8—738no—
542C4×Q8—731no—
543C4×Q8—733no—
544C4×Q8—733no—
545C4×Q8—14612no—
546C4×Q8—14612no—
547C4×Q8—14612no—
548C4×Q8—14612no—
549C4×Q8—1464no—
550C4×Q8—1464no—
551C4×Q8—1464no—
552C4×Q8C2×#6440811yescharacteristic, complemented
553C4×D4—733no—
554C4×D4—733no—
555C4×D4—733no—
556C4×D4—733no—
557C4×D4—733no—
558C4×D4—733no—
559C4×D4—733no—
560C4×D4C2×#6440813yes—
561#117—14612no—
562#117—14612no—
563C2×C4⋊C4—733no—
564C2×C4⋊C4—733no—
565C2×C4⋊C4—733no—
566C2×C4⋊C4—733no—
567C2×C4⋊C4—736no—
568C2×C4⋊C4—733no—
569C2×C4⋊C4—736no—
570C2×C4⋊C4—733no—
571C2×C4⋊C4—733no—
572C2×C4⋊C4—733no—
573C2×C4⋊C4—733no—
574C2×C4⋊C4—733no—
575C2×C4⋊C4—14612no—
576C2×C22⋊C4—733no—
577C2×C22⋊C4—733no—
578C2×C22⋊C4—733no—
579C2×C22⋊C4—731no—
580C2×C22⋊C4—733no—
581C2×C22⋊C4—733no—
582C2×C22⋊C4—731no—
583C2×C22⋊C4—731no—
584C2×C42—736no—
585C2×C42—733no—
586C2×C42—733no—
587C2×C42—736no—
588C2×C42—733no—
589C2×C42—733no—
590C2×C42—733no—
591C2×C42—733no—
592C2×C42—733no—
593C2×C42—14612no—
594#95—731no—
595#95—733no—
596#95—733no—
597#95—733no—
598#95—733no—
599#95—736no—
600#95—736no—
601#95—733no—
602#95—733no—
603#95—733no—
604#95—731no—
605#95—736no—
606#95—733no—
607C24—731no—
608C24—731no—
609C2×Q8—24no—
610C2×Q8—24no—
611C2×Q8—734no—
612C2×Q8—734no—
613C2×Q8—733no—
614C2×Q8—736no—
615C2×Q8—736no—
616C2×Q8—733no—
617C2×Q8—733no—
618C2×Q8—14612no—
619C2×Q8—14612no—
620C2×Q8—1466no—
621C2×Q8—1466no—
622C2×Q8—1466no—
623C2×Q8—1466no—
624C2×Q8—14612no—
625C2×Q8—14612no—
626C2×Q8—1464no—
627C2×Q8—1464no—
628C2×Q8C22×#6440813yes—
629C2×Q8C22×#6440813yes—
630C2×Q8C22×#6440811yescharacteristic
631C2×D4—731no—
632C2×D4—731no—
633C2×D4—731no—
634C2×D4—1462no—
635C2×D4—1462no—
636C2×D4C22×#6440811yescharacteristic
637C22×C4—2923no—
638C22×C4—733no—
639C22×C4—731no—
640C22×C4—731no—
641C22×C4—733no—
642C22×C4—733no—
643C22×C4—733no—
644C22×C4—733no—
645C22×C4—733no—
646C22×C4—733no—
647C22×C4—733no—
648C22×C4—731no—
649C22×C4—733no—
650C22×C4—733no—
651C22×C4—733no—
652C22×C4—731no—
653C22×C4—733no—
654C22×C4—733no—
655C22×C4—733no—
656C22×C4—731no—
657C22×C4—1466no—
658C22×C4—1466no—
659C22×C4—1466no—
660C22×C4—1466no—
661C22×C4—1466no—
662C22×C4—1466no—
663C22×C4—1462no—
664C22×C4—1462no—
665C22×C4—1462no—
666C22×C4C22×#6440813yes—
667C22×C4C22×#6440813yes—
668C4⋊C4—2923no—
669C4⋊C4—7312no—
670C4⋊C4—733no—
671C4⋊C4—733no—
672C4⋊C4—736no—
673C4⋊C4—736no—
674C4⋊C4—736no—
675C4⋊C4—733no—
676C4⋊C4—733no—
677C4⋊C4—736no—
678C4⋊C4—1466no—
679C4⋊C4—1466no—
680C4⋊C4—14612no—
681C4⋊C4—1466no—
682C4⋊C4—1466no—
683C4⋊C4—1466no—
684C4⋊C4—1466no—
685C4⋊C4C22×#6440813yes—
686C4⋊C4C22×#6440813yes—
687C4⋊C4C22×#6440816yes—
688C22⋊C4—2923no—
689C22⋊C4—733no—
690C22⋊C4—733no—
691C22⋊C4—733no—
692C22⋊C4—733no—
693C22⋊C4—733no—
694C22⋊C4—733no—
695C22⋊C4—1462no—
696C22⋊C4—1462no—
697C22⋊C4—1466no—
698C22⋊C4—1466no—
699C22⋊C4—1462no—
700C22⋊C4C22×#6440813yes—
701C22⋊C4C22×#6440813yes—
702C42—2926no—
703C42—7312no—
704C42—733no—
705C42—733no—
706C42—733no—
707C42—1466no—
708C42—1466no—
709C42—1466no—
710C42—1466no—
711C42—14612no—
712C42—1466no—
713C42C22×#6440813yes—
714C23—731no—
715C23—732no—
716C23—732no—
717C23—731no—
718C23—731no—
719C23—1461no—
720C23—1461no—
721C23—1461no—
722C23—1461no—
723C23—1461no—
724C23—1461no—
725C23—1461no—
726C23—1461no—
727C23—1461no—
728C23—1461no—
729C23C23×#6440811yescharacteristic
730C23C23×#6440811yescharacteristic
731Q8—26no—
732Q8—26no—
733Q8—7312no—
734Q8—14612no—
735Q8—14612no—
736Q8—1466no—
737Q8—1466no—
738Q8D4×#6440814yes—
739D4—22no—
740D4—1462no—
741D4—1462no—
742D4—1462no—
743C2×C4—26no—
744C2×C4—26no—
745C2×C4—29212no—
746C2×C4—733no—
747C2×C4—736no—
748C2×C4—736no—
749C2×C4—732no—
750C2×C4—736no—
751C2×C4—732no—
752C2×C4—731no—
753C2×C4—733no—
754C2×C4—733no—
755C2×C4—733no—
756C2×C4—1466no—
757C2×C4—1466no—
758C2×C4—1463no—
759C2×C4—1463no—
760C2×C4—1463no—
761C2×C4—1463no—
762C2×C4—1463no—
763C2×C4—1463no—
764C2×C4—1461no—
765C2×C4—1461no—
766C2×C4—1463no—
767C2×C4—1463no—
768C2×C4—1461no—
769C2×C4—1461no—
770C2×C4—1463no—
771C2×C4—1463no—
772C2×C4—1463no—
773C2×C4—1461no—
774C2×C4—1463no—
775C2×C4—1463no—
776C2×C4—1461no—
777C2×C4—1461no—
778C2×C4—1461no—
779C2×C4—1463no—
780C2×C4—1463no—
781C2×C4—1466no—
782C2×C4—1466no—
783C2×C4—1463no—
784C2×C4—1461no—
785C2×C4—1463no—
786C2×C4—1461no—
787C2×C4—1461no—
788C2×C4—1461no—
789C2×C4—1468no—
790C2×C4—1466no—
791C2×C4—1466no—
792C2×C4C23×#6440811yescharacteristic
793C2×C4C23×#6440813yes—
794C2×C4C23×#6440813yes—
795C2×C4C23×#6440813yes—
796C2×C4C23×#6440813yes—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—2921no—
803C22—2921no—
804C22—2921no—
805C22—2921no—
806C22—731no—
807C22—731no—
808C22—731no—
809C22—731no—
810C22—731no—
811C22—731no—
812C22—732no—
813C22—1462no—
814C22—1462no—
815C22—1462no—
816C22—1462no—
817C22—1461no—
818C22—1461no—
819C22—1461no—
820C22—1461no—
821C22—1461no—
822C22#1798965512yescomplemented
823C22C24×#6440811yescharacteristic
824C4—23no—
825C4—23no—
826C4—21no—
827C4—23no—
828C4—2923no—
829C4—2921no—
830C4—2923no—
831C4—2923no—
832C4—2921no—
833C4—736no—
834C4—1466no—
835C4—1462no—
836C4—1462no—
837C4—1463no—
838C4—1463no—
839C4—1461no—
840C4—1463no—
841C4C2×D4×#6440816yes—
842C2—22no—
843C2—41no—
844C2—2921no—
845C2—731no—
846C2—731no—
847C2—731no—
848C2—731no—
849C2—1462no—
850C2C22×D4×#6440811yescharacteristic
851C2C2×#1798965511yescharacteristic
852C22−1+4×#6440811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
FittingD4×Q8×C73C4
prime radicalC2×D4×D73C23
cosocleC22×D73C25
hypercenterD4×Q8#64408
hypocenterC73#34291
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#17989655C2semidirect
2. C22×Q8×#64408C2semidirect
3. #22626460C2semidirect
4. #22626457C2semidirect
5. #22626455C2semidirect
7. #22626446C2semidirect
8. Q8×C22⋊#64408C2semidirect
9. Q8×C22⋊#64408C2semidirect
10. #22626422C2semidirect
11. #22626418C2semidirect
12. C22⋊Q8×#64408C2semidirect
14. #22626371C2semidirect
63. Q8×D292C4semidirect
64. D4×Dic146C4semidirect
65. #17989252C4semidirect
66. Q8×C22⋊D73C4semidirect
67. Q8×C22⋊D73C4semidirect
68. #17989250C4semidirect
69. #17989250C4semidirect
75. D4×Q8×C73C4semidirect
85. Q8×#64408D4semidirect
127. C22×Dic146C2×C4semidirect
134. C2×Q8×D73C2×C4semidirect
135. C2×Q8×D73C2×C4semidirect
142. #14556591C2×C4semidirect
143. #14556590C2×C4semidirect
144. #14556590C2×C4semidirect
145. #14556589C2×C4semidirect
146. #14556589C2×C4semidirect
148. #14556571C2×C4semidirect
150. #14556570C2×C4semidirect
152. #14556569C2×C4semidirect
154. #14556568C2×C4semidirect
156. #14556567C2×C4semidirect
157. Q8×Dic73C2×C4semidirect
158. C4×Dic146C2×C4semidirect
159. #14556556C2×C4semidirect
174. C22×Q8×C73C2×C4semidirect
175. C4⋊Q8×C73C2×C4semidirect
177. C22⋊Q8×C73C2×C4semidirect
178. C4×Q8×C73C2×C4semidirect
375. C22×C73#519semidirect
390. C2×D73#519semidirect
442. C73#34291semidirect
452. D4×Q8#64408semidirect
517. C22×Q8C2×#64408semidirect
528. C4⋊Q8C2×#64408semidirect
540. C22⋊Q8C2×#64408semidirect
552. C4×Q8C2×#64408semidirect
822. C22#17989655semidirect

Maximal subgroups

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

subgroupindex
C2×#179896552
C22×Q8×#644082
#226264602
#226264572
#226264552
#226264472
#226264462
Q8×C22⋊#644082
#226264222
#226264182
C22⋊Q8×#644082
#226263852
#226263712
D4×Q8×D732
#3429173