Finite Group Databasebeta

← #34030839

Subgroups — #34030839

Order 18688.

2960 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989656C211yesmaximal, characteristic, complemented
2C2×#17989655C211yesmaximal, characteristic, complemented
3#22626462C213yesmaximal, complemented
4#22626458C213yesmaximal, complemented
5#22626455C213yesmaximal, complemented
6#22626447C213yesmaximal, complemented
7#22626446C211yesmaximal, characteristic, complemented
8#22626436C211yesmaximal, characteristic, complemented
9Q8×C22⋊#64408C211yesmaximal, characteristic, complemented
10#22626419C213yesmaximal, complemented
11#22626418C213yesmaximal, complemented
12#124×#64408C213yesmaximal, complemented
13#22626388C213yesmaximal, complemented
14C4×Q8×#64408C211yesmaximal, characteristic, complemented
15#548×D73C211yesmaximal, characteristic
16#17989656—28no—
17#17989655—28no—
18C2×Q8×#64408C2211yescharacteristic
19C2×Q8×#64408C2213yes—
20C2×Q8×#64408C2211yescharacteristic
21C2×Q8×#64408C2213yes—
22C2×Q8×#64408C2211yescharacteristic
23C2×Q8×#64408C2211yescharacteristic
24C2×D4×#64408C2213yes—
25C2×D4×#64408C2213yes—
26C2×#14556670C2213yes—
27C2×#14556670C2213yes—
28C2×#14556670C2213yes—
29C22×C4⋊#64408C2213yes—
30(C2×#64408)⋊Q8C2213yes—
31(C2×#64408)⋊Q8C2213yes—
32#17989539C2213yes—
33#17989539C2213yes—
34#17989539C2213yes—
35#17989539C2213yes—
36#17989538C2213yes—
37#17989538C2213yes—
38#17989538C2213yes—
39#17989538C2213yes—
40#17989537C2211yescharacteristic
41#17989537C2213yes—
42#17989537C2213yes—
43#17989537C2213yes—
44#17989537C2216yes—
45#17989537C2216yes—
46#17989536C2216yes—
47#17989535C2216yes—
48#17989534C2216yes—
49#17989531C2213yes—
50#17989529C2213yes—
51#17989529C2213yes—
52C4⋊C4×#64408C2213yes—
53C4⋊C4×#64408C2213yes—
54C4×C4⋊#64408C2213yes—
55C4×C4⋊#64408C2213yes—
56C22⋊C4×#64408C2216yes—
57C22⋊C4×#64408C2216yes—
58C4×C22⋊#64408C2213yes—
59C4×C22⋊#64408C2213yes—
60C42×#64408C2213yes—
61C2×#41×D73C2211yescharacteristic
62C22×Q8×D73C2211yescharacteristic
63#17989249C411yescharacteristic, complemented
64#17989248C411yescharacteristic, complemented
65#17989247C413yescomplemented
66#17989246C413yescomplemented
67#17989245C413yescomplemented
68#17989244C411yescharacteristic, complemented
69#17989243C413yescomplemented
70#124×D73C2213yes—
71C22⋊Q8×D73C2213yes—
72#121×D73C2213yes—
73C4×Q8×D73C2211yescharacteristic
74C4×D4×D73C2213yes—
75#548×C73C411yescharacteristic, complemented
76C23×#64408C2316yes—
77Q8×#64408—212no—
78Q8×#64408—212no—
79Q8×#64408—24no—
80Q8×#64408—24no—
81Q8×#64408—24no—
82Q8×#64408D418yescomplemented
83D4×#64408—212no—
84D4×#64408—212no—
85#14556670—212no—
86#14556670—212no—
87#14556670—212no—
88C2×C4⋊#64408—212no—
89C2×C4⋊#64408C2313yes—
90C2×C4⋊#64408C2313yes—
91C2×C4⋊#64408C2311yescharacteristic
92C2×C4⋊#64408C2313yes—
93C2×C4⋊#64408C2313yes—
94C2×C4⋊#64408C2313yes—
95C2×C4⋊#64408C2313yes—
96C2×C4⋊#64408C2313yes—
97C2×C4⋊#64408C2313yes—
98C2×C4⋊#64408C2313yes—
99C2×C22⋊#64408C2313yes—
100C2×C22⋊#64408C2311yescharacteristic
101C2×C22⋊#64408C2313yes—
102C2×C22⋊#64408C2313yes—
103C2×C22⋊#64408C2311yescharacteristic
104C2×C22⋊#64408C2313yes—
105C2×C22⋊#64408C2313yes—
106C2×C22⋊#64408C2313yes—
107C2×C22⋊#64408C2316yes—
108C2×C4×#64408C2313yes—
109C2×C4×#64408C2313yes—
110C2×C4×#64408C2316yes—
111C2×C4×#64408C2313yes—
112C2×C4×#64408C2311yescharacteristic
113C2×C4×#64408C2313yes—
114C2×C4×#64408C2313yes—
115C2×C4×#64408C2313yes—
116C2×C4×#64408C2313yes—
117(C2×#64408)⋊C4C2311yescharacteristic
118(C2×#64408)⋊C4C2313yes—
119(C2×#64408)⋊C4C2313yes—
120(C2×#64408)⋊C4C2313yes—
121(C2×#64408)⋊C4C2313yes—
122(C2×#64408)⋊C4C2316yes—
123(C2×#64408)⋊C4C2316yes—
124(C2×#64408)⋊C4C2311yescharacteristic
125(C2×#64408)⋊C4C2316yes—
126C2×#11924029C2×C411yescharacteristic
127C2×#11924028C2×C413yes—
128C2×#11924027C2×C413yes—
129#41×D73—24no—
130#41×D73—24no—
131C22×Dic146C2×C413yescomplemented
132C2×Q8×D73—24no—
133C2×Q8×D73—24no—
134C2×Q8×D73C2×C411yescharacteristic, complemented
135C2×Q8×D73C2×C413yescomplemented
136C2×Q8×D73C2313yes—
137C2×Q8×D73C2311yescharacteristic
138C2×D4×D73C2313yes—
139C2×D4×D73C2313yes—
140C22×C4×D73C2313yes—
141C22×C4×D73C2313yes—
142#14556580C2×C413yescomplemented
143#14556579C2×C413yescomplemented
144#14556578C2×C413yescomplemented
145#14556577C2×C416yescomplemented
146#14556577C2×C416yescomplemented
147#14556571C2×C413yescomplemented
148#14556570C2×C413yescomplemented
149#14556569C2×C416yescomplemented
150#14556568C2×C416yescomplemented
151#14556567C2×C413yescomplemented
152#14556566C2×C413yescomplemented
153#14556565C2×C413yescomplemented
154#14556564C2×C416yescomplemented
155#14556563C2×C416yescomplemented
156#14556562C2×C413yescomplemented
157Q8×Dic73C2×C411yescharacteristic, complemented
158C4×Dic146C2×C413yescomplemented
159#14556556C2×C413yescomplemented
160C4×D292C2×C413yescomplemented
161D4×Dic73C2×C413yescomplemented
162#14556553C2×C413yescomplemented
163C4×C22⋊D73C2×C413yescomplemented
164C4×C22⋊D73C2×C413yescomplemented
165#14556551C2×C413yescomplemented
166#14556551C2×C413yescomplemented
167C4⋊C4×D73C2313yes—
168C4⋊C4×D73C2313yes—
169C22⋊C4×D73C2313yes—
170C22⋊C4×D73C2316yes—
171C22⋊C4×D73C2311yescharacteristic
172C42×D73C2313yes—
173C2×#41×C73C2×C411yescharacteristic
174C22×Q8×C73C2×C411yescharacteristic, complemented
175#124×C73C2×C413yescomplemented
176C22⋊Q8×C73C2×C413yescomplemented
177#121×C73C2×C413yescomplemented
178C4×Q8×C73C2×C411yescharacteristic, complemented
179C4×D4×C73C2×C413yescomplemented
180C22×#64408—212no—
181C22×#64408—46no—
182C22×#64408—46no—
183C22×#64408C2413yes—
184C22×#64408C2413yes—
185C22×#64408C2411yescharacteristic
186C22×#64408C2413yes—
187C22×#64408C2411yescharacteristic
188C22×#64408C2413yes—
189C22×#64408C2411yescharacteristic
190C22×#64408C2411yescharacteristic
191C4⋊#64408—26no—
192C4⋊#64408—26no—
193C4⋊#64408—26no—
194C4⋊#64408—22no—
195C4⋊#64408—26no—
196C4⋊#64408—26no—
197C4⋊#64408—26no—
198C4⋊#64408—43no—
199C4⋊#64408—43no—
200C4⋊#64408C2×D4112yes—
201C22⋊#64408—26no—
202C22⋊#64408—22no—
203C22⋊#64408—26no—
204C22⋊#64408—26no—
205C22⋊#64408—22no—
206C22⋊#64408—26no—
207C22⋊#64408—43no—
208C22⋊#64408—46no—
209C22⋊#64408—43no—
210C4×#64408—212no—
211C4×#64408—22no—
212C4×#64408—26no—
213C4×#64408—26no—
214C4×#64408—26no—
215C4×#64408—43no—
216C4×#64408—43no—
217C4×#64408—43no—
218C4×#64408C2×D4112yes—
219C23×D73C2413yes—
220C23×D73C2411yescharacteristic
221#11924029—24no—
222#11924028—212no—
223#11924027—212no—
224C2×Dic146—212no—
225C2×Dic146C22×C416yes—
226C2×Dic146C22×C413yes—
227C2×Dic146C22×C413yes—
228Q8×D73—24no—
229Q8×D73—26no—
230Q8×D73—26no—
231Q8×D73—212no—
232Q8×D73C2×D414yes—
233Q8×D73#4114yes—
234C2×D292C22×C413yes—
235C2×D292C22×C413yes—
236C2×C22⋊D73C22×C416yes—
237C2×C22⋊D73C22×C413yes—
238C2×C22⋊D73C22×C413yes—
239D4×D73—26no—
240D4×D73—26no—
241D4×D73—43no—
242D4×D73—43no—
243C22×Dic73C22×C413yes—
244C22×Dic73C22×C413yes—
245C2×C4×D73—26no—
246C2×C4×D73—26no—
247C2×C4×D73—26no—
248C2×C4×D73—26no—
249C2×C4×D73C22×C413yes—
250C2×C4×D73C22×C413yes—
251C2×C4×D73C22×C413yes—
252C2×C4×D73C22×C413yes—
253C2×C4×D73C2411yescharacteristic
254C2×C4×D73C2413yes—
255C2×C4×D73C2413yes—
256C2×C4×D73C2411yescharacteristic
257C2×C4×D73C2413yes—
258C4⋊Dic73C22×C413yes—
259C4⋊Dic73C22×C413yes—
260#11924007C22×C413yes—
261#11924007C22×C413yes—
262#11924007C22×C416yes—
263C22⋊Dic73C22×C411yescharacteristic
264C22⋊Dic73C22×C413yes—
265C22⋊Dic73C22×C416yes—
266#11924005C22×C411yescharacteristic
267#11924005C22×C413yes—
268#11924005C22×C411yescharacteristic
269#11924005C22×C413yes—
270#11924005C22×C416yes—
271#11924005C22×C416yes—
272C4×Dic73C22×C413yes—
273C4×Dic73C22×C413yes—
274C4×Dic73C22×C413yes—
275#41×C73—24no—
276C2×Q8×C73—24no—
277C2×Q8×C73C22×C413yes—
278C2×Q8×C73C22×C411yescharacteristic
279C2×D4×C73C22×C413yes—
280C2×D4×C73C22×C413yes—
281C22×C4×C73C22×C413yes—
282C22×C4×C73C22×C413yes—
283C4⋊C4×C73C22×C413yes—
284C4⋊C4×C73C22×C413yes—
285C22⋊C4×C73C22×C411yescharacteristic
286C22⋊C4×C73C22×C413yes—
287C22⋊C4×C73C22×C416yes—
288C42×C73C22×C413yes—
289C23×C73C23×C413yes—
290C23×C73C23×C411yescharacteristic
291C22×D73—21no—
292C22×D73—23no—
293C22×D73—21no—
294C22×D73—23no—
295C22×D73—23no—
296C22×D73—21no—
297C22×D73—21no—
298C22×D73—21no—
299C22×D73—23no—
300C22×D73—23no—
301C22×D73—21no—
302C22×D73—23no—
303C22×D73C23×C413yes—
304C22×D73C23×C411yescharacteristic
305C22×D73C2511yescharacteristic
306C2×#64408—21no—
307C2×#64408—21no—
308C2×#64408—21no—
309C2×#64408—21no—
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—23no—
320C2×#64408—23no—
321C2×#64408—21no—
322C2×#64408—23no—
323C2×#64408—23no—
324C2×#64408—21no—
325C2×#64408—21no—
326C2×#64408—23no—
327C2×#64408—812no—
328C2×#64408C22×D416yes—
329C2×#64408C22×D412yes—
330C2×#644082−1+412yes—
331Q8×C73—26no—
332Q8×C73C4×D414yes—
333D4×C73—26no—
334D4×C73—43no—
335C2×C4×C73—26no—
336C2×C4×C73—26no—
337C2×C4×C73C23×C411yescharacteristic
338C2×C4×C73C23×C413yes—
339C2×C4×C73C23×C413yes—
340C2×C4×C73C23×C411yescharacteristic
341C2×C4×C73C23×C413yes—
342C22⋊D73—212no—
343C22⋊D73—43no—
344C22⋊D73—43no—
345C2×Dic73—26no—
346C2×Dic73—26no—
347C2×Dic73C23×C411yescharacteristic
348C2×Dic73C23×C413yes—
349C2×Dic73C23×C413yes—
350C2×Dic73C23×C411yescharacteristic
351C2×Dic73C23×C413yes—
352D292—26no—
353D292—43no—
354C4×D73—21no—
355C4×D73—23no—
356C4×D73—21no—
357C4×D73—23no—
358C4×D73—21no—
359C4×D73—23no—
360C4×D73—23no—
361C4×D73—21no—
362C4×D73—26no—
363C4×D73—26no—
364C4×D73—26no—
365C4×D73—26no—
366C4×D73C22×D416yes—
367C4×D73C2×#4116yes—
368Dic146—26no—
369Dic146—212no—
370Dic146C4×D4112yes—
371C22×C73—21no—
372C22×C73—23no—
373C22×C73—21no—
374C22×C73—23no—
375C22×C73—21no—
376C22×C73—23no—
377C22×C73C24×C411yescharacteristic
378C2×D73—21no—
379C2×D73—23no—
380C2×D73—21no—
381C2×D73—23no—
382C2×D73—21no—
383C2×D73—23no—
384C2×D73—41no—
385C2×D73—43no—
386C2×D73—43no—
387C2×D73—41no—
388C2×D73—41no—
389C2×D73—43no—
390C2×D73—41no—
391C2×D73—43no—
392C2×D73C23×D411yescharacteristic
393C2×D73C22×#4111yescharacteristic
394C2×D73C2×2−1+411yescharacteristic
395C2×D73#58511yescharacteristic
396C2×D73#58511yescharacteristic
397C2×D73#58511yescharacteristic
398#64408—22no—
399#64408—26no—
400#64408—22no—
401#64408—41no—
402#64408—43no—
403#64408—41no—
404#64408—43no—
405#64408—43no—
406C4×C73—23no—
407C4×C73—21no—
408C4×C73—23no—
409C4×C73—21no—
410C4×C73C2×C4×D416yes—
411Dic73—23no—
412Dic73—21no—
413Dic73—23no—
414Dic73—21no—
415Dic73C2×C4×D416yes—
416#34312—731nomaximal, Sylow
417C2×C73—43no—
418C2×C73—41no—
419C2×C73C22×C4×D411yescharacteristic
420C2×C73#342811yescharacteristic
421C2×C73C4×2−1+411yescharacteristic
422D73—41no—
423D73—43no—
424D73#349711yescharacteristic
425D73#350011yescharacteristic
426D73#351611yescharacteristic
427D73#352411yescharacteristic
428C2×#548—731no—
429C2×#520—731no—
430C2×#519—731no—
431#2367—733no—
432#2363—733no—
433#2360—733no—
434#2352—733no—
435#2351—731no—
436#2341—731no—
437Q8×C22⋊C4—731no—
438#2324—733no—
439#2323—733no—
440C4×#124—733no—
441#2293—733no—
442C42×Q8—731no—
443C73#3431211yescharacteristic, complemented, Sylow
444C22×#41—731no—
445C23×Q8—731no—
446#548—731no—
447#548—731no—
448#548—733no—
449#548—733no—
450#548—733no—
451#548—731no—
452#548—733no—
453#548#6440811yescharacteristic, complemented
454C2×#124—733no—
455C2×C22⋊Q8—733no—
456C2×#121—733no—
457#520—1468no—
458#519—1468no—
459C2×C4×Q8—731no—
460C2×C4×Q8—731no—
461C2×C4×Q8—733no—
462C2×C4×Q8—731no—
463C2×C4×Q8—731no—
464C2×C4×Q8—731no—
465C2×C4×Q8—733no—
466C2×C4×D4—733no—
467C2×C4×D4—733no—
468C2×C4×D4—733no—
469C2×#117—733no—
470C2×#117—733no—
471C2×#117—733no—
472C22×C4⋊C4—733no—
473#391—733no—
474#391—733no—
475#390—733no—
476#390—733no—
477#390—733no—
478#390—733no—
479#389—733no—
480#389—733no—
481#389—733no—
482#389—733no—
483#388—736no—
484#388—736no—
485#388—733no—
486#388—733no—
487#388—731no—
488#388—733no—
489#387—736no—
490#386—736no—
491#385—736no—
492#382—733no—
493#380—733no—
494#380—733no—
495C4×C4⋊C4—733no—
496C4×C4⋊C4—733no—
497C4×C4⋊C4—733no—
498C4×C4⋊C4—733no—
499C4×C22⋊C4—733no—
500C4×C22⋊C4—733no—
501C4×C22⋊C4—736no—
502C4×C22⋊C4—736no—
503C43—733no—
504C2×#41—731no—
505C2×#41—733no—
506C2×#41—733no—
507C2×#41—1464no—
508C2×#41—1464no—
509C2×#41C2×#6440811yescharacteristic
510C22×Q8—731no—
511C22×Q8—733no—
512C22×Q8—733no—
513C22×Q8—731no—
514C22×Q8—733no—
515C22×Q8—1464no—
516C22×Q8—1464no—
517C22×Q8C2×#6440811yescharacteristic, complemented
518C22×D4—733no—
519C22×D4—733no—
520C23×C4—736no—
521C23×C4—733no—
522C23×C4—733no—
523#124—733no—
524#124—733no—
525#124—736no—
526#124—736no—
527#124—733no—
528#124C2×#6440813yescomplemented
529C22⋊Q8—733no—
530C22⋊Q8—733no—
531C22⋊Q8—736no—
532C22⋊Q8—733no—
533C22⋊Q8—736no—
534C22⋊Q8C2×#6440813yescomplemented
535#121—733no—
536#121—736no—
537#121—733no—
538#121—733no—
539#121—736no—
540#121C2×#6440813yescomplemented
541C4×Q8—738no—
542C4×Q8—731no—
543C4×Q8—733no—
544C4×Q8—733no—
545C4×Q8—14612no—
546C4×Q8—14612no—
547C4×Q8—1464no—
548C4×Q8—1464no—
549C4×Q8—1464no—
550C4×Q8C2×#6440811yescharacteristic, complemented
551C4×D4—733no—
552C4×D4—733no—
553C4×D4—733no—
554C4×D4—733no—
555C4×D4—733no—
556C4×D4—733no—
557C4×D4—733no—
558C4×D4—14612no—
559C4×D4—14612no—
560C4×D4C2×#6440813yescomplemented
561#117—14612no—
562#117—14612no—
563#117—14612no—
564C2×C4⋊C4—733no—
565C2×C4⋊C4—733no—
566C2×C4⋊C4—733no—
567C2×C4⋊C4—733no—
568C2×C4⋊C4—733no—
569C2×C4⋊C4—733no—
570C2×C4⋊C4—733no—
571C2×C4⋊C4—731no—
572C2×C4⋊C4—733no—
573C2×C4⋊C4—733no—
574C2×C4⋊C4—733no—
575C2×C4⋊C4—733no—
576C2×C4⋊C4—14612no—
577C2×C22⋊C4—733no—
578C2×C22⋊C4—736no—
579C2×C22⋊C4—733no—
580C2×C22⋊C4—731no—
581C2×C22⋊C4—733no—
582C2×C22⋊C4—736no—
583C2×C22⋊C4—733no—
584C2×C22⋊C4—731no—
585C2×C22⋊C4—733no—
586C2×C22⋊C4—733no—
587C2×C22⋊C4—731no—
588C2×C22⋊C4—733no—
589C2×C42—733no—
590C2×C42—733no—
591C2×C42—733no—
592C2×C42—733no—
593C2×C42—733no—
594C2×C42—733no—
595C2×C42—736no—
596C2×C42—733no—
597C2×C42—733no—
598C2×C42—731no—
599#95—731no—
600#95—733no—
601#95—733no—
602#95—733no—
603#95—736no—
604#95—736no—
605#95—733no—
606#95—736no—
607#95—731no—
608C24—733no—
609C24—731no—
610#41—24no—
611#41—14612no—
612#41—14612no—
613#41—1464no—
614C2×Q8—24no—
615C2×Q8—734no—
616C2×Q8—734no—
617C2×Q8—733no—
618C2×Q8—736no—
619C2×Q8—733no—
620C2×Q8—14612no—
621C2×Q8—1466no—
622C2×Q8—1466no—
623C2×Q8—14612no—
624C2×Q8—1464no—
625C2×Q8C22×#6440813yes—
626C2×Q8C22×#6440811yescharacteristic
627C2×D4—2923no—
628C2×D4—2923no—
629C2×D4—733no—
630C2×D4—733no—
631C2×D4—736no—
632C2×D4—733no—
633C2×D4—733no—
634C2×D4—1466no—
635C2×D4—1466no—
636C2×D4C22×#6440813yes—
637C2×D4C22×#6440813yes—
638C22×C4—2926no—
639C22×C4—2926no—
640C22×C4—733no—
641C22×C4—731no—
642C22×C4—733no—
643C22×C4—731no—
644C22×C4—733no—
645C22×C4—733no—
646C22×C4—733no—
647C22×C4—733no—
648C22×C4—733no—
649C22×C4—733no—
650C22×C4—731no—
651C22×C4—733no—
652C22×C4—733no—
653C22×C4—731no—
654C22×C4—733no—
655C22×C4—733no—
656C22×C4—731no—
657C22×C4—733no—
658C22×C4—731no—
659C22×C4—1466no—
660C22×C4—1466no—
661C22×C4—1466no—
662C22×C4—1466no—
663C22×C4—14612no—
664C22×C4C22×#6440813yes—
665C22×C4C22×#6440813yes—
666C4⋊C4—2923no—
667C4⋊C4—2923no—
668C4⋊C4—7312no—
669C4⋊C4—733no—
670C4⋊C4—733no—
671C4⋊C4—736no—
672C4⋊C4—733no—
673C4⋊C4—733no—
674C4⋊C4—1466no—
675C4⋊C4—1466no—
676C4⋊C4—1462no—
677C4⋊C4—1466no—
678C4⋊C4—1466no—
679C4⋊C4—1466no—
680C4⋊C4—1466no—
681C4⋊C4C22×#6440813yes—
682C4⋊C4C22×#6440813yes—
683C22⋊C4—2923no—
684C22⋊C4—2926no—
685C22⋊C4—2923no—
686C22⋊C4—731no—
687C22⋊C4—733no—
688C22⋊C4—736no—
689C22⋊C4—731no—
690C22⋊C4—731no—
691C22⋊C4—733no—
692C22⋊C4—733no—
693C22⋊C4—736no—
694C22⋊C4—736no—
695C22⋊C4—1462no—
696C22⋊C4—1466no—
697C22⋊C4—1462no—
698C22⋊C4—1466no—
699C22⋊C4—1466no—
700C22⋊C4—1466no—
701C22⋊C4C22×#6440811yescharacteristic
702C22⋊C4C22×#6440813yes—
703C22⋊C4C22×#6440816yes—
704C42—2923no—
705C42—2923no—
706C42—2923no—
707C42—7312no—
708C42—733no—
709C42—733no—
710C42—733no—
711C42—1462no—
712C42—1466no—
713C42—1466no—
714C42—14612no—
715C42—1466no—
716C42C22×#6440813yes—
717C23—731no—
718C23—733no—
719C23—731no—
720C23—1461no—
721C23—1463no—
722C23—1463no—
723C23—1461no—
724C23—1463no—
725C23—1461no—
726C23—1463no—
727C23—1463no—
728C23—1461no—
729C23—1463no—
730C23—1461no—
731C23—1461no—
732C23C23×#6440813yes—
733C23C23×#6440811yescharacteristic
734Q8—26no—
735Q8—7312no—
736Q8—14612no—
737Q8—1466no—
738Q8D4×#6440814yes—
739D4—26no—
740D4—43no—
741D4—2923no—
742D4—2923no—
743D4—2923no—
744D4—14612no—
745D4—1466no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—58412no—
749C2×C4—733no—
750C2×C4—736no—
751C2×C4—736no—
752C2×C4—732no—
753C2×C4—736no—
754C2×C4—732no—
755C2×C4—731no—
756C2×C4—733no—
757C2×C4—733no—
758C2×C4—731no—
759C2×C4—1466no—
760C2×C4—1466no—
761C2×C4—1461no—
762C2×C4—1463no—
763C2×C4—1463no—
764C2×C4—1463no—
765C2×C4—1461no—
766C2×C4—1461no—
767C2×C4—1461no—
768C2×C4—1463no—
769C2×C4—1463no—
770C2×C4—1463no—
771C2×C4—1461no—
772C2×C4—1463no—
773C2×C4—1461no—
774C2×C4—1463no—
775C2×C4—1463no—
776C2×C4—1461no—
777C2×C4—1463no—
778C2×C4—1463no—
779C2×C4—1461no—
780C2×C4—1463no—
781C2×C4—1461no—
782C2×C4—1461no—
783C2×C4—1463no—
784C2×C4—1466no—
785C2×C4—1466no—
786C2×C4—1461no—
787C2×C4—1461no—
788C2×C4—1463no—
789C2×C4—1463no—
790C2×C4—1461no—
791C2×C4—1461no—
792C2×C4—1466no—
793C2×C4—1466no—
794C2×C4C23×#6440811yescharacteristic
795C2×C4C23×#6440813yes—
796C2×C4C23×#6440813yes—
797C2×C4C23×#6440811yescharacteristic
798C2×C4C23×#6440813yes—
799C22—21no—
800C22—23no—
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—2923no—
806C22—2921no—
807C22—2923no—
808C22—2921no—
809C22—2921no—
810C22—2923no—
811C22—2923no—
812C22—2921no—
813C22—731no—
814C22—731no—
815C22—731no—
816C22—731no—
817C22—731no—
818C22—731no—
819C22—1461no—
820C22—1463no—
821C22—1461no—
822C22—1463no—
823C22—1463no—
824C22—1461no—
825C22C24×#6440811yescharacteristic
826C4—21no—
827C4—23no—
828C4—23no—
829C4—21no—
830C4—2923no—
831C4—2921no—
832C4—2921no—
833C4—2923no—
834C4—2923no—
835C4—736no—
836C4—1466no—
837C4—1462no—
838C4—1462no—
839C4—1461no—
840C4—1463no—
841C4—1463no—
842C4—1461no—
843C4C2×D4×#6440816yes—
844C2—41no—
845C2—43no—
846C2—2923no—
847C2—2921no—
848C2—731no—
849C2—731no—
850C2—731no—
851C2—731no—
852C2C22×D4×#6440811yescharacteristic
853C2#2262691111yescharacteristic
854C22−1+4×#6440811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
Fitting#548×C73C4
prime radical#548×D73C2
cosocleC22×D73C25
hypercenter#548#64408
hypocenterC73#34312
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#17989656C2semidirect
2. C2×#17989655C2semidirect
3. #22626462C2semidirect
4. #22626458C2semidirect
5. #22626455C2semidirect
6. #22626447C2semidirect
7. #22626446C2semidirect
8. #22626436C2semidirect
9. Q8×C22⋊#64408C2semidirect
10. #22626419C2semidirect
11. #22626418C2semidirect
12. #124×#64408C2semidirect
13. #22626388C2semidirect
14. C4×Q8×#64408C2semidirect
63. #17989249C4semidirect
64. #17989248C4semidirect
65. #17989247C4semidirect
66. #17989246C4semidirect
67. #17989245C4semidirect
68. #17989244C4semidirect
69. #17989243C4semidirect
75. #548×C73C4semidirect
82. Q8×#64408D4semidirect
131. C22×Dic146C2×C4semidirect
134. C2×Q8×D73C2×C4semidirect
135. C2×Q8×D73C2×C4semidirect
142. #14556580C2×C4semidirect
143. #14556579C2×C4semidirect
144. #14556578C2×C4semidirect
145. #14556577C2×C4semidirect
146. #14556577C2×C4semidirect
147. #14556571C2×C4semidirect
148. #14556570C2×C4semidirect
149. #14556569C2×C4semidirect
150. #14556568C2×C4semidirect
151. #14556567C2×C4semidirect
152. #14556566C2×C4semidirect
153. #14556565C2×C4semidirect
154. #14556564C2×C4semidirect
155. #14556563C2×C4semidirect
156. #14556562C2×C4semidirect
157. Q8×Dic73C2×C4semidirect
158. C4×Dic146C2×C4semidirect
159. #14556556C2×C4semidirect
160. C4×D292C2×C4semidirect
161. D4×Dic73C2×C4semidirect
162. #14556553C2×C4semidirect
163. C4×C22⋊D73C2×C4semidirect
164. C4×C22⋊D73C2×C4semidirect
165. #14556551C2×C4semidirect
166. #14556551C2×C4semidirect
174. C22×Q8×C73C2×C4semidirect
175. #124×C73C2×C4semidirect
176. C22⋊Q8×C73C2×C4semidirect
177. #121×C73C2×C4semidirect
178. C4×Q8×C73C2×C4semidirect
179. C4×D4×C73C2×C4semidirect
443. C73#34312semidirect
453. #548#64408semidirect
517. C22×Q8C2×#64408semidirect
528. #124C2×#64408semidirect
534. C22⋊Q8C2×#64408semidirect
540. #121C2×#64408semidirect
550. C4×Q8C2×#64408semidirect
560. C4×D4C2×#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179896562
C2×#179896552
#226264622
#226264582
#226264552
#226264472
#226264462
#226264362
Q8×C22⋊#644082
#226264192
#226264182
#124×#644082
#226263882
C4×Q8×#644082
#548×D732
#3431273