Finite Group Databasebeta

← #33106365

Subgroups — #33106365

Order 18688.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988688C211yesmaximal, characteristic, complemented
2C2×#17988588C211yesmaximal, characteristic
3#22612940C211yesmaximal, characteristic, complemented
4#22612761C211yesmaximal, characteristic
5#22610793C211yesmaximal, characteristic, complemented
6#22610623C211yesmaximal, characteristic, complemented
7#22610574C211yesmaximal, characteristic, complemented
8#22610365C211yesmaximal, characteristic, complemented
9#22610274C211yesmaximal, characteristic, complemented
10#22610267C211yesmaximal, characteristic, complemented
11#22610180C211yesmaximal, characteristic, complemented
12#22610121C211yesmaximal, characteristic, complemented
13#102×Dic73C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C2×#452×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C2×Q8×Dic73C2211yescharacteristic
18C2×D4×Dic73C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21#17988688—24no—
22C2×#14556525C2211yescharacteristic
23C2×#14556525C2211yescharacteristic
24#17988588—24no—
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33#17988494C2211yescharacteristic
34#17988494C2211yescharacteristic
35#17988494C2211yescharacteristic
36#17988486—21no—
37#17988486C2211yescharacteristic
38#17988473—21no—
39#17988467—21no—
40#17988467—21no—
41#17988462—21no—
42#17988450—21no—
43#17988447C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45C22⋊C4×Dic73—21no—
46C4×C22⋊Dic73C2211yescharacteristic
47C2×#14556498—21no—
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C22×#41×C73C2211yescharacteristic
55C22×Q16×C73C2211yescharacteristic
56C22×SD16×C73C2211yescharacteristic
57C2×C22⋊Q8×C73C2211yescharacteristic
58#452×C73C418yescomplemented
59C2×#103×C73C2211yescharacteristic
60C2×#102×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C23×Dic73—21no—
63C23×Dic73—21no—
64C23×Dic73—21no—
65C2×#11924012—22no—
66C2×#11924012—22no—
67C2×#11924012—41no—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70Q8×Dic73—22no—
71Q8×Dic73—41no—
72D4×Dic73—22no—
73D4×Dic73—22no—
74D4×Dic73—41no—
75D4×Dic73—41no—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73—41no—
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73D411yescharacteristic
89C2×C22⋊Dic73D411yescharacteristic
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94#14556525—22no—
95#14556525—41no—
96#14556515—22no—
97#14556515—22no—
98#14556515—22no—
99#14556515—41no—
100#14556512—22no—
101#14556512D414yes—
102#14556501—22no—
103C8×Dic73—41no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498D411yescharacteristic
114#14556498D411yescharacteristic
115C2×#41×C73—22no—
116C2×#41×C73—22no—
117C2×#41×C73—22no—
118C2×#41×C73—41no—
119C2×#41×C73—41no—
120C2×#41×C73C2×C414yes—
121C22×Q8×C73C2311yescharacteristic
122C22×Q8×C73C2311yescharacteristic
123C22×D4×C73—21no—
124C22×D4×C73C2311yescharacteristic
125C23×C4×C73—21no—
126C23×C4×C73C2311yescharacteristic
127C2×Q16×C73—41no—
128C2×Q16×C73—41no—
129C2×Q16×C73C2×C414yescomplemented
130C2×SD16×C73—22no—
131C2×SD16×C73—22no—
132C2×SD16×C73C2×C414yescomplemented
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22⋊Q8×C73—22no—
136C22⋊Q8×C73C2×C414yescomplemented
137C2×C4⋊C4×C73—21no—
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140#103×C73C2×C414yescomplemented
141#102×C73C2×C414yescomplemented
142C22⋊C8×C73C2×C414yescomplemented
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—42no—
148C22×Dic73—42no—
149C22×Dic73—42no—
150C22×Dic73—42no—
151C22×Dic73—42no—
152C22×Dic73—42no—
153C22×Dic73—81no—
154C22×Dic73—81no—
155C22×Dic73—81no—
156C22×Dic73C2×D411yescharacteristic
157C22×Dic73C2×D411yescharacteristic
158C22×Dic73C2×D411yescharacteristic
159C22×Dic73C2×D411yescharacteristic
160#11924012—44no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831C2×D412yes—
167C4⋊Dic73—21no—
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—21no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—42no—
175C4⋊Dic73—42no—
176C4⋊Dic73—81no—
177C4⋊Dic73C2×D412yes—
178C22⋊Dic73—22no—
179C22⋊Dic73—41no—
180C22⋊Dic73—42no—
181C22⋊Dic73—42no—
182C22⋊Dic73—81no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—42no—
188C4×Dic73—81no—
189C24×C73—21no—
190C24×C73C2×D411yescharacteristic
191#41×C73—28no—
192#41×C73—44no—
193#41×C73—44no—
194#41×C73—44no—
195C2×Q8×C73—21no—
196C2×Q8×C73—21no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C2×Q8×C73—21no—
201C2×Q8×C73—21no—
202C2×Q8×C73—21no—
203C2×Q8×C73—21no—
204C2×Q8×C73—21no—
205C2×Q8×C73C22×C412yes—
206C2×Q8×C73C22×C412yes—
207C2×D4×C73—24no—
208C2×D4×C73—21no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—42no—
212C2×D4×C73—42no—
213C2×D4×C73C22×C412yes—
214C2×D4×C73C2×D412yes—
215C2×D4×C73#4112yes—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—24no—
224C22×C4×C73—42no—
225C22×C4×C73—42no—
226C22×C4×C73C22×C412yes—
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73#4112yes—
229C22×C4×C73C2411yescharacteristic
230Q16×C73—44no—
231SD16×C73—28no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73C22×C412yes—
237C2×C8×C73C22×C412yes—
238C4⋊C4×C73—24no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73C22×C412yes—
241C22⋊C4×C73—24no—
242C23×C73—22no—
243C23×C73—21no—
244C23×C73—22no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—22no—
260Q8×C73—22no—
261Q8×C73—41no—
262Q8×C73—41no—
263Q8×C73—41no—
264Q8×C73—41no—
265D4×C73—22no—
266D4×C73—22no—
267D4×C73—22no—
268D4×C73—48no—
269D4×C73C4×D414yes—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—48no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73C4×D412yes—
287C2×C4×C73C23×C411yescharacteristic
288C2×C4×C73C22×D411yescharacteristic
289C2×C4×C73C2×#4111yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C2×C4×C73H(5,𝔽2)11yescharacteristic
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—22no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—84no—
317C2×Dic73—84no—
318C2×Dic73—84no—
319C2×Dic73#13712yes—
320C8×C73—22no—
321C8×C73—22no—
322#10596831—22no—
323#10596831—41no—
324C22×C73—22no—
325C22×C73—24no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—41no—
331C22×C73—42no—
332C22×C73—41no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—42no—
338C22×C73C2×C4×D411yescharacteristic
339C22×C73D4211yescharacteristic
340C22×C73#54611yescharacteristic
341C22×C73C2×#13711yescharacteristic
342C22×C73#57511yescharacteristic
343C22×C73#57611yescharacteristic
344C22×C73#57811yescharacteristic
345C4×C73—22no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73C2×C4×D411yescharacteristic
350C4×C73#51811yescharacteristic
351C4×C73#54611yescharacteristic
352C4×C73#55111yescharacteristic
353Dic73—22no—
354Dic73—41no—
355Dic73—42no—
356Dic73—41no—
357Dic73—41no—
358Dic73—81no—
359Dic73—81no—
360Dic73—81no—
361#22862—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—44no—
364C2×C73#235811yescharacteristic
365C2×C73C4×#13711yescharacteristic
366C2×C73#295111yescharacteristic
367C2×C73#327311yescharacteristic
368C2×C73#327611yescharacteristic
369C2×C73#331411yescharacteristic
370C2×C73#331511yescharacteristic
371C2×#452D7311yescharacteristic
372C2×#440—731no—
373C2×#417—731no—
374#2360—731no—
375#2339—731no—
376#1969—731no—
377#1935—731no—
378#1928—731no—
379#1894—731no—
380#1878—731no—
381#1877—731no—
382#1862—731no—
383#1852—731no—
384C4×#102—731no—
385#1753—731no—
386C73#2286211yescharacteristic, complemented, Sylow
387C22×#41C2×D7311yescharacteristic
388C22×Q16C2×D7311yescharacteristic
389C22×SD16C2×D7311yescharacteristic
390C22×M16—731no—
391C2×C22⋊Q8C2×D7311yescharacteristic
392C2×C4×Q8—731no—
393C2×C4×D4—731no—
394C2×C4×D4—731no—
395C22×C4⋊C4—731no—
396#452Dic7318yescomplemented
397#440—1464no—
398C2×#107—731no—
399C2×#107—731no—
400#417—1464no—
401C2×#103—731no—
402C2×#103—731no—
403C2×#103—731no—
404C2×#103—731no—
405C2×#103C2×D7311yescharacteristic
406C2×#102—731no—
407C2×#102—731no—
408C2×#102C2×D7311yescharacteristic
409C2×C22⋊C8C2×D7311yescharacteristic
410C2×#97—731no—
411C2×C4×C8—731no—
412#391—731no—
413#391—731no—
414#391—731no—
415#389—731no—
416#389—1461no—
417#387—1461no—
418#386—1461no—
419#386—1461no—
420#385—1461no—
421#381—1461no—
422#380—731no—
423C4×C4⋊C4—731no—
424C4×C22⋊C4—731no—
425C4×C22⋊C4—1461no—
426C2×#95—1461no—
427#340—731no—
428#340—731no—
429#340—731no—
430#340—731no—
431#336—731no—
432#336—731no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C2×#41C2×Dic7314yes—
439C22×Q8C22×D7311yescharacteristic
440C22×Q8C22×D7311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D7311yescharacteristic
443C23×C4—21no—
444C23×C4—1461no—
445C23×C4—1461no—
446C23×C4—1461no—
447C23×C4C22×D7311yescharacteristic
448C2×Q16—41no—
449C2×Q16—41no—
450C2×Q16C2×Dic7314yescomplemented
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16C2×Dic7314yescomplemented
454C2×M16—2921no—
455C2×M16—1462no—
456C2×M16—1462no—
457C22×C8—731no—
458C22×C8—731no—
459C22×C8C22×D7311yescharacteristic
460C22×C8C22×D7311yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8C2×Dic7314yescomplemented
463C4×Q8—2921no—
464C4×Q8—1462no—
465C4×D4—2921no—
466C4×D4—2921no—
467C4×D4—1462no—
468C4×D4—1462no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—2921no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—731no—
473C2×C4⋊C4—731no—
474C2×C4⋊C4—731no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4—1461no—
477C2×C4⋊C4—1462no—
478C2×C4⋊C4—1461no—
479C2×C4⋊C4C22×D7311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—731no—
482C2×C22⋊C4—731no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C22⋊C4—1461no—
486C2×C42—731no—
487C2×C42—731no—
488C2×C42—1461no—
489C2×C42—1461no—
490#107—2921no—
491#107—1462no—
492#103—2921no—
493#103—1462no—
494#103—1462no—
495#103—1462no—
496#103C2×Dic7314yescomplemented
497#102—734no—
498#102—1462no—
499#102C2×Dic7314yescomplemented
500C22⋊C8C2×Dic7314yescomplemented
501#97—1462no—
502C4×C8—2921no—
503#95—731no—
504#95—731no—
505#95—1461no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511#95—1461no—
512#95—1461no—
513#95—1461no—
514C24—21no—
515C24D4×D7311yescharacteristic
516#41—28no—
517#41—44no—
518#41—44no—
519#41—44no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8C22×Dic7312yes—
531C2×Q8C22×Dic7312yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C22×Dic7312yes—
539C2×D4D4×D7312yes—
540C2×D4#1192402712yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—2922no—
552C22×C4—2922no—
553C22×C4—2922no—
554C22×C4—2922no—
555C22×C4—2922no—
556C22×C4—2922no—
557C22×C4—5841no—
558C22×C4—5841no—
559C22×C4—5841no—
560C22×C4—731no—
561C22×C4—731no—
562C22×C4—731no—
563C22×C4—731no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4C22×Dic7312yes—
569C22×C4D4×D7311yescharacteristic
570C22×C4#1192402712yes—
571C22×C4C23×D7311yescharacteristic
572Q16—44no—
573SD16—28no—
574M16—2924no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—732no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C2×C8C22×Dic7312yes—
586C2×C8C22×Dic7312yes—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—2922no—
590C4⋊C4—2922no—
591C4⋊C4—5841no—
592C4⋊C4—732no—
593C4⋊C4—1461no—
594C4⋊C4—1461no—
595C4⋊C4—1461no—
596C4⋊C4—1461no—
597C4⋊C4—1461no—
598C4⋊C4—1461no—
599C4⋊C4—1461no—
600C4⋊C4C22×Dic7312yes—
601C22⋊C4—24no—
602C22⋊C4—2922no—
603C22⋊C4—2922no—
604C22⋊C4—2921no—
605C22⋊C4—5841no—
606C22⋊C4—1462no—
607C42—2922no—
608C42—5841no—
609C42—1461no—
610C42—1461no—
611C42—1461no—
612C42—1461no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23D4×Dic7312yes—
627C23C2×D4×D7311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4D4×Dic7314yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—48no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—5844no—
669C2×C4—5844no—
670C2×C4—5844no—
671C2×C4—732no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1461no—
679C2×C4—1462no—
680C2×C4—1461no—
681C2×C4—1461no—
682C2×C4—1461no—
683C2×C4—1461no—
684C2×C4D4×Dic7312yes—
685C2×C4C23×Dic7311yescharacteristic
686C2×C4C2×D4×D7311yescharacteristic
687C2×C4C2×#1192402711yescharacteristic
688C2×C4C2×#1192402711yescharacteristic
689C2×C4#1455663611yescharacteristic
690C2×C4#1455663611yescharacteristic
691C8—22no—
692C8—22no—
693C8—2921no—
694C8—1462no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—22no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22C2×D4×Dic7311yescharacteristic
710C22#1798921911yescharacteristic
711C22#1798922411yescharacteristic
712C22#137×D7311yescharacteristic
713C22#1798938611yescharacteristic
714C22#1798938911yescharacteristic
715C22#1798940111yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2921no—
721C4—2922no—
722C4—2921no—
723C4—2921no—
724C4—5841no—
725C4—5841no—
726C4—5841no—
727C4—1462no—
728C4C2×D4×Dic7311yescharacteristic
729C4#1798906211yescharacteristic
730C4#1798922411yescharacteristic
731C4#1798926811yescharacteristic
732C2—42no—
733C2—44no—
734C2#2261291511yescharacteristic
735C2#137×Dic7311yescharacteristic
736C2#2261880711yescharacteristic
737C2#2262153511yescharacteristic
738C2#2262157511yescharacteristic
739C2#2262200511yescharacteristic
740C2#2262202011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#452×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#452D73
hypocenterC73#22862
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#17988688C2semidirect
3. #22612940C2semidirect
5. #22610793C2semidirect
6. #22610623C2semidirect
7. #22610574C2semidirect
8. #22610365C2semidirect
9. #22610274C2semidirect
10. #22610267C2semidirect
11. #22610180C2semidirect
12. #22610121C2semidirect
13. #102×Dic73C2semidirect
14. #22609717C2semidirect
58. #452×C73C4semidirect
129. C2×Q16×C73C2×C4semidirect
132. C2×SD16×C73C2×C4semidirect
136. C22⋊Q8×C73C2×C4semidirect
140. #103×C73C2×C4semidirect
141. #102×C73C2×C4semidirect
142. C22⋊C8×C73C2×C4semidirect
386. C73#22862semidirect
396. #452Dic73semidirect
450. C2×Q16C2×Dic73semidirect
453. C2×SD16C2×Dic73semidirect
462. C22⋊Q8C2×Dic73semidirect
496. #103C2×Dic73semidirect
499. #102C2×Dic73semidirect
500. C22⋊C8C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886882
C2×#179885882
#226129402
#226127612
#226107932
#226106232
#226105742
#226103652
#226102742
#226102672
#226101802
#226101212
#102×Dic732
#226097172
C2×#452×C732
#2286273