Finite Group Databasebeta

← #32991502

Subgroups — #32991502

Order 18688.

1350 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×#17989067C211yesmaximal, characteristic
2C22×#14556517C211yesmaximal, characteristic
3C2×#17988586C211yesmaximal, characteristic
4C2×#17988355C211yesmaximal, characteristic, complemented
5C2×#17988346C211yesmaximal, characteristic, complemented
6#22608160C211yesmaximal, characteristic, complemented
7C73×#1736C211yesmaximal, characteristic, complemented
8C22×#11924028C2211yescharacteristic
9C22×#11924012C2211yescharacteristic
10#17989067—22no—
11#17989067—22no—
12#17989067—22no—
13#17989067C414yescomplemented
14C2×C4×Dic146—21no—
15C2×C4×D292—21no—
16C2×#14556551—22no—
17C2×#14556549—21no—
18C22×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊C4×D73—21no—
20C22×C4×Dic73C2211yescharacteristic
21C2×#14556517—22no—
22C2×#14556517—22no—
23C2×#14556517C414yescomplemented
24#17988586—22no—
25#17988586C414yescomplemented
26C2×#14556514—21no—
27C2×#14556511—21no—
28C2×#14556498—22no—
29#17988355—22no—
30#17988346—22no—
31C22×M16×C73C2211yescharacteristic
32C2×#117×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34#340×C73—21no—
35#340×C73—21no—
36C2×#11924028—21no—
37C2×#11924028—21no—
38C2×#11924028—21no—
39C2×#11924028—21no—
40C2×#11924028—21no—
41C2×#11924028—21no—
42C2×#11924028C2×C412yes—
43C2×#11924028C2×C412yes—
44C2×#11924028C2×C412yes—
45C2×#11924028D412yes—
46C2×#11924028D412yes—
47C2×#11924028Q812yes—
48C22×Dic146D411yescharacteristic
49C22×D292D411yescharacteristic
50C22×C22⋊D73—21no—
51C23×Dic73—21no—
52C23×Dic73D412yes—
53C22×C4×D73—22no—
54C22×C4×D73—21no—
55C2×#11924012—21no—
56C2×#11924012—21no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012—21no—
60C2×#11924012C2×C412yescomplemented
61C22×#10596831—21no—
62C4×Dic146—24no—
63C4×Dic146—24no—
64C4×D292—24no—
65C4×D292—24no—
66#14556551—28no—
67#14556551—28no—
68#14556549—24no—
69#14556549—24no—
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73C2×C412yes—
75C2×C4⋊Dic73D412yes—
76C2×#11924007—22no—
77C4⋊C4×D73—24no—
78C4⋊C4×D73—24no—
79C2×#11924005—22no—
80C2×C4×Dic73—22no—
81C2×C4×Dic73—21no—
82C2×C4×Dic73—21no—
83C2×C4×Dic73—21no—
84C2×C4×Dic73—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73C2×C412yescomplemented
87#14556517—28no—
88#14556514—24no—
89#14556511—24no—
90#14556498—44no—
91C23×C4×C73—21no—
92C23×C4×C73C2311yescharacteristic
93C2×M16×C73—21no—
94C2×M16×C73—21no—
95C2×M16×C73—21no—
96C2×M16×C73—21no—
97C2×M16×C73—21no—
98C2×M16×C73C2×C412yescomplemented
99C22×C8×C73—21no—
100#117×C73—21no—
101#117×C73—21no—
102#117×C73C2×C412yes—
103#117×C73D412yes—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73C2×C412yescomplemented
110C2×C4⋊C4×C73D411yescharacteristic
111C2×C4⋊C4×C73D411yescharacteristic
112C2×C22⋊C4×C73—21no—
113C2×C42×C73—21no—
114C23×D73—21no—
115#11924028—22no—
116#11924028—22no—
117#11924028—22no—
118#11924028—22no—
119#11924028—22no—
120#11924028—22no—
121#11924028—22no—
122#11924028—22no—
123#11924028—22no—
124#11924028—22no—
125#11924028—22no—
126#11924028—22no—
127#11924028C4214yes—
128#11924028C22⋊C414yes—
129#11924028C4⋊C414yes—
130#11924028C4⋊C414yes—
131C2×Dic146—21no—
132C2×Dic146—21no—
133C2×Dic146—21no—
134C2×Dic146C22⋊C412yes—
135C2×Dic146C22⋊C412yes—
136C2×Dic146C4⋊C412yes—
137C2×D292—21no—
138C2×D292—21no—
139C2×D292—21no—
140C2×D292C22⋊C412yes—
141C2×D292C22⋊C412yes—
142C2×D292C4⋊C412yes—
143C2×C22⋊D73—22no—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C22×Dic73—21no—
150C22×Dic73—22no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—22no—
155C22×Dic73—41no—
156C22×Dic73—41no—
157C22×Dic73—41no—
158C22×Dic73—41no—
159C22×Dic73—42no—
160C22×Dic73—42no—
161C22×Dic73C22⋊C414yes—
162C2×C4×D73—22no—
163C2×C4×D73—22no—
164C2×C4×D73—22no—
165C2×C4×D73—22no—
166C2×C4×D73—22no—
167C2×C4×D73—22no—
168C2×C4×D73—28no—
169C2×C4×D73—82no—
170C2×C4×D73—82no—
171#11924012—22no—
172#11924012—22no—
173#11924012—41no—
174#11924012—41no—
175C2×#10596831—22no—
176C2×#10596831—41no—
177C2×#10596831—41no—
178C4⋊Dic73—22no—
179C4⋊Dic73—22no—
180C4⋊Dic73—22no—
181C4⋊Dic73—22no—
182#11924007—28no—
183#11924005—28no—
184C4×Dic73—28no—
185C4×Dic73—22no—
186C4×Dic73—22no—
187C4×Dic73—41no—
188C4×Dic73—41no—
189C24×C73C2×D411yescharacteristic
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—22no—
193C22×C4×C73—42no—
194C22×C4×C73—42no—
195C22×C4×C73—41no—
196C22×C4×C73—41no—
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×Q811yescharacteristic
207C22×C4×C73#4111yescharacteristic
208C22×C4×C73#4111yescharacteristic
209C22×C4×C73#4111yescharacteristic
210C22×C4×C73#4111yescharacteristic
211M16×C73—22no—
212M16×C73—22no—
213M16×C73—41no—
214M16×C73—41no—
215C2×C8×C73—22no—
216C2×C8×C73—41no—
217C2×C8×C73—41no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—41no—
223C4⋊C4×C73—41no—
224C4⋊C4×C73C22⋊C412yes—
225C4⋊C4×C73C22⋊C412yes—
226C22⋊C4×C73—22no—
227C22⋊C4×C73—22no—
228C42×C73—22no—
229C42×C73—22no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73C2×C22⋊C411yescharacteristic
235C23×C73C4×D411yescharacteristic
236C23×C73C4×D411yescharacteristic
237C23×C73#12011yescharacteristic
238C23×C73#12011yescharacteristic
239C23×C73#12111yescharacteristic
240C23×C73C22⋊Q811yescharacteristic
241C22×D73—22no—
242C22×D73—22no—
243C22×D73—22no—
244C22×D73—41no—
245C22×D73—41no—
246C22×D73—41no—
247C22×D73—41no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—44no—
255C2×C4×C73—42no—
256C2×C4×C73—82no—
257C2×C4×C73—81no—
258C2×C4×C73—81no—
259C2×C4×C73C2×C4211yescharacteristic
260C2×C4×C73C2×C22⋊C411yescharacteristic
261C2×C4×C73C2×C22⋊C411yescharacteristic
262C2×C4×C73C2×C22⋊C411yescharacteristic
263C2×C4×C73C2×C22⋊C411yescharacteristic
264C2×C4×C73C2×C4⋊C411yescharacteristic
265C2×C4×C73C2×C4⋊C411yescharacteristic
266C2×C4×C73C2×C4⋊C411yescharacteristic
267C2×C4×C73#11711yescharacteristic
268C2×C4×C73#11711yescharacteristic
269C2×C4×C73C4×D411yescharacteristic
270C2×C4×C73C4×D411yescharacteristic
271C2×C4×C73C4×D411yescharacteristic
272C2×C4×C73C4×D411yescharacteristic
273C2×C4×C73C4×D411yescharacteristic
274C2×C4×C73C4×D411yescharacteristic
275C2×C4×C73#12011yescharacteristic
276C2×C4×C73#12011yescharacteristic
277C2×C4×C73#12111yescharacteristic
278C2×C4×C73#12111yescharacteristic
279C2×C4×C73#12111yescharacteristic
280C2×C4×C73C22⋊Q811yescharacteristic
281C2×C4×C73C22⋊Q811yescharacteristic
282C2×C4×C73C22⋊Q811yescharacteristic
283C2×C4×C73#12311yescharacteristic
284C2×C4×C73#12311yescharacteristic
285C2×C4×C73#12311yescharacteristic
286C2×C4×C73#12311yescharacteristic
287C22⋊D73—24no—
288C22⋊D73—24no—
289C22⋊D73—24no—
290C22⋊D73—24no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—24no—
295C2×Dic73—24no—
296C2×Dic73—42no—
297C2×Dic73—42no—
298C2×Dic73—42no—
299C2×Dic73—42no—
300C2×Dic73—42no—
301C2×Dic73—42no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73—44no—
305C2×Dic73—82no—
306D292—22no—
307D292—22no—
308D292—22no—
309D292#9514yescomplemented
310C4×D73—24no—
311C4×D73—24no—
312C4×D73—24no—
313C4×D73—24no—
314C4×D73—88no—
315Dic146—22no—
316Dic146—22no—
317Dic146—22no—
318Dic146#9514yescomplemented
319C8×C73—42no—
320#10596831—42no—
321C22×C73—21no—
322C22×C73—21no—
323C22×C73—21no—
324C22×C73—21no—
325C22×C73—21no—
326C22×C73—21no—
327C22×C73—21no—
328C22×C73—21no—
329C22×C73—21no—
330C22×C73—21no—
331C22×C73—21no—
332C22×C73—21no—
333C22×C73C4×C22⋊C411yescharacteristic
334C22×C73#37911yescharacteristic
335C22×C73#38011yescharacteristic
336C22×C73#38511yescharacteristic
337C22×C73#38511yescharacteristic
338C22×C73#38611yescharacteristic
339C22×C73#38611yescharacteristic
340C22×C73#45311yescharacteristic
341C22×C73#45411yescharacteristic
342C22×C73#45511yescharacteristic
343C22×C73#45611yescharacteristic
344C2×D73—24no—
345C2×D73—42no—
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—42no—
349C2×D73—42no—
350C2×D73—42no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—82no—
354C4×C73C2×#9511yescharacteristic
355C4×C73C4×C22⋊C411yescharacteristic
356C4×C73#38011yescharacteristic
357C4×C73#38111yescharacteristic
358C4×C73#38511yescharacteristic
359C4×C73#38511yescharacteristic
360C4×C73#38611yescharacteristic
361C4×C73#38611yescharacteristic
362Dic73—24no—
363Dic73—44no—
364Dic73—44no—
365#10781—731nomaximal, Sylow
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—21no—
369C2×C73—21no—
370C2×C73C22⋊#9511yescharacteristic
371C2×C73#179211yescharacteristic
372C2×C73#179311yescharacteristic
373C2×C73#185911yescharacteristic
374C2×C73#186011yescharacteristic
375C2×C73#188211yescharacteristic
376C2×C73#188311yescharacteristic
377D73—44no—
378C2×#520—731no—
379C22×#104—731no—
380C2×#417—731no—
381C2×#343—731no—
382#1736D7311yescharacteristic, complemented
383C2×#339—731no—
384C4⋊#95—731no—
385C73#1078111yescharacteristic, complemented, Sylow
386C22×#41—731no—
387C22×M16—731no—
388C22×M16C2×D7311yescharacteristic
389#520—734no—
390#520—1462no—
391#520—1462no—
392#520—1462no—
393C2×C4×Q8—1461no—
394C2×C4×D4—1461no—
395C2×C4×D4—1462no—
396C2×#117—1461no—
397C2×#117C2×D7311yescharacteristic
398C22×C4⋊C4—731no—
399C22×C4⋊C4—1461no—
400C22×C4⋊C4C2×D7311yescharacteristic
401C22×C42—731no—
402C2×#104—734no—
403C2×#104—1462no—
404C2×#104—1462no—
405#417—734no—
406#417—1462no—
407C2×#103—1461no—
408C2×#102—1461no—
409C2×#95—1462no—
410#343—1462no—
411#340—21no—
412#340—21no—
413#339—1462no—
414C2×#41—732no—
415C2×#41—732no—
416C2×#41—732no—
417C2×#41—732no—
418C2×#41—732no—
419C2×#41—732no—
420C2×#41—1461no—
421C2×#41—1461no—
422C2×#41—1461no—
423C2×#41—1461no—
424C2×#41—1461no—
425C2×#41—1461no—
426C22×Q8—731no—
427C22×D4—731no—
428C22×D4—1461no—
429C23×C4—21no—
430C23×C4—732no—
431C23×C4—1462no—
432C23×C4—1461no—
433C23×C4—1461no—
434C23×C4C22×D7311yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—732no—
441C2×M16—1461no—
442C2×M16—1461no—
443C2×M16—1461no—
444C2×M16—1461no—
445C2×M16—1461no—
446C2×M16C4×D7312yescomplemented
447C22×C8—21no—
448C22×C8—1461no—
449C4×Q8—1464no—
450C4×Q8—1464no—
451C4×D4—1464no—
452C4×D4—1464no—
453C4×D4—1468no—
454C4×D4—1468no—
455#117—21no—
456#117—21no—
457#117—1464no—
458#117—1464no—
459#117C4×D7312yes—
460#117D29212yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—732no—
467C2×C4⋊C4—732no—
468C2×C4⋊C4—1464no—
469C2×C4⋊C4—1462no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1464no—
475C2×C4⋊C4C4×D7312yescomplemented
476C2×C4⋊C4C22⋊D7311yescharacteristic
477C2×C4⋊C4C22⋊D7311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1462no—
480C2×C42—21no—
481C2×C42—732no—
482C2×C42—1461no—
483C2×C42—1461no—
484C2×C42—1461no—
485C2×C42—1461no—
486C2×C42—1461no—
487C2×C42—1462no—
488#104—1468no—
489#103—1464no—
490#102—1464no—
491#95—2924no—
492C24—1461no—
493C24D4×D7311yescharacteristic
494#41—734no—
495#41—734no—
496#41—734no—
497#41—734no—
498#41—1462no—
499#41—1462no—
500#41—1462no—
501#41—1462no—
502#41—1462no—
503#41—1462no—
504#41—1462no—
505#41—1462no—
506#41—1462no—
507#41—1462no—
508#41—1462no—
509#41—1462no—
510C2×Q8—732no—
511C2×Q8—732no—
512C2×Q8—732no—
513C2×Q8—1461no—
514C2×Q8—1461no—
515C2×Q8—1461no—
516C2×D4—732no—
517C2×D4—732no—
518C2×D4—732no—
519C2×D4—1462no—
520C2×D4—1462no—
521C2×D4—1462no—
522C2×D4—1462no—
523C2×D4—1462no—
524C2×D4—1462no—
525C2×D4—1461no—
526C2×D4—1461no—
527C2×D4—1461no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—2921no—
536C22×C4—2921no—
537C22×C4—2921no—
538C22×C4—2921no—
539C22×C4—2922no—
540C22×C4—2922no—
541C22×C4—5842no—
542C22×C4—5842no—
543C22×C4—734no—
544C22×C4—1468no—
545C22×C4—1462no—
546C22×C4—1462no—
547C22×C4—1462no—
548C22×C4—1462no—
549C22×C4—1462no—
550C22×C4—1461no—
551C22×C4—1462no—
552C22×C4—1462no—
553C22×C4—1462no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4C2×C4×D7311yescharacteristic
558C22×C4C2×C4×D7311yescharacteristic
559C22×C4C2×C4×D7311yescharacteristic
560C22×C4D4×D7311yescharacteristic
561C22×C4D4×D7311yescharacteristic
562C22×C4D4×D7311yescharacteristic
563C22×C4D4×D7311yescharacteristic
564C22×C4C2×C22⋊D7311yescharacteristic
565C22×C4C2×D29211yescharacteristic
566C22×C4Q8×D7311yescharacteristic
567C22×C4#1192402711yescharacteristic
568C22×C4#1192402811yescharacteristic
569C22×C4#1192402811yescharacteristic
570C22×C4#1192402911yescharacteristic
571M16—22no—
572M16—22no—
573M16—41no—
574M16—41no—
575M16—2921no—
576M16—2921no—
577M16—1462no—
578M16—1462no—
579C2×C8—22no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—2921no—
583C2×C8—2921no—
584C2×C8—1462no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—1468no—
592C4⋊C4—1462no—
593C4⋊C4—1462no—
594C4⋊C4—1462no—
595C4⋊C4—1462no—
596C4⋊C4#1192400512yes—
597C4⋊C4#1192400512yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—1468no—
601C42—22no—
602C42—22no—
603C42—2921no—
604C42—2921no—
605C42—1468no—
606C42—1462no—
607C42—1462no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—2921no—
613C23—2921no—
614C23—2921no—
615C23—2921no—
616C23—1462no—
617C23—1462no—
618C23—1462no—
619C23C22⋊C4×D7311yescharacteristic
620C23#1455655111yescharacteristic
621C23#1455655311yescharacteristic
622C23#1455655911yescharacteristic
623C23#1455656111yescharacteristic
624C23#1455656411yescharacteristic
625C23#1455656911yescharacteristic
626Q8—734no—
627Q8—1462no—
628Q8—1462no—
629Q8—1462no—
630D4—734no—
631D4—1464no—
632D4—1464no—
633D4—1464no—
634D4—1464no—
635D4—1462no—
636D4—1462no—
637D4—1462no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—44no—
645C2×C4—42no—
646C2×C4—82no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—2922no—
650C2×C4—2922no—
651C2×C4—2922no—
652C2×C4—2922no—
653C2×C4—2922no—
654C2×C4—2922no—
655C2×C4—2922no—
656C2×C4—2922no—
657C2×C4—2924no—
658C2×C4—5848no—
659C2×C4—5842no—
660C2×C4—1464no—
661C2×C4—1464no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1464no—
666C2×C4—1464no—
667C2×C4—1464no—
668C2×C4—1464no—
669C2×C4C42×D7311yescharacteristic
670C2×C4C22⋊C4×D7311yescharacteristic
671C2×C4C22⋊C4×D7311yescharacteristic
672C2×C4C22⋊C4×D7311yescharacteristic
673C2×C4C2×#1192400511yescharacteristic
674C2×C4C4⋊C4×D7311yescharacteristic
675C2×C4C4⋊C4×D7311yescharacteristic
676C2×C4C4⋊C4×D7311yescharacteristic
677C2×C4#1455654811yescharacteristic
678C2×C4#1455654911yescharacteristic
679C2×C4#1455655111yescharacteristic
680C2×C4C4×C22⋊D7311yescharacteristic
681C2×C4C4×C22⋊D7311yescharacteristic
682C2×C4#1455655311yescharacteristic
683C2×C4C4×D29211yescharacteristic
684C2×C4C4×D29211yescharacteristic
685C2×C4#1455655911yescharacteristic
686C2×C4#1455656111yescharacteristic
687C2×C4#1455656211yescharacteristic
688C2×C4#1455656411yescharacteristic
689C2×C4#1455656611yescharacteristic
690C2×C4#1455656711yescharacteristic
691C2×C4#1455656911yescharacteristic
692C2×C4#1455657111yescharacteristic
693C2×C4#1455657311yescharacteristic
694C2×C4#1455657311yescharacteristic
695C2×C4#1455657611yescharacteristic
696C2×C4#1455657611yescharacteristic
697C8—42no—
698C8—2922no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—2922no—
712C22—2922no—
713C22—2922no—
714C22—2922no—
715C22—2922no—
716C22—2922no—
717C22—1464no—
718C22#1798843411yescharacteristic
719C22#1798844211yescharacteristic
720C22#1798844611yescharacteristic
721C22#1798845811yescharacteristic
722C22#1798846111yescharacteristic
723C22#1798846311yescharacteristic
724C22#1798846511yescharacteristic
725C22#1798875311yescharacteristic
726C22#1798875811yescharacteristic
727C22#1798876311yescharacteristic
728C22#1798876811yescharacteristic
729C4—42no—
730C4—42no—
731C4—82no—
732C4—2924no—
733C4—2924no—
734C4—1464no—
735C4#95×D7311yescharacteristic
736C4C4×#1192400511yescharacteristic
737C4#1798844411yescharacteristic
738C4#1798844911yescharacteristic
739C4#1798845811yescharacteristic
740C4#1798846111yescharacteristic
741C4#1798846311yescharacteristic
742C4#1798846511yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—2924no—
748C2#2260815211yescharacteristic
749C2#2260988311yescharacteristic
750C2#2260988811yescharacteristic
751C2#2261015411yescharacteristic
752C2#2261016111yescharacteristic
753C2#2261029711yescharacteristic
754C2#2261030411yescharacteristic
subgroupG/H
centerC23#14556559
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC73×#1736C2
socleC23×C73#120
prime radicalC22×#11924028C22
cosocleC23×C4×C73C23
hypercenter#1736D73
hypocenterC73#10781
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#17988355C2semidirect
5. C2×#17988346C2semidirect
6. #22608160C2semidirect
7. C73×#1736C2semidirect
13. #17989067C4semidirect
23. C2×#14556517C4semidirect
25. #17988586C4semidirect
60. C2×#11924012C2×C4semidirect
86. C2×C4×Dic73C2×C4semidirect
98. C2×M16×C73C2×C4semidirect
109. C2×C4⋊C4×C73C2×C4semidirect
309. D292#95semidirect
318. Dic146#95semidirect
382. #1736D73semidirect
385. C73#10781semidirect
446. C2×M16C4×D73semidirect
475. C2×C4⋊C4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890672
C22×#145565172
C2×#179885862
C2×#179883552
C2×#179883462
#226081602
C73×#17362
#1078173