Finite Group Databasebeta

← #33102326

Subgroups — #33102326

Order 18688.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989241C211yesmaximal, characteristic
2C2×#17988659C211yesmaximal, characteristic, complemented
3#22610903C211yesmaximal, characteristic, complemented
4#22610879C211yesmaximal, characteristic, complemented
5#22610367C211yesmaximal, characteristic, complemented
6#22610357C211yesmaximal, characteristic, complemented
7#22610253C211yesmaximal, characteristic, complemented
8#22610248C211yesmaximal, characteristic, complemented
9#22610019C211yesmaximal, characteristic, complemented
10#22610015C211yesmaximal, characteristic, complemented
11#22609938C211yesmaximal, characteristic, complemented
12#22609759C211yesmaximal, characteristic, complemented
13#22609652C211yesmaximal, characteristic, complemented
14C2×#17988349C211yesmaximal, characteristic, complemented
15C73×#2352C211yesmaximal, characteristic, complemented
16C22×#11924027—21no—
17C22×#11924012C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19#17989241—24no—
20#17989241C418yescomplemented
21C2×#14556591C2211yescharacteristic
22C2×#14556575—21no—
23C2×#14556575—21no—
24C2×#14556571—21no—
25C2×#14556565C2211yescharacteristic
26C2×#14556565C2211yescharacteristic
27C2×C4×D292C2211yescharacteristic
28C22×C4⋊Dic73C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30#17988659—24no—
31C2×C4⋊#10596831C2211yescharacteristic
32C2×#14556511C2211yescharacteristic
33C2×#14556511C2211yescharacteristic
34C2×#14556511C2211yescharacteristic
35C2×#14556511C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic
38C2×#14556502C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51C2×C4×D4×C73C2211yescharacteristic
52C2×#117×C73C2211yescharacteristic
53C22×C4⋊C4×C73C2211yescharacteristic
54#388×C73—21no—
55#387×C73—21no—
56#386×C73—21no—
57#382×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60C4×C4⋊C4×C73C2211yescharacteristic
61C4×C22⋊C4×C73—21no—
62C2×#11924027—28no—
63C2×#11924027—44no—
64C2×#11924027—44no—
65C22×Dic146—21no—
66C22×D292C2311yescharacteristic
67C22×C22⋊D73—21no—
68C22×C22⋊D73—21no—
69C23×Dic73—21no—
70C23×Dic73—21no—
71C22×C4×D73—21no—
72C2×#11924012—22no—
73C2×#11924012—22no—
74C2×#11924012—41no—
75C22×#10596831—22no—
76C22×#10596831—22no—
77C22×#10596831—41no—
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82#14556591—22no—
83#14556591C2×C414yescomplemented
84#14556575—28no—
85#14556575—28no—
86#14556571—28no—
87#14556565—22no—
88#14556565—22no—
89#14556565C2×C414yes—
90#14556565C2×C414yescomplemented
91C4×D292—22no—
92C4×D292C2×C414yescomplemented
93C2×C4⋊Dic73—21no—
94C2×C4⋊Dic73—22no—
95C2×C4⋊Dic73—22no—
96C2×C4⋊Dic73—21no—
97C2×C4⋊Dic73—21no—
98C2×C4⋊Dic73C2×C414yes—
99C2×C4⋊Dic73C2×C414yescomplemented
100C2×C4⋊Dic73C2311yescharacteristic
101C2×C4⋊Dic73C2311yescharacteristic
102C2×C4⋊Dic73C2311yescharacteristic
103C2×#11924005—21no—
104C2×#11924005—21no—
105C2×#11924005—21no—
106C4⋊#10596831—22no—
107#14556511—22no—
108#14556511—22no—
109#14556511—41no—
110#14556511—41no—
111C22⋊#10596831—22no—
112C22⋊#10596831—22no—
113#14556502—22no—
114C22×D4×C73D411yescharacteristic
115C23×C4×C73—21no—
116C23×C4×C73C2311yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C4×D4×C73C2×C414yes—
119C4×D4×C73D414yes—
120#117×C73—22no—
121#117×C73—41no—
122C2×C4⋊C4×C73—22no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73—41no—
125C2×C4⋊C4×C73D411yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73D411yescharacteristic
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C42×C73—21no—
136C2×C42×C73—21no—
137C2×C42×C73C2311yescharacteristic
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—21no—
143C23×D73—21no—
144#11924027—432no—
145C2×Dic146—24no—
146C2×Dic146—42no—
147C2×Dic146—42no—
148C2×D292—21no—
149C2×D292—21no—
150C2×D292—21no—
151C2×D292—21no—
152C2×D292—21no—
153C2×D292C22×C412yes—
154C2×C22⋊D73—24no—
155C2×C22⋊D73—24no—
156C2×C22⋊D73—42no—
157C2×C22⋊D73—42no—
158C2×C22⋊D73—42no—
159C2×C22⋊D73—42no—
160C22×Dic73—24no—
161C22×Dic73—24no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—42no—
166C22×Dic73—42no—
167C22×Dic73—42no—
168C22×Dic73—42no—
169C2×C4×D73—24no—
170C2×C4×D73—42no—
171C2×C4×D73—42no—
172#11924012—44no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—44no—
185C2×#10596831#4112yescomplemented
186C4⋊Dic73—24no—
187C4⋊Dic73—24no—
188C4⋊Dic73—24no—
189C4⋊Dic73—21no—
190C4⋊Dic73—21no—
191C4⋊Dic73—21no—
192C4⋊Dic73C22×C412yes—
193C4⋊Dic73C22×C412yes—
194C4⋊Dic73C22×C412yes—
195#11924005—24no—
196#11924005—24no—
197#11924005—24no—
198C24×C73C2×D411yescharacteristic
199C24×C73C2×D411yescharacteristic
200C2×D4×C73—22no—
201C2×D4×C73—22no—
202C2×D4×C73C22⋊C414yes—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—42no—
216C22×C4×C73—42no—
217C22×C4×C73—81no—
218C22×C4×C73C22×C412yes—
219C22×C4×C73C22×C412yes—
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D412yes—
225C22×C4×C73C2×D412yes—
226C22×C4×C73C2411yescharacteristic
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—42no—
235C4⋊C4×C73C22⋊C414yes—
236C4⋊C4×C73#4112yescomplemented
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—81no—
240C22⋊C4×C73C22⋊C414yes—
241C22⋊C4×C73C22⋊C414yes—
242C42×C73—42no—
243C42×C73—81no—
244C42×C73C22×C412yes—
245C42×C73C2×D412yes—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73C2×C22⋊C412yes—
257C23×C73C2×C22⋊C412yes—
258C23×C73AGL(1,ℤ/8)12yes—
259C23×C73AGL(1,ℤ/8)12yes—
260C23×C73C22×D411yescharacteristic
261C22×D73—22no—
262C22×D73—41no—
263C22×D73—41no—
264C22×D73—41no—
265C22×D73—41no—
266C22×D73—41no—
267C22×D73—41no—
268D4×C73—28no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—84no—
298C2×C4×C73C2×C22⋊C412yes—
299C2×C4×C73C2×C22⋊C412yes—
300C2×C4×C73C2×C22⋊C412yes—
301C2×C4×C73C2×C22⋊C412yes—
302C2×C4×C73C23×C411yescharacteristic
303C2×C4×C73C22×D411yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C732−1+411yescharacteristic
308C22⋊D73—48no—
309C22⋊D73—48no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—48no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—48no—
321D292—22no—
322D292—22no—
323D292—41no—
324D292—41no—
325C4×D73—48no—
326Dic146—48no—
327#10596831—22no—
328#10596831—41no—
329#10596831—41no—
330#10596831—41no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73#41814yes—
345C22×C73C22×C22⋊C411yescharacteristic
346C22×C73#54611yescharacteristic
347C22×C73#54711yescharacteristic
348C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C73#57711yescharacteristic
351C22×C73#57811yescharacteristic
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—81no—
356C2×D73—81no—
357C2×D73—81no—
358C2×D73—81no—
359C4×C73—22no—
360C4×C73—22no—
361C4×C73—22no—
362C4×C73—22no—
363C4×C73—42no—
364C4×C73—81no—
365C4×C73—81no—
366C4×C73—81no—
367C4×C73C4×#4111yescharacteristic
368C4×C73#52011yescharacteristic
369C4×C73#54611yescharacteristic
370C4×C73#54711yescharacteristic
371Dic73—42no—
372Dic73—42no—
373Dic73—42no—
374#22495—731nomaximal, Sylow
375C2×C73—24no—
376C2×C73—42no—
377C2×C73#233911yescharacteristic
378C2×C73C2×#41811yescharacteristic
379C2×C73#289811yescharacteristic
380C2×C73#330611yescharacteristic
381C2×C73#330811yescharacteristic
382C2×C73#334311yescharacteristic
383C2×C73#334511yescharacteristic
384D73—82no—
385C2×#547—731no—
386C2×#435—731no—
387#2352D7311yescharacteristic, complemented
388#1993—731no—
389#1987—731no—
390#1895—731no—
391#1893—731no—
392#1875—731no—
393#1874—731no—
394#1824—731no—
395#1823—731no—
396#1804—731no—
397#1762—731no—
398#1736—731no—
399C2×#340—731no—
400C73#2249511yescharacteristic, complemented, Sylow
401C22×#41—1461no—
402C22×M16—731no—
403C23×C8—731no—
404#547—738no—
405#547—1464no—
406C2×C4⋊Q8—731no—
407C2×#123—1461no—
408C2×#123—1461no—
409C2×C22⋊Q8—1461no—
410C2×#121—731no—
411C2×#121—731no—
412C2×C4×D4—731no—
413C2×C4×D4C2×D7311yescharacteristic
414C2×#117C2×D7311yescharacteristic
415C22×C4⋊C4—731no—
416C22×C4⋊C4—731no—
417C22×C4⋊C4C2×D7311yescharacteristic
418#435—1464no—
419C2×C4⋊C8—731no—
420C2×#102—731no—
421C2×#102—731no—
422C2×#102—731no—
423C2×#102—731no—
424C2×C22⋊C8—731no—
425C2×C22⋊C8—731no—
426C2×#97—731no—
427#388—21no—
428#387—21no—
429#386—21no—
430#382C2×D7311yescharacteristic
431#380C2×D7311yescharacteristic
432#380C2×D7311yescharacteristic
433C4×C4⋊C4C2×D7311yescharacteristic
434C4×C22⋊C4—21no—
435#340—731no—
436#340—731no—
437#340—731no—
438#340—731no—
439#340—731no—
440#340—731no—
441#340—731no—
442#340—731no—
443#340—731no—
444#340—731no—
445#340—731no—
446#340—731no—
447C2×#41—2924no—
448C2×#41—2924no—
449C2×#41—1468no—
450C22×Q8—1461no—
451C22×D4—731no—
452C22×D4—1461no—
453C22×D4—1461no—
454C22×D4C22⋊D7311yescharacteristic
455C23×C4—21no—
456C23×C4—1461no—
457C23×C4—1461no—
458C23×C4—1461no—
459C23×C4C22×D7311yescharacteristic
460C23×C4C22×D7311yescharacteristic
461C2×M16—2921no—
462C2×M16—1462no—
463C2×M16—1462no—
464C22×C8—2921no—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—731no—
468C22×C8—731no—
469C22×C8—1462no—
470C22×C8—1462no—
471C4⋊Q8—734no—
472C4⋊Q8—1462no—
473#123—1468no—
474#123—1468no—
475C22⋊Q8—1468no—
476#121—734no—
477#121—734no—
478#121—1462no—
479#121—1462no—
480C4×D4—734no—
481C4×D4—1462no—
482C4×D4C4×D7314yes—
483C4×D4D29214yes—
484#117—22no—
485#117—41no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—734no—
490C2×C4⋊C4—734no—
491C2×C4⋊C4—731no—
492C2×C4⋊C4—731no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—1461no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1462no—
498C2×C4⋊C4—1462no—
499C2×C4⋊C4C22⋊D7311yescharacteristic
500C2×C4⋊C4C22×D7311yescharacteristic
501C2×C4⋊C4C22×D7311yescharacteristic
502C2×C4⋊C4C22×D7311yescharacteristic
503C2×C4⋊C4C22×D7311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4C22⋊D7311yescharacteristic
511C2×C22⋊C4C22⋊D7311yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C22×D7311yescharacteristic
515C4⋊C8—1462no—
516#102—2921no—
517#102—2921no—
518#102—1462no—
519#102—1462no—
520C22⋊C8—1462no—
521C22⋊C8—1462no—
522#97—1462no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528C24—1461no—
529C24C2×C22⋊D7311yescharacteristic
530C24C2×C22⋊D7311yescharacteristic
531#41—29232no—
532C2×Q8—2922no—
533C2×Q8—2922no—
534C2×Q8—1464no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—2922no—
538C2×D4—2922no—
539C2×D4—2922no—
540C2×D4—2922no—
541C2×D4—732no—
542C2×D4—1464no—
543C2×D4—1464no—
544C2×D4—1461no—
545C2×D4—1461no—
546C2×D4—1461no—
547C2×D4—1461no—
548C2×D4—1461no—
549C2×D4#1192400514yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—2922no—
566C22×C4—2922no—
567C22×C4—2922no—
568C22×C4—2922no—
569C22×C4—2922no—
570C22×C4—2922no—
571C22×C4—1464no—
572C22×C4—1464no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1461no—
576C22×C4—1464no—
577C22×C4C2×C4×D7312yes—
578C22×C4C2×C4×D7312yes—
579C22×C4C2×C22⋊D7311yescharacteristic
580C22×C4C2×C22⋊D7311yescharacteristic
581C22×C4C2×C22⋊D7311yescharacteristic
582C22×C4C2×C22⋊D7311yescharacteristic
583C22×C4C2×D29212yes—
584C22×C4C2×D29212yes—
585C22×C4C23×D7311yescharacteristic
586M16—2924no—
587C2×C8—2924no—
588C2×C8—732no—
589C2×C8—1461no—
590C2×C8—1461no—
591C2×C8—1461no—
592C2×C8—1461no—
593C2×C8—1461no—
594C2×C8—1461no—
595C2×C8—1461no—
596C2×C8—1461no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8—1461no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—732no—
609C4⋊C4—732no—
610C4⋊C4—732no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1461no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4#1192400514yes—
618C4⋊C4#1192402712yescomplemented
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—1464no—
623C22⋊C4—1464no—
624C22⋊C4—1464no—
625C22⋊C4#1192400514yes—
626C22⋊C4#1192400514yes—
627C42—42no—
628C42—81no—
629C42C2×C4×D7312yes—
630C42C2×D29212yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—2921no—
642C23—2921no—
643C23—2921no—
644C23—2921no—
645C23—2921no—
646C23—2921no—
647C23—1462no—
648C23C2×#1192400512yes—
649C23C2×#1192400512yes—
650C23#1455661612yes—
651C23#1455661612yes—
652C23C22×C22⋊D7311yescharacteristic
653Q8—2928no—
654D4—28no—
655D4—2928no—
656D4—2928no—
657D4—2921no—
658D4—2921no—
659D4—1462no—
660D4—1462no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—2928no—
691C2×C4—2928no—
692C2×C4—2928no—
693C2×C4—2921no—
694C2×C4—2921no—
695C2×C4—2921no—
696C2×C4—2921no—
697C2×C4—2921no—
698C2×C4—2921no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4C2×#1192400512yes—
703C2×C4C2×#1192400512yes—
704C2×C4C2×#1192400512yes—
705C2×C4C2×#1192400512yes—
706C2×C4C22×C4×D7311yescharacteristic
707C2×C4C22×D29211yescharacteristic
708C2×C4#41×D7311yescharacteristic
709C2×C4C2×#1192402711yescharacteristic
710C2×C4#1455663611yescharacteristic
711C2×C4#1455663811yescharacteristic
712C8—2921no—
713C8—2921no—
714C8—2921no—
715C8—1462no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—2922no—
730C22—2922no—
731C22—2922no—
732C22—5841no—
733C22—5841no—
734C22—5841no—
735C22—5841no—
736C22#1798859114yes—
737C22C22×#1192400511yescharacteristic
738C22#1798923111yescharacteristic
739C22#1798923611yescharacteristic
740C22C2×#1455661611yescharacteristic
741C22C2×#1455661611yescharacteristic
742C22#1798939811yescharacteristic
743C22#1798940211yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—2922no—
753C4—2922no—
754C4—2922no—
755C4C4×#1192402711yescharacteristic
756C4#1798906611yescharacteristic
757C4#1798923211yescharacteristic
758C4#1798924111yescharacteristic
759C2—24no—
760C2—42no—
761C2—5842no—
762C2#2261275611yescharacteristic
763C2C2×#1798859111yescharacteristic
764C2#2261846111yescharacteristic
765C2#2262189211yescharacteristic
766C2#2262192211yescharacteristic
767C2#2262237111yescharacteristic
768C2#2262239511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2352C2
socleC23×C73C22×D4
prime radicalC2×#17989241C2
cosocleC22×C4×C73C24
hypercenter#2352D73
hypocenterC73#22495
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#17988659C2semidirect
3. #22610903C2semidirect
4. #22610879C2semidirect
5. #22610367C2semidirect
6. #22610357C2semidirect
7. #22610253C2semidirect
8. #22610248C2semidirect
9. #22610019C2semidirect
10. #22610015C2semidirect
11. #22609938C2semidirect
12. #22609759C2semidirect
13. #22609652C2semidirect
14. C2×#17988349C2semidirect
15. C73×#2352C2semidirect
20. #17989241C4semidirect
83. #14556591C2×C4semidirect
90. #14556565C2×C4semidirect
92. C4×D292C2×C4semidirect
99. C2×C4⋊Dic73C2×C4semidirect
185. C2×#10596831#41semidirect
236. C4⋊C4×C73#41semidirect
387. #2352D73semidirect
400. C73#22495semidirect
618. C4⋊C4#11924027semidirect

Maximal subgroups

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

subgroupindex
C2×#179892412
C2×#179886592
#226109032
#226108792
#226103672
#226103572
#226102532
#226102482
#226100192
#226100152
#226099382
#226097592
#226096522
C2×#179883492
C73×#23522
#2249573