Finite Group Databasebeta

← #33102196

Subgroups — #33102196

Order 18688.

1474 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989237C211yesmaximal, characteristic
2C2×#17988650C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D73C211yesmaximal, characteristic, complemented
4#22610890C211yesmaximal, characteristic, complemented
5#22610881C211yesmaximal, characteristic, complemented
6#22610360C211yesmaximal, characteristic, complemented
7#22610356C211yesmaximal, characteristic, complemented
8#22610245C211yesmaximal, characteristic, complemented
9#22610018C211yesmaximal, characteristic, complemented
10#22610016C211yesmaximal, characteristic, complemented
11#22609929C211yesmaximal, characteristic, complemented
12#102×Dic73C211yesmaximal, characteristic, complemented
13C2×#17988349C211yesmaximal, characteristic, complemented
14#340×D73C211yesmaximal, characteristic, complemented
15C73×#1874C211yesmaximal, characteristic, complemented
16C22×#11924027—21no—
17C23×#10596831C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19#17989237—24no—
20#17989237C418yescomplemented
21C2×#14556590C2211yescharacteristic
22C2×#14556573—21no—
23C2×#14556572—21no—
24C2×#14556568—21no—
25C2×#14556562C2211yescharacteristic
26C2×D4×Dic73C2211yescharacteristic
27C2×C4×C22⋊D73—21no—
28C2×C4×C22⋊D73C2211yescharacteristic
29C22×C4⋊Dic73C2211yescharacteristic
30C2×C4⋊C4×D73C2211yescharacteristic
31C2×C4⋊C4×D73C2211yescharacteristic
32#17988650—24no—
33C2×#14556520C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×#14556512C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×C8×Dic73C2211yescharacteristic
38#17988482—21no—
39#17988460—21no—
40#17988458—21no—
41#17988456C2211yescharacteristic
42#17988447C2211yescharacteristic
43#17988444C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C2×#121×C73C2211yescharacteristic
56C22×C4⋊C4×C73C2211yescharacteristic
57C2×#102×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C2×#11924027—28no—
63C2×#11924027—44no—
64C2×#11924027—44no—
65C22×Dic146—21no—
66C22×C22⋊D73—21no—
67C22×C22⋊D73D411yescharacteristic
68C23×Dic73—21no—
69C23×Dic73—21no—
70C22×C4×D73—21no—
71C22×C4×D73—21no—
72C22×C4×D73C2311yescharacteristic
73C22×#10596831—22no—
74C22×#10596831—22no—
75C22×#10596831—41no—
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C2×C8×D73—22no—
79C2×C8×D73—22no—
80C2×C8×D73—41no—
81#14556590—22no—
82#14556590C2×C414yescomplemented
83#14556573—28no—
84#14556572—28no—
85#14556568—28no—
86#14556562—22no—
87#14556562C2×C414yescomplemented
88D4×Dic73—22no—
89D4×Dic73C2×C414yescomplemented
90C4×C22⋊D73—44no—
91C4×C22⋊D73C2×C414yes—
92C4×C22⋊D73D414yes—
93C2×C4⋊Dic73—22no—
94C2×C4⋊Dic73—21no—
95C2×C4⋊Dic73C2×C414yescomplemented
96C2×C4⋊Dic73C2311yescharacteristic
97C2×C4⋊Dic73C2311yescharacteristic
98C2×C4⋊Dic73C2311yescharacteristic
99C2×C4⋊Dic73C2311yescharacteristic
100C2×#11924007—21no—
101C2×#11924007—21no—
102C2×#11924007—21no—
103C2×#11924007—21no—
104C2×#11924007—21no—
105C2×#11924007D411yescharacteristic
106C4⋊C4×D73—22no—
107C4⋊C4×D73—22no—
108C4⋊C4×D73—41no—
109C4⋊C4×D73C2×C414yescomplemented
110C2×C22⋊Dic73—21no—
111C2×C22⋊Dic73—21no—
112C2×C22⋊Dic73—21no—
113C2×C22⋊Dic73D411yescharacteristic
114C2×#11924005—21no—
115C2×#11924005D411yescharacteristic
116C2×C4×Dic73—21no—
117C2×C4×Dic73C2311yescharacteristic
118#14556520—22no—
119#14556512—22no—
120#14556512—41no—
121#14556503—22no—
122C8×Dic73—22no—
123#14556498—21no—
124#14556498—21no—
125#14556498—21no—
126C22×D4×C73—21no—
127C22×D4×C73C2311yescharacteristic
128C23×C4×C73—21no—
129C23×C4×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132#121×C73—22no—
133#121×C73C2×C414yescomplemented
134C2×C4⋊C4×C73—22no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73—41no—
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C22⋊C4×C73—21no—
141#102×C73—22no—
142#102×C73—41no—
143C22⋊C8×C73—22no—
144C23×D73C2×D411yescharacteristic
145#11924027—432no—
146C2×Dic146—24no—
147C2×Dic146—42no—
148C2×Dic146—42no—
149C2×C22⋊D73—24no—
150C2×C22⋊D73—42no—
151C2×C22⋊D73—42no—
152C2×C22⋊D73C22⋊C414yes—
153C2×C22⋊D73D814yes—
154C2×C22⋊D73SD1614yes—
155C22×Dic73—24no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—24no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—42no—
162C22×Dic73—42no—
163C22×Dic73—42no—
164C22×Dic73—42no—
165C22×Dic73C2×D411yescharacteristic
166C22×Dic73C2×D411yescharacteristic
167C22×Dic73C2×D411yescharacteristic
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—24no—
173C2×C4×D73—42no—
174C2×C4×D73—42no—
175C2×C4×D73—42no—
176C2×C4×D73—42no—
177C2×C4×D73—81no—
178C2×C4×D73C22×C412yes—
179C2×C4×D73C2×D412yes—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—44no—
186C2×#10596831#4112yescomplemented
187C8×D73—44no—
188C4⋊Dic73—24no—
189C4⋊Dic73—21no—
190C4⋊Dic73—21no—
191C4⋊Dic73—21no—
192C4⋊Dic73—21no—
193C4⋊Dic73—21no—
194C4⋊Dic73—21no—
195C4⋊Dic73C22×C412yes—
196C4⋊Dic73C22×C412yes—
197#11924007—24no—
198#11924007—24no—
199#11924007—42no—
200#11924007—42no—
201#11924007—81no—
202#11924007C22⋊C414yes—
203C22⋊Dic73—24no—
204C22⋊Dic73—24no—
205C22⋊Dic73—42no—
206C22⋊Dic73C22⋊C414yes—
207#11924005—42no—
208#11924005C22⋊C414yes—
209C4×Dic73—42no—
210C4×Dic73C22×C412yes—
211C4×Dic73C2×D412yes—
212C24×C73—21no—
213C24×C73C2×D411yescharacteristic
214C2×D4×C73—24no—
215C2×D4×C73—21no—
216C2×D4×C73—21no—
217C2×D4×C73—21no—
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—42no—
221C2×D4×C73—42no—
222C2×D4×C73C22×C412yes—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—42no—
231C22×C4×C73—42no—
232C22×C4×C73—81no—
233C22×C4×C73C22×C412yes—
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2×D412yes—
236C22×C4×C73C2411yescharacteristic
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—42no—
248C4⋊C4×C73C22×C412yes—
249C4⋊C4×C73#4112yescomplemented
250C22⋊C4×C73—24no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—22no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73C2×C22⋊C412yes—
263C23×C73C2×D812yes—
264C23×C73C2×SD1612yes—
265C23×C73C22×D411yescharacteristic
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73C2×C22⋊C412yes—
271C22×D73C2×D812yes—
272C22×D73C2×SD1612yes—
273D4×C73—22no—
274D4×C73—22no—
275D4×C73—48no—
276D4×C73—41no—
277D4×C73—41no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
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—84no—
294C2×C4×C73C2×C22⋊C412yes—
295C2×C4×C73C23×C411yescharacteristic
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C732−1+411yescharacteristic
301C22⋊D73—48no—
302C22⋊D73#102116yescomplemented
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—48no—
314C2×Dic73—48no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73C2×C22⋊C412yes—
322C2×Dic73C2×C22⋊C412yes—
323C2×Dic73C2×C22⋊C412yes—
324C2×Dic73C2×D812yes—
325C2×Dic73C2×SD1612yes—
326C4×D73—22no—
327C4×D73—22no—
328C4×D73—22no—
329C4×D73—22no—
330C4×D73—48no—
331C4×D73—84no—
332Dic146—48no—
333C8×C73—41no—
334C8×C73—41no—
335#10596831—22no—
336#10596831—41no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
349C22×C73—81no—
350C22×C73C2×#10214yes—
351C22×C73C22×C22⋊C411yescharacteristic
352C22×C73#54611yescharacteristic
353C22×C73#54711yescharacteristic
354C22×C73C22×D811yescharacteristic
355C22×C73C22×SD1611yescharacteristic
356C22×C73#57711yescharacteristic
357C22×C73#57811yescharacteristic
358C2×D73—22no—
359C2×D73—22no—
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—22no—
364C2×D73C2×#10214yes—
365C4×C73—22no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73—81no—
369C4×C73C4×#4111yescharacteristic
370C4×C73#52011yescharacteristic
371C4×C73#54611yescharacteristic
372C4×C73#54711yescharacteristic
373Dic73—22no—
374Dic73—22no—
375Dic73—42no—
376Dic73—42no—
377Dic73—81no—
378Dic73—81no—
379Dic73C2×#10214yes—
380#22485—731nomaximal, Sylow
381C2×C73—24no—
382C2×C73—82no—
383C2×C73#233911yescharacteristic
384C2×C73C22×#10211yescharacteristic
385C2×C73#289811yescharacteristic
386C2×C73#329411yescharacteristic
387C2×C73#329811yescharacteristic
388C2×C73#333411yescharacteristic
389C2×C73#333511yescharacteristic
390D73—24no—
391C2×#547—731no—
392C2×C8×D4—731no—
393D4×C4⋊C4—731no—
394#1990—731no—
395#1988—731no—
396#1893—731no—
397#1893—731no—
398#1874—731no—
399#1874D7311yescharacteristic, complemented
400#1823—731no—
401#1823—731no—
402#1802—731no—
403C4×#102—731no—
404C2×#340—731no—
405C2×#340—731no—
406C73#2248511yescharacteristic, complemented, Sylow
407C22×#41—1461no—
408C23×C8—731no—
409C23×C8—731no—
410#547—738no—
411#547—1464no—
412C2×C4⋊Q8—731no—
413C2×#123—1461no—
414C2×#123—1461no—
415C2×C22⋊Q8—1461no—
416C2×#121—731no—
417C2×#121C2×D7311yescharacteristic
418C2×C4×D4—731no—
419C2×C4×D4—731no—
420C2×C4×D4—1461no—
421C22×C4⋊C4—731no—
422C22×C4⋊C4—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4C2×D7311yescharacteristic
425C8×D4—1464no—
426C2×C4⋊C8—731no—
427C2×#102—731no—
428C2×#102—731no—
429C2×#102C2×D7311yescharacteristic
430C2×#102C2×D7311yescharacteristic
431C2×C22⋊C8—731no—
432C2×C22⋊C8C2×D7311yescharacteristic
433C2×C4×C8—731no—
434#389—1461no—
435#385—1461no—
436#385—1461no—
437#384—731no—
438#380—731no—
439#380—731no—
440C4×C4⋊C4—731no—
441#340—731no—
442#340—731no—
443#340—731no—
444#340—731no—
445#340—731no—
446#340—731no—
447#340—731no—
448#340—731no—
449#340—731no—
450#340—731no—
451#340C2×D7311yescharacteristic
452#340C2×D7311yescharacteristic
453C2×#41—2924no—
454C2×#41—2924no—
455C2×#41—1468no—
456C22×Q8—1461no—
457C22×D4—21no—
458C22×D4—731no—
459C22×D4—1461no—
460C22×D4C22×D7311yescharacteristic
461C23×C4—21no—
462C23×C4—731no—
463C23×C4—1461no—
464C23×C4—1461no—
465C23×C4—1461no—
466C23×C4—1461no—
467C23×C4C22×D7311yescharacteristic
468C22×C8—2921no—
469C22×C8—2921no—
470C22×C8—731no—
471C22×C8—731no—
472C22×C8—1462no—
473C22×C8—1462no—
474C22×C8—1462no—
475C22×C8—1462no—
476C22×C8C22×D7311yescharacteristic
477C22×C8C22×D7311yescharacteristic
478C4⋊Q8—734no—
479C4⋊Q8—1462no—
480#123—1468no—
481#123—1468no—
482C22⋊Q8—1468no—
483#121—22no—
484#121—734no—
485#121—1462no—
486#121C4×D7314yescomplemented
487C4×D4—2924no—
488C4×D4—734no—
489C4×D4—734no—
490C4×D4—734no—
491C4×D4—1462no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—2921no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—734no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—734no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—1462no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1462no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1462no—
512C2×C4⋊C4C22×D7311yescharacteristic
513C2×C4⋊C4C22×D7311yescharacteristic
514C2×C4⋊C4C22×D7311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C22⋊C4—1461no—
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C22⋊C4—1461no—
522C2×C42—731no—
523C2×C42—1461no—
524C4⋊C8—1462no—
525#102—22no—
526#102—41no—
527#102—2921no—
528#102—1462no—
529C22⋊C8—22no—
530C22⋊C8—1462no—
531C4×C8—1462no—
532#95—1461no—
533#95—1461no—
534#95—1461no—
535C24—21no—
536C24—731no—
537C24D4×D7311yescharacteristic
538#41—29232no—
539C2×Q8—2922no—
540C2×Q8—2922no—
541C2×Q8—1464no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—2922no—
551C2×D4—2922no—
552C2×D4—734no—
553C2×D4—734no—
554C2×D4—734no—
555C2×D4—1464no—
556C2×D4C2×C4×D7312yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—2922no—
568C22×C4—2922no—
569C22×C4—2922no—
570C22×C4—2922no—
571C22×C4—2922no—
572C22×C4—2922no—
573C22×C4—2922no—
574C22×C4—2922no—
575C22×C4—5841no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—731no—
579C22×C4—732no—
580C22×C4—732no—
581C22×C4—1464no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1464no—
585C22×C4—1464no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4C2×C4×D7312yes—
593C22×C4D4×D7311yescharacteristic
594C22×C4D4×D7312yes—
595C22×C4C23×D7311yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—2924no—
603C2×C8—2924no—
604C2×C8—732no—
605C2×C8—1461no—
606C2×C8—1461no—
607C2×C8—1461no—
608C2×C8—1461no—
609C2×C8—1461no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—42no—
615C4⋊C4—2922no—
616C4⋊C4—2922no—
617C4⋊C4—5841no—
618C4⋊C4—734no—
619C4⋊C4—732no—
620C4⋊C4—732no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1461no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1461no—
627C4⋊C4—1464no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4C2×C4×D7312yes—
631C4⋊C4#1192402712yescomplemented
632C22⋊C4—24no—
633C22⋊C4—2922no—
634C22⋊C4—2922no—
635C22⋊C4—734no—
636C22⋊C4—734no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—2922no—
640C42—732no—
641C42—732no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—732no—
654C23—732no—
655C23—732no—
656C23—1461no—
657C23—1461no—
658C23—1461no—
659C23—1461no—
660C23C22⋊C4×D7312yes—
661C23D8×D7312yes—
662C23SD16×D7312yes—
663C23C2×D4×D7311yescharacteristic
664Q8—2928no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—41no—
669D4—41no—
670D4—2928no—
671D4—7316no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—84no—
688C2×C4—2928no—
689C2×C4—2928no—
690C2×C4—2921no—
691C2×C4—2921no—
692C2×C4—2921no—
693C2×C4—2921no—
694C2×C4—2928no—
695C2×C4—2921no—
696C2×C4—2921no—
697C2×C4—2921no—
698C2×C4—2921no—
699C2×C4—2921no—
700C2×C4—2921no—
701C2×C4—5844no—
702C2×C4—732no—
703C2×C4—732no—
704C2×C4—732no—
705C2×C4—732no—
706C2×C4—732no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1461no—
710C2×C4—1461no—
711C2×C4—1461no—
712C2×C4—1461no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4C22⋊C4×D7312yes—
718C2×C4C22×C4×D7311yescharacteristic
719C2×C4C2×D4×D7311yescharacteristic
720C2×C4#41×D7311yescharacteristic
721C2×C4C2×#1192402711yescharacteristic
722C2×C4#1455663611yescharacteristic
723C2×C4#1455663811yescharacteristic
724C8—41no—
725C8—41no—
726C8—2921no—
727C8—1462no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—734no—
742C22—1462no—
743C22—1462no—
744C22—1462no—
745C22—1462no—
746C22—1462no—
747C22—1462no—
748C22#102×D7314yes—
749C22C2×C22⋊C4×D7311yescharacteristic
750C22#1798922411yescharacteristic
751C22#1798923511yescharacteristic
752C22C2×D8×D7311yescharacteristic
753C22C2×SD16×D7311yescharacteristic
754C22#1798939711yescharacteristic
755C22#1798940311yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—81no—
760C4—2922no—
761C4—2922no—
762C4—5841no—
763C4—5841no—
764C4—734no—
765C4—1462no—
766C4—1462no—
767C4C4×#1192402711yescharacteristic
768C4#1798906611yescharacteristic
769C4#1798922611yescharacteristic
770C4#1798923711yescharacteristic
771C2—24no—
772C2—82no—
773C2—1464no—
774C2#2261275711yescharacteristic
775C2C2×#102×D7311yescharacteristic
776C2#2261846211yescharacteristic
777C2#2262173711yescharacteristic
778C2#2262178911yescharacteristic
779C2#2262227311yescharacteristic
780C2#2262228611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1874C2
socleC23×C73C22×D4
prime radicalC2×#17989237C2
cosocleC22×C4×C73C24
hypercenter#1874D73
hypocenterC73#22485
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#17988650C2semidirect
3. C4⋊C4×C22⋊D73C2semidirect
4. #22610890C2semidirect
5. #22610881C2semidirect
6. #22610360C2semidirect
7. #22610356C2semidirect
8. #22610245C2semidirect
9. #22610018C2semidirect
10. #22610016C2semidirect
11. #22609929C2semidirect
12. #102×Dic73C2semidirect
13. C2×#17988349C2semidirect
14. #340×D73C2semidirect
15. C73×#1874C2semidirect
20. #17989237C4semidirect
82. #14556590C2×C4semidirect
87. #14556562C2×C4semidirect
89. D4×Dic73C2×C4semidirect
95. C2×C4⋊Dic73C2×C4semidirect
109. C4⋊C4×D73C2×C4semidirect
133. #121×C73C2×C4semidirect
186. C2×#10596831#41semidirect
249. C4⋊C4×C73#41semidirect
302. C22⋊D73#102semidirect
399. #1874D73semidirect
406. C73#22485semidirect
486. #121C4×D73semidirect
631. C4⋊C4#11924027semidirect

Maximal subgroups

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

subgroupindex
C2×#179892372
C2×#179886502
C4⋊C4×C22⋊D732
#226108902
#226108812
#226103602
#226103562
#226102452
#226100182
#226100162
#226099292
#102×Dic732
C2×#179883492
#340×D732
C73×#18742
#2248573