Finite Group Databasebeta

← #33007287

Subgroups — #33007287

Order 18688.

2470 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D73C211yesmaximal, characteristic
2C2×#17988487C212yesmaximal
3C2×#17988438C211yesmaximal, characteristic, complemented
4C2×#17988432C211yesmaximal, characteristic, complemented
5#22608168C212yesmaximal, complemented
6#22608167C212yesmaximal, complemented
7#22608159C212yesmaximal, complemented
8#22608154C211yesmaximal, characteristic, complemented
9#22608152C211yesmaximal, characteristic, complemented
10#22608152C211yesmaximal, characteristic, complemented
11C73×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D73C2211yescharacteristic
13C23×C4×D73C2211yescharacteristic
14C2×C4×C22⋊D73—24no—
15C2×C4×C22⋊D73—24no—
16C2×C4×C22⋊D73C418yescomplemented
17C22×#11924007C2211yescharacteristic
18C22×#11924007C2212yes—
19C22×C22⋊Dic73C2211yescharacteristic
20C22×C22⋊Dic73C2212yes—
21C22×#11924005C2211yescharacteristic
22C22×#11924005C2212yes—
23C22×#11924005C2212yes—
24C22×C4×Dic73C2212yes—
25C22×C4×Dic73C2212yes—
26C22×C4×Dic73C2211yescharacteristic
27#17988487C4116yescomplemented
28#17988438—24no—
29#17988432—24no—
30C2×#14556498C2211yescharacteristic
31C2×#14556498C2211yescharacteristic
32C2×#14556498C2212yes—
33C2×#14556498C2212yes—
34C2×#14556498C2212yes—
35C2×#14556498C2212yes—
36C24×C4×C73C2211yescharacteristic
37C22×C22⋊C4×C73C2212yes—
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2212yes—
41C24×D73C2311yescharacteristic
42C22×C22⋊D73—22no—
43C22×C22⋊D73—22no—
44C22×C22⋊D73—24no—
45C22×C22⋊D73C2×C418yes—
46C22×C22⋊D73C2×C414yes—
47C23×Dic73C2311yescharacteristic
48C23×Dic73C2312yes—
49C23×Dic73C2312yes—
50C23×Dic73C2311yescharacteristic
51C23×Dic73C2311yescharacteristic
52C22×C4×D73—22no—
53C22×C4×D73—22no—
54C22×C4×D73—42no—
55C22×C4×D73—42no—
56C22×C4×D73C2×C414yes—
57C4×C22⋊D73—232no—
58C2×#11924007—24no—
59C2×#11924007—22no—
60C2×#11924007—22no—
61C2×#11924007—24no—
62C2×#11924007C2×C414yes—
63C2×#11924007C2×C418yescomplemented
64C2×C22⋊Dic73—22no—
65C2×C22⋊Dic73—22no—
66C2×C22⋊Dic73—42no—
67C2×C22⋊Dic73—42no—
68C2×C22⋊Dic73C2×C414yes—
69C2×C22⋊Dic73C2×C418yescomplemented
70C2×#11924005—22no—
71C2×#11924005—22no—
72C2×#11924005—42no—
73C2×#11924005—42no—
74C2×#11924005—42no—
75C2×#11924005—42no—
76C2×#11924005C2×C414yes—
77C2×#11924005C2×C418yescomplemented
78C2×#11924005C2×C418yescomplemented
79C2×C4×Dic73—24no—
80C2×C4×Dic73—24no—
81C2×C4×Dic73—24no—
82C2×C4×Dic73—42no—
83C2×C4×Dic73—42no—
84C2×C4×Dic73C2×C414yes—
85C2×C4×Dic73C2×C418yescomplemented
86C2×C4×Dic73D414yes—
87C2×C4×Dic73D414yes—
88#14556498—24no—
89#14556498—22no—
90#14556498—22no—
91#14556498—42no—
92#14556498—42no—
93#14556498—42no—
94C25×C73C2311yescharacteristic
95C23×C4×C73—22no—
96C23×C4×C73—22no—
97C23×C4×C73—42no—
98C23×C4×C73—42no—
99C23×C4×C73C2×C414yes—
100C23×C4×C73C2312yes—
101C23×C4×C73C2311yescharacteristic
102C23×C4×C73C2312yes—
103C23×C4×C73C2311yescharacteristic
104C2×C22⋊C4×C73—42no—
105C2×C22⋊C4×C73—42no—
106C2×C22⋊C4×C73C2×C418yescomplemented
107#95×C73—22no—
108#95×C73—22no—
109#95×C73—42no—
110C23×D73—21no—
111C23×D73—21no—
112C23×D73—22no—
113C23×D73—21no—
114C23×D73—21no—
115C23×D73—22no—
116C23×D73—22no—
117C23×D73—21no—
118C23×D73—21no—
119C23×D73C22×C412yes—
120C23×D73C22×C414yes—
121C2×C22⋊D73—28no—
122C2×C22⋊D73—28no—
123C2×C22⋊D73—216no—
124C2×C22⋊D73—216no—
125C2×C22⋊D73C42116yescomplemented
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—22no—
131C22×Dic73—22no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—22no—
135C22×Dic73—22no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73—22no—
142C22×Dic73—22no—
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73C22×C414yes—
147C22×Dic73C22×C414yes—
148C22×Dic73C22×C412yes—
149C22×Dic73C22×C412yes—
150C22×Dic73C22×C412yes—
151C22×Dic73C22×C414yes—
152C22×Dic73C2×D412yes—
153C22×Dic73C2×D412yes—
154C22×Dic73C2×D412yes—
155C22×Dic73C2×D412yes—
156C22×Dic73#4114yes—
157C2×C4×D73—28no—
158C2×C4×D73—44no—
159C2×C4×D73—44no—
160C2×C4×D73—48no—
161C2×C4×D73—48no—
162#11924007—28no—
163#11924007—216no—
164C22⋊Dic73—28no—
165C22⋊Dic73—48no—
166#11924005—28no—
167#11924005—48no—
168#11924005—48no—
169C4×Dic73—216no—
170C4×Dic73—48no—
171C4×Dic73C22⋊C4116yescomplemented
172C24×C73—21no—
173C24×C73—21no—
174C24×C73—22no—
175C24×C73—21no—
176C24×C73—22no—
177C24×C73—22no—
178C24×C73—21no—
179C24×C73—21no—
180C24×C73—21no—
181C24×C73C22×C414yes—
182C24×C73C22×C412yes—
183C24×C73C2411yescharacteristic
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—22no—
187C22×C4×C73—22no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—22no—
191C22×C4×C73—22no—
192C22×C4×C73—22no—
193C22×C4×C73—22no—
194C22×C4×C73—22no—
195C22×C4×C73—22no—
196C22×C4×C73—22no—
197C22×C4×C73—22no—
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—22no—
202C22×C4×C73—28no—
203C22×C4×C73—44no—
204C22×C4×C73—44no—
205C22×C4×C73—48no—
206C22×C4×C73—48no—
207C22×C4×C73C22×C414yes—
208C22×C4×C73C22×C414yes—
209C22×C4×C73C22×C412yes—
210C22×C4×C73C22×C412yes—
211C22×C4×C73C2×D412yes—
212C22×C4×C73C2×D412yes—
213C22⋊C4×C73—48no—
214C23×C73—22no—
215C23×C73—22no—
216C23×C73—24no—
217C23×C73—24no—
218C23×C73—24no—
219C23×C73—22no—
220C23×C73—22no—
221C23×C73—24no—
222C23×C73—24no—
223C23×C73—22no—
224C23×C73—22no—
225C23×C73—24no—
226C23×C73—42no—
227C23×C73—42no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—42no—
233C23×C73—42no—
234C23×C73—42no—
235C23×C73—42no—
236C23×C73C2×C4214yes—
237C23×C73C23×C411yescharacteristic
238C23×C73C23×C412yes—
239C23×C73C22×D411yescharacteristic
240C23×C73C22×D411yescharacteristic
241C23×C73C2×#4112yes—
242C23×C73H(5,𝔽2)12yes—
243C23×C73H(5,𝔽2)12yes—
244C23×C73H(5,𝔽2)11yescharacteristic
245C23×C73H(5,𝔽2)11yescharacteristic
246C23×C732−1+411yescharacteristic
247C23×C732−1+411yescharacteristic
248C22×D73—22no—
249C22×D73—22no—
250C22×D73—24no—
251C22×D73—24no—
252C22×D73—24no—
253C22×D73—24no—
254C22×D73—22no—
255C22×D73—22no—
256C22×D73—24no—
257C22×D73—22no—
258C22×D73—22no—
259C22×D73—24no—
260C22×D73—42no—
261C22×D73—42no—
262C22×D73—41no—
263C22×D73—41no—
264C22×D73—41no—
265C22×D73—41no—
266C22×D73—42no—
267C22×D73—42no—
268C22×D73—42no—
269C22×D73—42no—
270C22×D73C2×C4214yes—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—24no—
274C2×C4×C73—24no—
275C2×C4×C73—22no—
276C2×C4×C73—24no—
277C2×C4×C73—24no—
278C2×C4×C73—24no—
279C2×C4×C73—24no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—24no—
283C2×C4×C73—24no—
284C2×C4×C73—416no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73—42no—
289C2×C4×C73—42no—
290C2×C4×C73—42no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73C2×C22⋊C414yes—
296C22⋊D73—232no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—24no—
305C2×Dic73—24no—
306C2×Dic73—24no—
307C2×Dic73—24no—
308C2×Dic73—24no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—24no—
312C2×Dic73—42no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73C2×C4214yes—
323C2×Dic73C2×C22⋊C414yes—
324C2×Dic73C2×C22⋊C414yes—
325C2×Dic73#11714yes—
326C2×Dic73C4×D418yes—
327C2×Dic73C4×D418yes—
328C4×D73—416no—
329C22×C73—24no—
330C22×C73—24no—
331C22×C73—24no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—44no—
337C22×C73—44no—
338C22×C73—44no—
339C22×C73—44no—
340C22×C73C22×C4211yescharacteristic
341C22×C73C22×C22⋊C411yescharacteristic
342C22×C73C2×#11711yescharacteristic
343C22×C73C2×C4×D412yes—
344C22×C73C2×C4×D412yes—
345C22×C73#51812yes—
346C22×C73#51811yescharacteristic
347C22×C73#51811yescharacteristic
348C22×C73#51812yes—
349C22×C73#52012yes—
350C22×C73#52011yescharacteristic
351C22×C73#52011yescharacteristic
352C22×C73#52012yes—
353C22×C73#53512yes—
354C22×C73#53512yes—
355C22×C73#53511yescharacteristic
356C22×C73#53611yescharacteristic
357C22×C73#53711yescharacteristic
358C22×C73#53711yescharacteristic
359C22×C73#54012yes—
360C22×C73#54012yes—
361C22×C73#54212yes—
362C22×C73#54212yes—
363C2×D73—24no—
364C2×D73—24no—
365C2×D73—24no—
366C2×D73—42no—
367C2×D73—42no—
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—44no—
371C2×D73—44no—
372C2×D73—44no—
373C2×D73—44no—
374C4×C73—24no—
375C4×C73—42no—
376C4×C73—44no—
377C4×C73—44no—
378Dic73—24no—
379Dic73—42no—
380Dic73—44no—
381Dic73—44no—
382Dic73C4×C22⋊C418yes—
383#13785—731nomaximal, Sylow
384C2×C73—44no—
385C2×C73C2×C4×C22⋊C411yescharacteristic
386C2×C73#227511yescharacteristic
387C2×C73#227511yescharacteristic
388C2×C73#230911yescharacteristic
389C2×C73#231111yescharacteristic
390C2×C73#231911yescharacteristic
391C2×C73#231911yescharacteristic
392C2×C73#232412yes—
393C2×C73#232412yes—
394C2×C73#232612yes—
395C2×C73#232812yes—
396D73—44no—
397C22×C4×D4—731no—
398C2×#390—732no—
399C2×C4×C4⋊C4—731no—
400C2×#376—731no—
401#1437—732no—
402#1437—732no—
403C4⋊#95—732no—
404C22⋊#95—731no—
405C22⋊#95—731no—
406C22⋊#95—731no—
407C22⋊#95D7311yescharacteristic, complemented
408C73#1378511yescharacteristic, complemented, Sylow
409C23×D4—731no—
410C24×C4—731no—
411C24×C4C2×D7311yescharacteristic
412C2×C4×D4—738no—
413C2×C4×D4—1464no—
414C2×C4×D4—1464no—
415C22×C4⋊C4—731no—
416C22×C4⋊C4—732no—
417C22×C22⋊C4—732no—
418C22×C22⋊C4—732no—
419C22×C22⋊C4—732no—
420C22×C22⋊C4—731no—
421C22×C22⋊C4—731no—
422C22×C22⋊C4C2×D7312yes—
423C22×C42—732no—
424C22×C42—731no—
425C22×C42—732no—
426#390—7316no—
427C4×C4⋊C4—1464no—
428#376—1464no—
429C2×#95—732no—
430C2×#95—732no—
431C2×#95—732no—
432C2×#95—731no—
433C2×#95—731no—
434C2×#95—732no—
435C2×#95C2×D7311yescharacteristic
436C2×#95C2×D7311yescharacteristic
437C2×#95C2×D7312yes—
438C25—731no—
439C25C22×D7311yescharacteristic
440C22×D4—734no—
441C22×D4—738no—
442C22×D4—1462no—
443C22×D4—1462no—
444C22×D4—1464no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—2922no—
450C23×C4—2922no—
451C23×C4—734no—
452C23×C4—731no—
453C23×C4—731no—
454C23×C4—732no—
455C23×C4—732no—
456C23×C4—731no—
457C23×C4—1462no—
458C23×C4—1462no—
459C23×C4C4×D7314yes—
460C23×C4C22×D7312yes—
461C23×C4C22×D7312yes—
462C23×C4C22×D7311yescharacteristic
463C23×C4C22×D7311yescharacteristic
464C4×D4—14632no—
465C2×C4⋊C4—734no—
466C2×C4⋊C4—738no—
467C2×C4⋊C4—1462no—
468C2×C4⋊C4—1462no—
469C2×C4⋊C4—1464no—
470C2×C4⋊C4—1464no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—2922no—
474C2×C22⋊C4—2922no—
475C2×C22⋊C4—2922no—
476C2×C22⋊C4—2922no—
477C2×C22⋊C4—2922no—
478C2×C22⋊C4—2922no—
479C2×C22⋊C4—738no—
480C2×C22⋊C4—738no—
481C2×C22⋊C4—738no—
482C2×C22⋊C4—734no—
483C2×C22⋊C4—734no—
484C2×C22⋊C4—1462no—
485C2×C22⋊C4—1462no—
486C2×C22⋊C4—1462no—
487C2×C22⋊C4—1462no—
488C2×C22⋊C4C4×D7318yescomplemented
489C2×C42—2922no—
490C2×C42—2922no—
491C2×C42—734no—
492C2×C42—734no—
493C2×C42—734no—
494C2×C42—738no—
495C2×C42—1464no—
496C2×C42—1464no—
497C2×C42—1464no—
498#95—22no—
499#95—22no—
500#95—42no—
501#95—2922no—
502#95—2922no—
503#95—2922no—
504#95—1464no—
505#95—1462no—
506#95—1462no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—734no—
517C24—732no—
518C24—1461no—
519C24—1461no—
520C24—1462no—
521C24—1461no—
522C24—1462no—
523C24—1462no—
524C24—1461no—
525C24—1461no—
526C24—1461no—
527C24C2×C4×D7314yes—
528C24C2×C4×D7312yes—
529C24C23×D7311yescharacteristic
530C2×D4—7316no—
531C2×D4—1468no—
532C2×D4—1468no—
533C2×D4—14616no—
534C2×D4—14616no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—2928no—
559C22×C4—2928no—
560C22×C4—2924no—
561C22×C4—2924no—
562C22×C4—732no—
563C22×C4—734no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—734no—
567C22×C4—732no—
568C22×C4—732no—
569C22×C4—732no—
570C22×C4—734no—
571C22×C4—734no—
572C22×C4—732no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1461no—
576C22×C4—1461no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4—1462no—
583C22×C4—1462no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4—1468no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4C2×C4×D7314yes—
595C22×C4C2×C4×D7314yes—
596C22×C4C2×C4×D7312yes—
597C22×C4C2×C4×D7312yes—
598C22×C4D4×D7312yes—
599C22×C4D4×D7312yes—
600C4⋊C4—14616no—
601C4⋊C4—1468no—
602C22⋊C4—48no—
603C22⋊C4—2928no—
604C22⋊C4—2928no—
605C22⋊C4—2928no—
606C22⋊C4—1468no—
607C22⋊C4—1468no—
608C42—2928no—
609C42—7316no—
610C42—14616no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—42no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—2922no—
634C23—2922no—
635C23—2921no—
636C23—2921no—
637C23—2921no—
638C23—2921no—
639C23—2922no—
640C23—2922no—
641C23—2922no—
642C23—2922no—
643C23—734no—
644C23—1462no—
645C23—1462no—
646C23—1464no—
647C23—1464no—
648C23—1464no—
649C23—1464no—
650C23—1462no—
651C23—1462no—
652C23—1464no—
653C23—1462no—
654C23—1462no—
655C23—1464no—
656C23C42×D7314yes—
657C23C22×C4×D7311yescharacteristic
658C23C22×C4×D7312yes—
659C23C2×D4×D7311yescharacteristic
660C23C2×D4×D7311yescharacteristic
661C23#41×D7312yes—
662C23#1455663612yes—
663C23#1455663612yes—
664C23#1455663611yescharacteristic
665C23#1455663711yescharacteristic
666C23#1455663811yescharacteristic
667C23#1455663911yescharacteristic
668D4—14632no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—29216no—
694C2×C4—2922no—
695C2×C4—2922no—
696C2×C4—2922no—
697C2×C4—2922no—
698C2×C4—2922no—
699C2×C4—2922no—
700C2×C4—2922no—
701C2×C4—2922no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—734no—
705C2×C4—734no—
706C2×C4—734no—
707C2×C4—738no—
708C2×C4—738no—
709C2×C4—734no—
710C2×C4—1462no—
711C2×C4—1464no—
712C2×C4—1464no—
713C2×C4—1464no—
714C2×C4—1464no—
715C2×C4—1464no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1464no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4C22⋊C4×D7314yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—2922no—
738C22—2922no—
739C22—2922no—
740C22—2922no—
741C22—2924no—
742C22—2924no—
743C22—2924no—
744C22—2924no—
745C22—1464no—
746C22—1464no—
747C22—1464no—
748C22C2×C42×D7311yescharacteristic
749C22C2×C22⋊C4×D7311yescharacteristic
750C22#117×D7311yescharacteristic
751C22C4×D4×D7312yes—
752C22C4×D4×D7312yes—
753C22#1798905912yes—
754C22#1798906011yescharacteristic
755C22#1798906011yescharacteristic
756C22#1798906012yes—
757C22#1798906612yes—
758C22#1798906711yescharacteristic
759C22#1798906811yescharacteristic
760C22#1798906812yes—
761C22#1798915212yes—
762C22#1798915212yes—
763C22#1798915311yescharacteristic
764C22#1798916011yescharacteristic
765C22#1798916611yescharacteristic
766C22#1798916711yescharacteristic
767C22#1798918712yes—
768C22#1798918912yes—
769C22#1798920512yes—
770C22#1798920712yes—
771C4—24no—
772C4—42no—
773C4—44no—
774C4—44no—
775C4—2922no—
776C4—2924no—
777C4—2924no—
778C4—738no—
779C4—1464no—
780C2—44no—
781C2—2924no—
782C2C4×C22⋊C4×D7311yescharacteristic
783C2#2261228911yescharacteristic
784C2#2261229011yescharacteristic
785C2#2261251211yescharacteristic
786C2#2261252011yescharacteristic
787C2#2261257111yescharacteristic
788C2#2261257311yescharacteristic
789C2#2261262112yes—
790C2#2261262312yes—
791C2#2261263712yes—
792C2#2261265212yes—
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC73×C22⋊#95C2
socle, cosocleC24×C73C24
prime radicalC23×C22⋊D73C22
hypercenterC22⋊#95D73
hypocenterC73#13785
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#17988438C2semidirect
4. C2×#17988432C2semidirect
5. #22608168C2semidirect
6. #22608167C2semidirect
7. #22608159C2semidirect
8. #22608154C2semidirect
9. #22608152C2semidirect
10. #22608152C2semidirect
11. C73×C22⋊#95C2semidirect
16. C2×C4×C22⋊D73C4semidirect
27. #17988487C4semidirect
63. C2×#11924007C2×C4semidirect
69. C2×C22⋊Dic73C2×C4semidirect
77. C2×#11924005C2×C4semidirect
78. C2×#11924005C2×C4semidirect
85. C2×C4×Dic73C2×C4semidirect
106. C2×C22⋊C4×C73C2×C4semidirect
125. C2×C22⋊D73C42semidirect
171. C4×Dic73C22⋊C4semidirect
407. C22⋊#95D73semidirect
408. C73#13785semidirect
488. C2×C22⋊C4C4×D73semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D732
C2×#179884872
C2×#179884382
C2×#179884322
#226081682
#226081672
#226081592
#226081542
#226081522
C73×C22⋊#952
#1378573