Finite Group Databasebeta

← #2077×D73 #33114808

Subgroups — #2077×D73 #33114808

Order 18688.

1270 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D73C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D73C211yesmaximal, characteristic
3#380×D73C211yesmaximal, characteristic
4#380×D73C211yesmaximal, characteristic
5#22611370C211yesmaximal, characteristic, complemented
6#22611369C211yesmaximal, characteristic, complemented
7#22611368C211yesmaximal, characteristic, complemented
8#22611367C211yesmaximal, characteristic, complemented
9#22611366C211yesmaximal, characteristic, complemented
10#22611365C211yesmaximal, characteristic, complemented
11#22611364C211yesmaximal, characteristic, complemented
12#340×D73C211yesmaximal, characteristic, complemented
13#340×D73C211yesmaximal, characteristic, complemented
14#340×D73C211yesmaximal, characteristic, complemented
15C73×#2077C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C2×C4⋊C4×D73C2211yescharacteristic
20C2×C4⋊C4×D73C2211yescharacteristic
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23C2×C22⋊C4×D73—21no—
24C2×C22⋊C4×D73—21no—
25C2×#14556523C2211yescharacteristic, complemented
26C2×#14556522C2211yescharacteristic, complemented
27C2×#14556522C2211yescharacteristic, complemented
28#106×D73—24no—
29C2×C22⋊#10596831C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C22⋊C8×D73—24no—
33#17988447C2211yescharacteristic
34#17988447C2211yescharacteristic
35#17988446—21no—
36#17988446—21no—
37#17988445—21no—
38#17988445—21no—
39#17988444C2211yescharacteristic
40#17988444C2211yescharacteristic
41#17988444C2211yescharacteristic
42#17988444C2211yescharacteristic
43#95×D73—21no—
44#95×D73—21no—
45#17988350C2211yescharacteristic, complemented
46#17988350C2211yescharacteristic, complemented
47#17988350C2211yescharacteristic, complemented
48#17988349C2211yescharacteristic, complemented
49#17988349C2211yescharacteristic, complemented
50#17988349C2211yescharacteristic, complemented
51#17988349C2211yescharacteristic, complemented
52#17988349C2211yescharacteristic, complemented
53#17988349C2211yescharacteristic, complemented
54C2×#106×C73C2211yescharacteristic, complemented
55C2×C22⋊C8×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic, complemented
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61C24×D73D411yescharacteristic
62C23×Dic73D411yescharacteristic
63C22×C4×D73—22no—
64C22×C4×D73—22no—
65C22×C4×D73—22no—
66C22×C4×D73—22no—
67C22×C4×D73—22no—
68C22×C4×D73—22no—
69C22×C4×D73—21no—
70C22×C4×D73—21no—
71C22×C4×D73—21no—
72C22×C4×D73—21no—
73C22×C4×D73D411yescharacteristic
74C22×C4×D73D411yescharacteristic
75C22×C4×D73C2311yescharacteristic
76C22×C4×D73C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C2×C8×D73—22no—
80C2×C8×D73—22no—
81C2×C8×D73—22no—
82C2×C8×D73—22no—
83C2×C8×D73—22no—
84C2×C8×D73D414yes—
85C2×C4⋊Dic73C2311yescharacteristic
86C2×C4⋊Dic73C2311yescharacteristic
87C2×C4⋊Dic73C2311yescharacteristic
88C2×C4⋊Dic73C2311yescharacteristic
89C2×#11924007—21no—
90C2×#11924007—21no—
91C2×#11924007—21no—
92C2×#11924007—21no—
93C4⋊C4×D73—22no—
94C4⋊C4×D73—22no—
95C4⋊C4×D73—22no—
96C4⋊C4×D73—22no—
97C4⋊C4×D73—22no—
98C4⋊C4×D73—22no—
99C4⋊C4×D73—22no—
100C4⋊C4×D73—22no—
101C2×C22⋊Dic73—21no—
102C2×C22⋊Dic73—21no—
103C2×#11924005—21no—
104C2×#11924005—21no—
105C2×#11924005—21no—
106C2×#11924005—21no—
107C22⋊C4×D73—44no—
108C22⋊C4×D73—44no—
109#14556523—22no—
110#14556522—22no—
111#14556522—22no—
112C22⋊#10596831—22no—
113#14556503—22no—
114#14556503—22no—
115#14556498—21no—
116#14556498—21no—
117#14556498—21no—
118#14556498—21no—
119#14556498—21no—
120#14556498—21no—
121C23×C4×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130#106×C73—22no—
131C22⋊C8×C73—22no—
132#95×C73—21no—
133#95×C73—21no—
134C23×D73—22no—
135C23×D73—22no—
136C23×D73—22no—
137C23×D73—22no—
138C23×D73—22no—
139C23×D73—22no—
140C23×D73SD1614yes—
141C23×D73C2×D411yescharacteristic
142C23×D73C2×D411yescharacteristic
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73C2×D411yescharacteristic
151C22×Dic73C2×D411yescharacteristic
152C2×C4×D73—22no—
153C2×C4×D73—22no—
154C2×C4×D73—22no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—22no—
162C2×C4×D73—22no—
163C2×C4×D73—22no—
164C2×C4×D73—44no—
165C2×C4×D73—44no—
166C2×C4×D73—44no—
167C2×C4×D73—44no—
168C2×C4×D73—42no—
169C2×C4×D73—42no—
170C2×C4×D73—42no—
171C2×C4×D73—42no—
172C2×C4×D73—42no—
173C2×C4×D73—42no—
174C2×C4×D73—42no—
175C2×C4×D73—42no—
176C2×C4×D73—42no—
177C2×C4×D73—42no—
178C2×C4×D73—42no—
179C2×C4×D73—42no—
180C2×C4×D73C2×D412yes—
181C2×C4×D73#4112yes—
182C2×C4×D73#4112yes—
183C2×C4×D73#4112yes—
184C2×C4×D73#4112yes—
185C2×C4×D73#4112yes—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831C2×D412yes—
192C8×D73—28no—
193C8×D73—44no—
194C4⋊Dic73—21no—
195C4⋊Dic73—21no—
196C4⋊Dic73—21no—
197C4⋊Dic73—21no—
198C4⋊Dic73—21no—
199C4⋊Dic73—21no—
200C4⋊Dic73—21no—
201C4⋊Dic73—21no—
202#11924007—42no—
203#11924007—42no—
204#11924007—42no—
205#11924007—42no—
206C22⋊Dic73—42no—
207C22⋊Dic73—42no—
208#11924005—42no—
209#11924005—42no—
210#11924005—42no—
211#11924005—42no—
212C24×C73C2×D411yescharacteristic
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
224C22×C4×C73C2411yescharacteristic
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73C2×D412yes—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73C2×SD1612yes—
248C23×C73C22×D411yescharacteristic
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—21no—
254C22×D73—21no—
255C22×D73—28no—
256C22×D73—28no—
257C22×D73—28no—
258C22×D73—44no—
259C22×D73—44no—
260C22×D73—44no—
261C22×D73—44no—
262C22×D73#12112yes—
263C22×D73#12312yes—
264C22×D73#12312yes—
265C22×D73C2×SD1612yes—
266C22×D73C2×SD1612yes—
267C22×D73#13512yes—
268C22×D73AGL(1,ℤ/8)12yes—
269C22×D73#13712yes—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
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×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73C22×D411yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—44no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73#12112yes—
312C2×Dic73#12312yes—
313C2×Dic73#12312yes—
314C4×D73—44no—
315C4×D73—41no—
316C4×D73—41no—
317C4×D73—41no—
318C4×D73—41no—
319C4×D73—44no—
320C4×D73—84no—
321C4×D73—84no—
322C4×D73—84no—
323C4×D73—84no—
324C4×D73#12314yes—
325C4×D73#12414yes—
326C4×D73#12614yes—
327C4×D73#12614yes—
328C8×C73—22no—
329C8×C73—41no—
330#10596831—22no—
331#10596831—41no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73C2×#12111yescharacteristic
340C22×C73C2×#12311yescharacteristic
341C22×C73C2×#12311yescharacteristic
342C22×C73C22×SD1611yescharacteristic
343C22×C73C2×#13511yescharacteristic
344C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C73C2×#13711yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—41no—
350C2×D73—41no—
351C2×D73—41no—
352C2×D73—41no—
353C2×D73—416no—
354C2×D73#39714yes—
355C2×D73#46514yes—
356C2×D73#46814yes—
357C2×D73#48114yes—
358C2×D73#48214yes—
359C2×D73#48314yes—
360C2×D73#48514yes—
361C4×C73—41no—
362C4×C73—81no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73—81no—
366C4×C73C2×#12311yescharacteristic
367C4×C73C2×#12411yescharacteristic
368C4×C73C2×#12611yescharacteristic
369C4×C73C2×#12611yescharacteristic
370Dic73—41no—
371Dic73—81no—
372Dic73—81no—
373Dic73—81no—
374Dic73—81no—
375Dic73#39714yes—
376C2×#2077—731nomaximal, Sylow
377C2×C73—42no—
378C2×C73C2×#39711yescharacteristic
379C2×C73C2×#46511yescharacteristic
380C2×C73C2×#46811yescharacteristic
381C2×C73C2×#48311yescharacteristic
382C2×C73C2×#48211yescharacteristic
383C2×C73C2×#48511yescharacteristic
384C2×C73C2×#48111yescharacteristic
385D73—42no—
386D73#207718yesdirect product factor
387C22×#106—731no—
388C22×C22⋊C8—731no—
389C2×#380—731no—
390C2×#380—731no—
391#2077—731no—
392#2077—731no—
393#2077—731no—
394#2077—731no—
395#2077—731no—
396#2077—731no—
397#2077—731no—
398#2077D7311yescharacteristic, direct product factor
399C2×#340—731no—
400C2×#340—731no—
401C2×#340—731no—
402C73C2×#207711yescharacteristic, complemented, Sylow
403C24×C4—731no—
404C23×C8—731no—
405C23×C8—731no—
406C22×C4⋊C4—731no—
407C22×C4⋊C4—731no—
408C22×C4⋊C4—731no—
409C22×C4⋊C4—731no—
410C22×C22⋊C4—1461no—
411C22×C22⋊C4—1461no—
412C2×#106—731no—
413C2×#106—731no—
414C2×#106—731no—
415C2×#106—1464no—
416C2×#106C2×D7311yescharacteristic, complemented
417C2×C22⋊C8—731no—
418C2×C22⋊C8—731no—
419C2×C22⋊C8—731no—
420C2×C22⋊C8—1464no—
421C2×C22⋊C8C2×D7311yescharacteristic
422#380—731no—
423#380—731no—
424#380—731no—
425#380—731no—
426#380—731no—
427#380—731no—
428#380—1461no—
429#380—1461no—
430#380—1461no—
431#380—1461no—
432#380C2×D7311yescharacteristic
433#380C2×D7311yescharacteristic
434C2×#95—1461no—
435C2×#95—1461no—
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#340C2×D7311yescharacteristic, complemented
446#340C2×D7311yescharacteristic, complemented
447#340C2×D7311yescharacteristic, complemented
448C25—731no—
449C23×C4—731no—
450C23×C4—731no—
451C23×C4—731no—
452C23×C4—731no—
453C23×C4—731no—
454C23×C4—1461no—
455C23×C4—1461no—
456C23×C4—1461no—
457C23×C4—1461no—
458C23×C4—1462no—
459C23×C4—1462no—
460C23×C4—1462no—
461C23×C4—1462no—
462C23×C4—1462no—
463C23×C4—1462no—
464C23×C4C22×D7311yescharacteristic
465C22×C8—731no—
466C22×C8—734no—
467C22×C8—731no—
468C22×C8—1462no—
469C22×C8—1462no—
470C22×C8—1462no—
471C22×C8—1462no—
472C22×C8—1462no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C2×C4⋊C4—731no—
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—1462no—
480C2×C4⋊C4—1462no—
481C2×C4⋊C4—1462no—
482C2×C4⋊C4—1462no—
483C2×C4⋊C4—1462no—
484C2×C4⋊C4—1462no—
485C2×C4⋊C4—1462no—
486C2×C4⋊C4—1462no—
487C2×C4⋊C4—1461no—
488C2×C4⋊C4—1461no—
489C2×C4⋊C4—1461no—
490C2×C4⋊C4—1461no—
491C2×C4⋊C4C22×D7311yescharacteristic
492C2×C4⋊C4C22×D7311yescharacteristic
493C2×C4⋊C4C22×D7311yescharacteristic
494C2×C4⋊C4C22×D7311yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—2924no—
498C2×C22⋊C4—2924no—
499C2×C22⋊C4—1461no—
500C2×C22⋊C4—1461no—
501C2×C22⋊C4—1461no—
502C2×C22⋊C4—1461no—
503C2×C22⋊C4—1461no—
504C2×C22⋊C4—1461no—
505#106—22no—
506#106—1462no—
507#106—1462no—
508#106—1462no—
509C22⋊C8—22no—
510C22⋊C8—1462no—
511C22⋊C8—1462no—
512C22⋊C8—1462no—
513#95—21no—
514#95—21no—
515#95—1461no—
516#95—1461no—
517#95—1461no—
518#95—1461no—
519#95—1461no—
520#95—1461no—
521C24—731no—
522C24—734no—
523C24—731no—
524C24—1462no—
525C24—1462no—
526C24—1462no—
527C24—1462no—
528C24—1462no—
529C24—1462no—
530C24D4×D7311yescharacteristic
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—2924no—
542C22×C4—2924no—
543C22×C4—2924no—
544C22×C4—2924no—
545C22×C4—2922no—
546C22×C4—2922no—
547C22×C4—2922no—
548C22×C4—2922no—
549C22×C4—2922no—
550C22×C4—2922no—
551C22×C4—2922no—
552C22×C4—2922no—
553C22×C4—2922no—
554C22×C4—2922no—
555C22×C4—2922no—
556C22×C4—2922no—
557C22×C4—731no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—732no—
561C22×C4—732no—
562C22×C4—732no—
563C22×C4—732no—
564C22×C4—731no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1461no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1461no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4D4×D7311yescharacteristic
585C22×C4C23×D7311yescharacteristic
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—2924no—
592C2×C8—732no—
593C2×C8—1468no—
594C2×C8—1461no—
595C2×C8—1461no—
596C2×C8—1461no—
597C2×C8—1461no—
598C2×C8—1461no—
599C2×C8D4×D7312yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—2922no—
609C4⋊C4—2922no—
610C4⋊C4—2922no—
611C4⋊C4—2922no—
612C4⋊C4—1461no—
613C4⋊C4—1461no—
614C4⋊C4—1461no—
615C4⋊C4—1461no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4—1461no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—2922no—
623C22⋊C4—2922no—
624C22⋊C4—2922no—
625C22⋊C4—2922no—
626C22⋊C4—2922no—
627C22⋊C4—2922no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—2924no—
635C23—2924no—
636C23—2924no—
637C23—2924no—
638C23—732no—
639C23—732no—
640C23—732no—
641C23—732no—
642C23—732no—
643C23—732no—
644C23—732no—
645C23—732no—
646C23—1468no—
647C23—1468no—
648C23—1468no—
649C23—1461no—
650C23—1461no—
651C23—1461no—
652C23—1461no—
653C23—1461no—
654C23—1461no—
655C23SD16×D7312yes—
656C23C2×D4×D7311yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—2924no—
677C2×C4—2924no—
678C2×C4—2924no—
679C2×C4—2921no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—2921no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—2921no—
686C2×C4—2921no—
687C2×C4—2921no—
688C2×C4—2921no—
689C2×C4—2921no—
690C2×C4—2921no—
691C2×C4—2921no—
692C2×C4—2921no—
693C2×C4—2921no—
694C2×C4—2921no—
695C2×C4—5844no—
696C2×C4—5844no—
697C2×C4—5844no—
698C2×C4—5844no—
699C2×C4—732no—
700C2×C4—732no—
701C2×C4—732no—
702C2×C4—734no—
703C2×C4—734no—
704C2×C4—734no—
705C2×C4—734no—
706C2×C4—1461no—
707C2×C4—1461no—
708C2×C4—1461no—
709C2×C4C2×D4×D7311yescharacteristic
710C2×C4#41×D7311yescharacteristic
711C2×C4#41×D7311yescharacteristic
712C2×C4#41×D7311yescharacteristic
713C2×C4#41×D7311yescharacteristic
714C2×C4#41×D7311yescharacteristic
715C8—22no—
716C8—41no—
717C8—2921no—
718C8—1462no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—29216no—
727C22—2921no—
728C22—2921no—
729C22—2921no—
730C22—2921no—
731C22—734no—
732C22—734no—
733C22—734no—
734C22—734no—
735C22—734no—
736C22—734no—
737C22—734no—
738C22—1462no—
739C22—1462no—
740C22—1462no—
741C22#121×D7311yescharacteristic
742C22#123×D7311yescharacteristic
743C22#123×D7311yescharacteristic
744C22C2×SD16×D7311yescharacteristic
745C22#135×D7311yescharacteristic
746C22AGL(1,ℤ/8)×D7311yescharacteristic
747C22#137×D7311yescharacteristic
748C4—41no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—2921no—
754C4—5841no—
755C4—5841no—
756C4—5841no—
757C4—5841no—
758C4—734no—
759C4#123×D7311yescharacteristic
760C4#124×D7311yescharacteristic
761C4#126×D7311yescharacteristic
762C4#126×D7311yescharacteristic
763C2—42no—
764C2—2922no—
765C2—738no—
766C2#397×D7311yescharacteristic
767C2#465×D7311yescharacteristic
768C2#468×D7311yescharacteristic
769C2#483×D7311yescharacteristic
770C2#482×D7311yescharacteristic
771C2#485×D7311yescharacteristic
772C2#481×D7311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2077C2
socleC23×C73C22×D4
prime radicalC24×D73D4
hypercenter#2077D73
hypocenterC73C2×#2077
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#106×D73C2semidirect
5. #22611370C2semidirect
6. #22611369C2semidirect
7. #22611368C2semidirect
8. #22611367C2semidirect
9. #22611366C2semidirect
10. #22611365C2semidirect
11. #22611364C2semidirect
12. #340×D73C2semidirect
13. #340×D73C2semidirect
14. #340×D73C2semidirect
15. C73×#2077C2semidirect
25. C2×#14556523C22semidirect
26. C2×#14556522C22semidirect
27. C2×#14556522C22semidirect
45. #17988350C22semidirect
46. #17988350C22semidirect
47. #17988350C22semidirect
48. #17988349C22semidirect
49. #17988349C22semidirect
50. #17988349C22semidirect
51. #17988349C22semidirect
52. #17988349C22semidirect
53. #17988349C22semidirect
54. C2×#106×C73C22semidirect
58. #340×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
386. D73#2077direct (N × H)
398. #2077D73direct (N × H)
402. C73C2×#2077semidirect
416. C2×#106C2×D73semidirect
445. #340C2×D73semidirect
446. #340C2×D73semidirect
447. #340C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D732
C2×C22⋊C8×D732
#380×D732
#226113702
#226113692
#226113682
#226113672
#226113662
#226113652
#226113642
#340×D732
C73×#20772
C2×#207773