Finite Group Databasebeta

← #33086729

Subgroups — #33086729

Order 18688.

1630 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D73C211yesmaximal, characteristic
2C2×#17988628C211yesmaximal, characteristic, complemented
3C2×#17988626C211yesmaximal, characteristic, complemented
4C2×#17988549C211yesmaximal, characteristic
5#380×D73C211yesmaximal, characteristic
6#22610132C211yesmaximal, characteristic, complemented
7#22610130C211yesmaximal, characteristic, complemented
8#22610128C211yesmaximal, characteristic, complemented
9#22610125C211yesmaximal, characteristic, complemented
10#22610122C211yesmaximal, characteristic, complemented
11#22610120C211yesmaximal, characteristic, complemented
12#22610117C211yesmaximal, characteristic, complemented
13#22609649C211yesmaximal, characteristic, complemented
14#22609649C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20C2×#14556549C2211yescharacteristic
21C2×#14556549C2211yescharacteristic
22C2×#14556548—21no—
23C2×#14556547—21no—
24#117×D73—24no—
25#117×D73—24no—
26C2×C4⋊C4×D73C2211yescharacteristic
27C2×C4⋊C4×D73C2211yescharacteristic
28C2×C4⋊C4×D73C2211yescharacteristic
29C2×C4⋊C4×D73C2211yescharacteristic
30C2×C22⋊C4×D73—21no—
31C2×C22⋊C4×D73—21no—
32C2×C42×D73—21no—
33#17988628—24no—
34#17988626—24no—
35C2×#14556525C2211yescharacteristic, complemented
36C2×#14556524C2211yescharacteristic, complemented
37C2×#14556524C2211yescharacteristic, complemented
38C2×#14556523C2211yescharacteristic, complemented
39C2×#14556522C2211yescharacteristic, complemented
40C2×#14556522C2211yescharacteristic, complemented
41#17988549C418yescomplemented
42C2×C22⋊#10596831C2211yescharacteristic
43C2×#14556503C2211yescharacteristic
44C2×#14556503C2211yescharacteristic
45#17988447C2211yescharacteristic
46#17988446—21no—
47#17988445—21no—
48#17988444C2211yescharacteristic
49#17988444C2211yescharacteristic
50#95×D73—21no—
51#17988350C2211yescharacteristic, complemented
52#17988350C2211yescharacteristic, complemented
53#17988349C2211yescharacteristic, complemented
54#17988349C2211yescharacteristic, complemented
55#17988349C2211yescharacteristic, complemented
56#17988349C2211yescharacteristic, complemented
57C2×#117×C73C2211yescharacteristic
58C2×#107×C73C2211yescharacteristic, complemented
59C2×#106×C73C2211yescharacteristic, complemented
60C2×C22⋊C8×C73C2211yescharacteristic
61#380×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic, complemented
63#340×C73C2211yescharacteristic, complemented
64C24×D73D411yescharacteristic
65C23×Dic73D411yescharacteristic
66C22×C4×D73—22no—
67C22×C4×D73—22no—
68C22×C4×D73—22no—
69C22×C4×D73—22no—
70C22×C4×D73—21no—
71C22×C4×D73—21no—
72C22×C4×D73—21no—
73C22×C4×D73—21no—
74C22×C4×D73C2×C414yes—
75C22×C4×D73D411yescharacteristic
76C22×C4×D73D411yescharacteristic
77C22×C4×D73Q814yes—
78C22×C4×D73C2311yescharacteristic
79C22×C4×D73C2311yescharacteristic
80C2×#11924011—22no—
81C2×#11924011—22no—
82C2×#11924011—22no—
83C2×#11924011—22no—
84C2×#11924011C2×C414yescomplemented
85C2×#11924011C2×C414yescomplemented
86C22×#10596831C2311yescharacteristic
87C22×#10596831C2311yescharacteristic
88#14556550—22no—
89#14556550—22no—
90#14556549—22no—
91#14556549—22no—
92#14556549D414yes—
93#14556549D414yes—
94#14556548—28no—
95#14556547—28no—
96C2×C4⋊Dic73C2311yescharacteristic
97C2×C4⋊Dic73C2311yescharacteristic
98C2×C4⋊Dic73C2311yescharacteristic
99C2×C4⋊Dic73C2311yescharacteristic
100C2×#11924007—21no—
101C2×#11924007—21no—
102C2×#11924007—21no—
103C2×#11924007—21no—
104C4⋊C4×D73—22no—
105C4⋊C4×D73—22no—
106C4⋊C4×D73—22no—
107C4⋊C4×D73—22no—
108C4⋊C4×D73—22no—
109C4⋊C4×D73—22no—
110C4⋊C4×D73—22no—
111C4⋊C4×D73—22no—
112C2×C22⋊Dic73—21no—
113C2×C22⋊Dic73—21no—
114C2×#11924005—21no—
115C2×#11924005—21no—
116C2×#11924005—21no—
117C2×#11924005—21no—
118C22⋊C4×D73—28no—
119C22⋊C4×D73—44no—
120C2×C4×Dic73—21no—
121C2×C4×Dic73—21no—
122C2×C4×Dic73—21no—
123C42×D73—28no—
124#14556525—22no—
125#14556524—22no—
126#14556524—22no—
127#14556523—22no—
128#14556522—22no—
129#14556522—22no—
130C22⋊#10596831C2×C414yescomplemented
131#14556503C2×C414yescomplemented
132#14556503C2×C414yescomplemented
133#14556498—21no—
134#14556498—21no—
135#14556498—21no—
136C23×C4×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139#117×C73—22no—
140#117×C73—22no—
141C2×C4⋊C4×C73C2311yescharacteristic
142C2×C4⋊C4×C73C2311yescharacteristic
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C22⋊C4×C73—21no—
146C2×C22⋊C4×C73—21no—
147C2×C42×C73—21no—
148#107×C73—22no—
149#106×C73—22no—
150C22⋊C8×C73C2×C414yescomplemented
151#95×C73—21no—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73—22no—
155C23×D73—22no—
156C23×D73—41no—
157C23×D73—41no—
158C23×D73C4⋊C414yes—
159C23×D73C2×D411yescharacteristic
160C23×D73C2×D411yescharacteristic
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73C4⋊C414yes—
168C22×Dic73C2×D411yescharacteristic
169C22×Dic73C2×D411yescharacteristic
170C2×C4×D73—22no—
171C2×C4×D73—22no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—22no—
177C2×C4×D73—22no—
178C2×C4×D73—28no—
179C2×C4×D73—28no—
180C2×C4×D73—28no—
181C2×C4×D73—28no—
182C2×C4×D73—24no—
183C2×C4×D73—24no—
184C2×C4×D73—42no—
185C2×C4×D73—42no—
186C2×C4×D73—42no—
187C2×C4×D73—42no—
188C2×C4×D73—42no—
189C2×C4×D73—42no—
190C2×C4×D73—42no—
191C2×C4×D73—42no—
192C2×C4×D73—42no—
193C2×C4×D73—42no—
194C2×C4×D73C4⋊C414yes—
195C2×C4×D73C4⋊C414yes—
196C2×C4×D73C22×C412yes—
197C2×C4×D73C22×C412yes—
198C2×C4×D73C2×D412yes—
199C2×C4×D73C2×D412yes—
200C2×C4×D73C2×Q812yes—
201C2×C4×D73C2×Q812yes—
202C2×C4×D73#4112yes—
203C2×C4×D73#4112yes—
204#11924011—28no—
205#11924011—28no—
206C2×#10596831—21no—
207C2×#10596831—21no—
208C2×#10596831—21no—
209C2×#10596831—21no—
210C2×#10596831C22×C412yes—
211C2×#10596831C22×C412yes—
212C4⋊Dic73—21no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73C2×D412yes—
219C4⋊Dic73C2×D412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—42no—
223#11924007—42no—
224C22⋊Dic73—24no—
225C22⋊Dic73—42no—
226#11924005—24no—
227#11924005—24no—
228#11924005—42no—
229#11924005—42no—
230C4×Dic73—24no—
231C4×Dic73—24no—
232C4×Dic73—24no—
233C24×C73C2×D411yescharacteristic
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73C22×C412yes—
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×Q812yes—
245C22×C4×C73C2411yescharacteristic
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73C22×C412yes—
251C2×C8×C73C22×C412yes—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73—21no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73—21no—
258C4⋊C4×C73C2×D412yes—
259C4⋊C4×C73C2×D412yes—
260C22⋊C4×C73—24no—
261C22⋊C4×C73—42no—
262C42×C73—24no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73C2×C4⋊C412yes—
270C23×C73C22×D411yescharacteristic
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—28no—
280C22×D73—28no—
281C22×D73—44no—
282C22×D73—44no—
283C22×D73—44no—
284C22×D73—44no—
285C22×D73—44no—
286C22×D73C2×C4⋊C412yes—
287C22×D73C2×C4⋊C412yes—
288C22×D73#12012yes—
289C22×D73#12312yes—
290C22×D73AGL(1,ℤ/8)12yes—
291C22×D73#13712yes—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73C2×C4⋊C412yes—
311C2×C4×C73C23×C411yescharacteristic
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C22×Q811yescharacteristic
315C2×C4×C73C2×#4111yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—28no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—41no—
329C2×Dic73—41no—
330C2×Dic73—41no—
331C2×Dic73—41no—
332C2×Dic73C2×C4⋊C412yes—
333C2×Dic73C2×C4⋊C412yes—
334C2×Dic73#12012yes—
335C2×Dic73#12312yes—
336C4×D73—28no—
337C4×D73—22no—
338C4×D73—22no—
339C4×D73—22no—
340C4×D73—22no—
341C4×D73—28no—
342C4×D73—48no—
343C4×D73—48no—
344C4×D73—84no—
345C4×D73—84no—
346C4×D73C4×D414yes—
347C4×D73C4×D414yes—
348C4×D73C22⋊Q814yes—
349C4×D73C22⋊Q814yes—
350C8×C73—22no—
351C8×C73—22no—
352#10596831—22no—
353#10596831—22no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73C22×C4⋊C411yescharacteristic
362C22×C73C2×#12011yescharacteristic
363C22×C73C2×#12311yescharacteristic
364C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C73C2×#13711yescharacteristic
366C22×C73#57511yescharacteristic
367C22×C73#57511yescharacteristic
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—22no—
372C2×D73—22no—
373C2×D73—22no—
374C2×D73—22no—
375C2×D73—22no—
376C2×D73—22no—
377C2×D73—22no—
378C2×D73—22no—
379C2×D73—22no—
380C2×D73—416no—
381C2×D73#38514yes—
382C2×D73#42814yescomplemented
383C4×C73—22no—
384C4×C73—42no—
385C4×C73—42no—
386C4×C73—81no—
387C4×C73—81no—
388C4×C73C2×C4×D411yescharacteristic
389C4×C73C2×C4×D411yescharacteristic
390C4×C73C2×C22⋊Q811yescharacteristic
391C4×C73C2×C22⋊Q811yescharacteristic
392Dic73—22no—
393Dic73—42no—
394Dic73—42no—
395Dic73—81no—
396Dic73—81no—
397Dic73#38514yes—
398#20846—731nomaximal, Sylow
399C2×C73—42no—
400C2×C73C2×#38511yescharacteristic
401C2×C73C2×#42811yescharacteristic
402C2×C73#291111yescharacteristic
403C2×C73#300611yescharacteristic
404C2×C73#300711yescharacteristic
405C2×C73#309411yescharacteristic
406C2×C73#309511yescharacteristic
407D73—24no—
408D73—24no—
409C22×#117—731no—
410C2×#428—731no—
411C2×#428—731no—
412C2×#407—731no—
413C2×#380—731no—
414#1854—731no—
415#1854—731no—
416#1854—731no—
417#1854D7311yescharacteristic, complemented
418#1853—731no—
419#1853—731no—
420#1852—731no—
421#1852—731no—
422#1736—731no—
423#1736—731no—
424C73#2084611yescharacteristic, complemented, Sylow
425C24×C4—731no—
426C22×M16—731no—
427C22×M16—731no—
428C2×#117—731no—
429C2×#117—731no—
430C2×#117—731no—
431C2×#117—1461no—
432C2×#117—1461no—
433C2×#117—1464no—
434C2×#117—1464no—
435C2×#117C2×D7311yescharacteristic
436C22×C4⋊C4—731no—
437C22×C4⋊C4—731no—
438C22×C4⋊C4—731no—
439C22×C4⋊C4—731no—
440C22×C22⋊C4—1461no—
441C22×C22⋊C4—1461no—
442C22×C42—1461no—
443#428—1464no—
444#428—1464no—
445C2×#107—731no—
446C2×#107—731no—
447C2×#107—731no—
448C2×#107C2×D7311yescharacteristic, complemented
449C2×#106—731no—
450C2×#106—731no—
451C2×#106—731no—
452C2×#106C2×D7311yescharacteristic, complemented
453#407—738no—
454C2×C22⋊C8—731no—
455C2×C22⋊C8—731no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8C2×D7311yescharacteristic
458#380—731no—
459#380—731no—
460#380—731no—
461#380—1461no—
462#380—1461no—
463#380C2×D7311yescharacteristic
464C2×#95—1461no—
465#340—731no—
466#340—731no—
467#340—731no—
468#340—731no—
469#340—731no—
470#340—731no—
471#340C2×D7311yescharacteristic, complemented
472#340C2×D7311yescharacteristic, complemented
473C25—731no—
474C23×C4—731no—
475C23×C4—731no—
476C23×C4—734no—
477C23×C4—731no—
478C23×C4—731no—
479C23×C4—734no—
480C23×C4—731no—
481C23×C4—1461no—
482C23×C4—1461no—
483C23×C4—1461no—
484C23×C4—1461no—
485C23×C4—1462no—
486C23×C4—1462no—
487C23×C4—1462no—
488C23×C4—1462no—
489C23×C4C22×D7311yescharacteristic
490C2×M16—734no—
491C2×M16—734no—
492C2×M16—1462no—
493C2×M16—1462no—
494C2×M16—1462no—
495C2×M16—1462no—
496C22×C8—731no—
497C22×C8—731no—
498C22×C8C22×D7311yescharacteristic
499C22×C8C22×D7311yescharacteristic
500#117—22no—
501#117—22no—
502#117—734no—
503#117—734no—
504#117—1468no—
505#117—1468no—
506#117—1462no—
507#117—1462no—
508#117—1462no—
509#117—1462no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—1462no—
515C2×C4⋊C4—1462no—
516C2×C4⋊C4—1462no—
517C2×C4⋊C4—1462no—
518C2×C4⋊C4—1462no—
519C2×C4⋊C4—1462no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1462no—
525C2×C4⋊C4—1462no—
526C2×C4⋊C4C22×D7311yescharacteristic
527C2×C4⋊C4C22×D7311yescharacteristic
528C2×C4⋊C4C22×D7311yescharacteristic
529C2×C4⋊C4C22×D7311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—2924no—
533C2×C22⋊C4—1468no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C42—21no—
541C2×C42—1468no—
542C2×C42—1461no—
543C2×C42—1461no—
544C2×C42—1461no—
545#107—22no—
546#107—1462no—
547#107—1462no—
548#107—1462no—
549#106—22no—
550#106—1462no—
551#106—1462no—
552#106—1462no—
553C22⋊C8—734no—
554C22⋊C8—734no—
555C22⋊C8—734no—
556C22⋊C8C4×D7314yescomplemented
557#95—21no—
558#95—1461no—
559#95—1461no—
560#95—1461no—
561C24—2921no—
562C24—2921no—
563C24—734no—
564C24—731no—
565C24—731no—
566C24—1462no—
567C24—1462no—
568C24—1462no—
569C24—1462no—
570C24D4×D7311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—2922no—
580C22×C4—2922no—
581C22×C4—2922no—
582C22×C4—2922no—
583C22×C4—2922no—
584C22×C4—2922no—
585C22×C4—2922no—
586C22×C4—2922no—
587C22×C4—2922no—
588C22×C4—2922no—
589C22×C4—731no—
590C22×C4—732no—
591C22×C4—732no—
592C22×C4—732no—
593C22×C4—732no—
594C22×C4—732no—
595C22×C4—732no—
596C22×C4—734no—
597C22×C4—731no—
598C22×C4—734no—
599C22×C4—734no—
600C22×C4—732no—
601C22×C4—732no—
602C22×C4—1464no—
603C22×C4—1464no—
604C22×C4—1462no—
605C22×C4—1462no—
606C22×C4—1468no—
607C22×C4—1468no—
608C22×C4—1468no—
609C22×C4—1468no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1461no—
615C22×C4—1461no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4C2×C4×D7312yes—
623C22×C4D4×D7311yescharacteristic
624C22×C4Q8×D7312yes—
625C22×C4C23×D7311yescharacteristic
626M16—1468no—
627M16—1468no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—732no—
633C2×C8—732no—
634C2×C8—1461no—
635C2×C8—1461no—
636C2×C8—1461no—
637C2×C8—1461no—
638C2×C8C2×C4×D7312yes—
639C2×C8C2×C4×D7312yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—2922no—
647C4⋊C4—2922no—
648C4⋊C4—732no—
649C4⋊C4—732no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1461no—
653C4⋊C4—1461no—
654C4⋊C4—1461no—
655C4⋊C4—1461no—
656C4⋊C4—1461no—
657C4⋊C4—1461no—
658C4⋊C4D4×D7312yes—
659C4⋊C4D4×D7312yes—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—2922no—
663C22⋊C4—2922no—
664C22⋊C4—2922no—
665C22⋊C4—1464no—
666C22⋊C4—1464no—
667C22⋊C4—1464no—
668C42—24no—
669C42—1464no—
670C42—1464no—
671C42—1464no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—2924no—
679C23—2924no—
680C23—2924no—
681C23—2924no—
682C23—2924no—
683C23—732no—
684C23—732no—
685C23—732no—
686C23—732no—
687C23—732no—
688C23—732no—
689C23—1468no—
690C23—1468no—
691C23—1461no—
692C23—1461no—
693C23—1461no—
694C23—1461no—
695C23—1461no—
696C23—1461no—
697C23—1461no—
698C23—1461no—
699C23C4⋊C4×D7312yes—
700C23C2×D4×D7311yescharacteristic
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—2928no—
720C2×C4—2928no—
721C2×C4—2921no—
722C2×C4—2921no—
723C2×C4—2921no—
724C2×C4—2921no—
725C2×C4—2921no—
726C2×C4—2921no—
727C2×C4—2921no—
728C2×C4—2921no—
729C2×C4—2921no—
730C2×C4—2921no—
731C2×C4—5844no—
732C2×C4—5844no—
733C2×C4—732no—
734C2×C4—732no—
735C2×C4—732no—
736C2×C4—734no—
737C2×C4—734no—
738C2×C4—734no—
739C2×C4—734no—
740C2×C4—732no—
741C2×C4—1468no—
742C2×C4—1468no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1468no—
746C2×C4—1461no—
747C2×C4—1461no—
748C2×C4—1462no—
749C2×C4—1462no—
750C2×C4—1462no—
751C2×C4—1462no—
752C2×C4C4⋊C4×D7312yes—
753C2×C4C22×C4×D7311yescharacteristic
754C2×C4C2×D4×D7311yescharacteristic
755C2×C4C2×D4×D7311yescharacteristic
756C2×C4C2×Q8×D7311yescharacteristic
757C2×C4#41×D7311yescharacteristic
758C2×C4#41×D7311yescharacteristic
759C8—22no—
760C8—22no—
761C8—1462no—
762C8—1462no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—29216no—
771C22—734no—
772C22—734no—
773C22—1462no—
774C22—1462no—
775C22—1462no—
776C22—1462no—
777C22—1462no—
778C22—1462no—
779C22—1462no—
780C22—1462no—
781C22—1462no—
782C22—1462no—
783C22—1462no—
784C22—1462no—
785C22C2×C4⋊C4×D7311yescharacteristic
786C22#120×D7311yescharacteristic
787C22#123×D7311yescharacteristic
788C22AGL(1,ℤ/8)×D7311yescharacteristic
789C22#137×D7311yescharacteristic
790C22#1798938411yescharacteristic
791C22#1798938411yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—81no—
796C4—81no—
797C4—2922no—
798C4—2922no—
799C4—5841no—
800C4—5841no—
801C4—734no—
802C4—1462no—
803C4C4×D4×D7311yescharacteristic
804C4C4×D4×D7311yescharacteristic
805C4C22⋊Q8×D7311yescharacteristic
806C4C22⋊Q8×D7311yescharacteristic
807C2—42no—
808C2—1464no—
809C2—1464no—
810C2#385×D7311yescharacteristic
811C2#428×D7311yescharacteristic
812C2#2261851911yescharacteristic
813C2#2261918011yescharacteristic
814C2#2261918811yescharacteristic
815C2#2261987011yescharacteristic
816C2#2261987811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1854C2
socleC23×C73C22×D4
prime radicalC24×D73D4
cosocleC22×C4×C73C24
hypercenter#1854D73
hypocenterC73#20846
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#17988628C2semidirect
3. C2×#17988626C2semidirect
6. #22610132C2semidirect
7. #22610130C2semidirect
8. #22610128C2semidirect
9. #22610125C2semidirect
10. #22610122C2semidirect
11. #22610120C2semidirect
12. #22610117C2semidirect
13. #22609649C2semidirect
14. #22609649C2semidirect
15. C73×#1854C2semidirect
35. C2×#14556525C22semidirect
36. C2×#14556524C22semidirect
37. C2×#14556524C22semidirect
38. C2×#14556523C22semidirect
39. C2×#14556522C22semidirect
40. C2×#14556522C22semidirect
41. #17988549C4semidirect
51. #17988350C22semidirect
52. #17988350C22semidirect
53. #17988349C22semidirect
54. #17988349C22semidirect
55. #17988349C22semidirect
56. #17988349C22semidirect
58. C2×#107×C73C22semidirect
59. C2×#106×C73C22semidirect
62. #340×C73C22semidirect
63. #340×C73C22semidirect
84. C2×#11924011C2×C4semidirect
85. C2×#11924011C2×C4semidirect
130. C22⋊#10596831C2×C4semidirect
131. #14556503C2×C4semidirect
132. #14556503C2×C4semidirect
150. C22⋊C8×C73C2×C4semidirect
382. C2×D73#428semidirect
417. #1854D73semidirect
424. C73#20846semidirect
448. C2×#107C2×D73semidirect
452. C2×#106C2×D73semidirect
471. #340C2×D73semidirect
472. #340C2×D73semidirect
556. C22⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D732
C2×#179886282
C2×#179886262
C2×#179885492
#380×D732
#226101322
#226101302
#226101282
#226101252
#226101222
#226101202
#226101172
#226096492
C73×#18542
#2084673