Finite Group Databasebeta

← #33086708

Subgroups — #33086708

Order 18688.

1590 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D73C211yesmaximal, characteristic
2C2×#17988624C211yesmaximal, characteristic, complemented
3C2×#17988622C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×D73C211yesmaximal, characteristic
5#22612313C211yesmaximal, 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#22609646C211yesmaximal, characteristic, complemented
14#22609646C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20C2×#14556549C2211yescharacteristic
21C2×#14556549C2211yescharacteristic
22C2×#14556549C2211yescharacteristic
23C2×#14556549C2211yescharacteristic
24C2×#14556548—21no—
25C2×#14556547—21no—
26#117×D73—24no—
27#117×D73—24no—
28C2×C4⋊C4×D73C2211yescharacteristic
29C2×C4⋊C4×D73C2211yescharacteristic
30C2×C22⋊C4×D73—21no—
31C2×C42×D73—21no—
32#17988624—24no—
33#17988622—24no—
34C2×#14556525C2211yescharacteristic, complemented
35C2×#14556524C2211yescharacteristic, complemented
36C2×#14556524C2211yescharacteristic, complemented
37C2×#14556523C2211yescharacteristic, complemented
38C2×#14556522C2211yescharacteristic, complemented
39C2×#14556522C2211yescharacteristic, complemented
40C2×C22⋊#10596831C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×#14556503C2211yescharacteristic
43C22⋊C8×D73C418yescomplemented
44#17988449—21no—
45#17988447C2211yescharacteristic
46#17988444C2211yescharacteristic
47#17988444C2211yescharacteristic
48#17988442—21no—
49C22⋊C4×Dic73—21no—
50#17988434—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×D73C2×C414yes—
73C22×C4×D73D411yescharacteristic
74C22×C4×D73D411yescharacteristic
75C22×C4×D73Q814yes—
76C22×C4×D73C2311yescharacteristic
77C22×C4×D73C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C2×C8×D73—22no—
81C2×C8×D73—22no—
82C2×C8×D73—22no—
83C2×C8×D73—22no—
84C2×C8×D73C2×C414yescomplemented
85C2×C8×D73C2×C414yescomplemented
86#14556550—22no—
87#14556550—22no—
88#14556549—22no—
89#14556549—22no—
90#14556549—22no—
91#14556549—22no—
92#14556549—22no—
93#14556549—22no—
94#14556549D414yes—
95#14556549D414yes—
96#14556548—28no—
97#14556547—28no—
98C2×C4⋊Dic73C2311yescharacteristic
99C2×C4⋊Dic73C2311yescharacteristic
100C2×C4⋊Dic73C2311yescharacteristic
101C2×C4⋊Dic73C2311yescharacteristic
102C2×#11924007—21no—
103C2×#11924007—21no—
104C4⋊C4×D73—22no—
105C4⋊C4×D73—22no—
106C4⋊C4×D73—22no—
107C4⋊C4×D73—22no—
108C2×C22⋊Dic73—21no—
109C2×C22⋊Dic73—21no—
110C2×#11924005—21no—
111C2×#11924005—21no—
112C2×#11924005—21no—
113C2×#11924005—21no—
114C2×#11924005—21no—
115C2×#11924005—21no—
116C22⋊C4×D73—28no—
117C2×C4×Dic73—21no—
118C2×C4×Dic73—21no—
119C2×C4×Dic73—21no—
120C2×C4×Dic73—21no—
121C2×C4×Dic73—21no—
122C42×D73—28no—
123#14556525—22no—
124#14556524—22no—
125#14556524—22no—
126#14556523—22no—
127#14556522—22no—
128#14556522—22no—
129C22⋊#10596831C2×C414yescomplemented
130#14556503C2×C414yes—
131#14556503C2×C414yes—
132#14556498—21no—
133#14556498—21no—
134#14556498—21no—
135C23×C4×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138#117×C73—22no—
139#117×C73—22no—
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C4⋊C4×C73C2311yescharacteristic
142C2×C4⋊C4×C73C2311yescharacteristic
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C22⋊C4×C73—21no—
145C2×C22⋊C4×C73—21no—
146C2×C42×C73—21no—
147#107×C73—22no—
148#106×C73—22no—
149C22⋊C8×C73C2×C414yescomplemented
150#95×C73—21no—
151C23×D73—22no—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73—22no—
155C23×D73—41no—
156C23×D73—41no—
157C23×D73C4⋊C414yes—
158C23×D73C2×D411yescharacteristic
159C23×D73C2×D411yescharacteristic
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73C4⋊C414yes—
167C22×Dic73C2×D411yescharacteristic
168C22×Dic73C2×D411yescharacteristic
169C2×C4×D73—22no—
170C2×C4×D73—22no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—22no—
176C2×C4×D73—22no—
177C2×C4×D73—28no—
178C2×C4×D73—28no—
179C2×C4×D73—28no—
180C2×C4×D73—28no—
181C2×C4×D73—24no—
182C2×C4×D73—24no—
183C2×C4×D73—42no—
184C2×C4×D73—42no—
185C2×C4×D73—42no—
186C2×C4×D73—42no—
187C2×C4×D73C4⋊C414yes—
188C2×C4×D73C4⋊C414yes—
189C2×C4×D73C22×C412yes—
190C2×C4×D73C22×C412yes—
191C2×C4×D73C2×D412yes—
192C2×C4×D73C2×D412yes—
193C2×C4×D73C2×Q812yes—
194C2×C4×D73C2×Q812yes—
195C2×C4×D73#4112yes—
196C2×C4×D73#4112yes—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831C22×C412yes—
202C2×#10596831C22×C412yes—
203C8×D73—28no—
204C8×D73—28no—
205C4⋊Dic73—21no—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—21no—
210C4⋊Dic73—21no—
211C4⋊Dic73C2×D412yes—
212C4⋊Dic73C2×D412yes—
213#11924007—24no—
214#11924007—24no—
215C22⋊Dic73—24no—
216C22⋊Dic73—42no—
217#11924005—24no—
218#11924005—24no—
219#11924005—42no—
220#11924005—42no—
221#11924005—42no—
222#11924005—42no—
223C4×Dic73—24no—
224C4×Dic73—24no—
225C4×Dic73—24no—
226C4×Dic73—42no—
227C4×Dic73—42no—
228C24×C73C2×D411yescharacteristic
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73C22×C412yes—
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×Q812yes—
240C22×C4×C73C2411yescharacteristic
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73C22×C412yes—
246C2×C8×C73C22×C412yes—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73C2×D412yes—
254C4⋊C4×C73C2×D412yes—
255C22⋊C4×C73—24no—
256C22⋊C4×C73—42no—
257C42×C73—24no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73C2×C4⋊C412yes—
265C23×C73C22×D411yescharacteristic
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—28no—
275C22×D73—28no—
276C22×D73—44no—
277C22×D73—44no—
278C22×D73—44no—
279C22×D73—44no—
280C22×D73—44no—
281C22×D73C2×C4⋊C412yes—
282C22×D73C2×C4⋊C412yes—
283C22×D73#12012yes—
284C22×D73#12312yes—
285C22×D73#13512yes—
286C22×D73#13512yes—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73C2×C4⋊C412yes—
306C2×C4×C73C23×C411yescharacteristic
307C2×C4×C73C22×D411yescharacteristic
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C22×Q811yescharacteristic
310C2×C4×C73C2×#4111yescharacteristic
311C2×C4×C73C2×#4111yescharacteristic
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—28no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—41no—
318C2×Dic73—41no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73C2×C4⋊C412yes—
328C2×Dic73C2×C4⋊C412yes—
329C2×Dic73#12012yes—
330C2×Dic73#12312yes—
331C4×D73—28no—
332C4×D73—22no—
333C4×D73—22no—
334C4×D73—22no—
335C4×D73—22no—
336C4×D73—28no—
337C4×D73—48no—
338C4×D73—48no—
339C4×D73C4×D414yes—
340C4×D73C4×D414yes—
341C4×D73C22⋊Q814yes—
342C4×D73C22⋊Q814yes—
343C8×C73—22no—
344C8×C73—22no—
345#10596831—22no—
346#10596831—22no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73C22×C4⋊C411yescharacteristic
355C22×C73C2×#12011yescharacteristic
356C22×C73C2×#12311yescharacteristic
357C22×C73C2×#13511yescharacteristic
358C22×C73C2×#13511yescharacteristic
359C22×C73#57511yescharacteristic
360C22×C73#57511yescharacteristic
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—22no—
364C2×D73—22no—
365C2×D73—22no—
366C2×D73—22no—
367C2×D73—22no—
368C2×D73—22no—
369C2×D73—22no—
370C2×D73—22no—
371C2×D73—22no—
372C2×D73—22no—
373C2×D73—416no—
374C2×D73#38514yes—
375C2×D73#42714yescomplemented
376C4×C73—22no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—81no—
380C4×C73—81no—
381C4×C73C2×C4×D411yescharacteristic
382C4×C73C2×C4×D411yescharacteristic
383C4×C73C2×C22⋊Q811yescharacteristic
384C4×C73C2×C22⋊Q811yescharacteristic
385Dic73—22no—
386Dic73—42no—
387Dic73—42no—
388Dic73—81no—
389Dic73—81no—
390Dic73#38514yes—
391#20843—731nomaximal, Sylow
392C2×C73—42no—
393C2×C73C2×#38511yescharacteristic
394C2×C73C2×#42711yescharacteristic
395C2×C73#291111yescharacteristic
396C2×C73#300211yescharacteristic
397C2×C73#300211yescharacteristic
398C2×C73#309111yescharacteristic
399C2×C73#309111yescharacteristic
400D73—24no—
401D73—24no—
402C22×#117—731no—
403C2×#427—731no—
404C2×#427—731no—
405C22×C22⋊C8—731no—
406#2280—731no—
407#1854—731no—
408#1854—731no—
409#1854—731no—
410#1854D7311yescharacteristic, complemented
411#1853—731no—
412#1853—731no—
413#1852—731no—
414#1852—731no—
415#1735—731no—
416#1735—731no—
417C73#2084311yescharacteristic, complemented, Sylow
418C24×C4—731no—
419C23×C8—731no—
420C23×C8—731no—
421C2×#117—731no—
422C2×#117—731no—
423C2×#117—731no—
424C2×#117—731no—
425C2×#117—731no—
426C2×#117—1461no—
427C2×#117—1461no—
428C2×#117—1464no—
429C2×#117—1464no—
430C2×#117C2×D7311yescharacteristic
431C22×C4⋊C4—731no—
432C22×C4⋊C4—731no—
433C22×C22⋊C4—1461no—
434C22×C42—1461no—
435#427—1464no—
436#427—1464no—
437C2×#107—731no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#107C2×D7311yescharacteristic, complemented
441C2×#106—731no—
442C2×#106—731no—
443C2×#106—731no—
444C2×#106C2×D7311yescharacteristic, complemented
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—738no—
449C2×C22⋊C8C2×D7311yescharacteristic
450#381—1461no—
451#380—731no—
452#380—731no—
453#380—731no—
454#380C2×D7311yescharacteristic
455#379—1461no—
456C4×C22⋊C4—1461no—
457C4×C22⋊C4—1461no—
458#340—731no—
459#340—731no—
460#340—731no—
461#340—731no—
462#340—731no—
463#340—731no—
464#340C2×D7311yescharacteristic, complemented
465#340C2×D7311yescharacteristic, complemented
466C25—731no—
467C23×C4—731no—
468C23×C4—731no—
469C23×C4—734no—
470C23×C4—731no—
471C23×C4—731no—
472C23×C4—734no—
473C23×C4—731no—
474C23×C4—1461no—
475C23×C4—1461no—
476C23×C4—1462no—
477C23×C4—1462no—
478C23×C4—1462no—
479C23×C4—1462no—
480C23×C4C22×D7311yescharacteristic
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—734no—
484C22×C8—734no—
485C22×C8—1462no—
486C22×C8—1462no—
487C22×C8—1462no—
488C22×C8—1462no—
489C22×C8C22×D7311yescharacteristic
490C22×C8C22×D7311yescharacteristic
491#117—22no—
492#117—22no—
493#117—734no—
494#117—734no—
495#117—1468no—
496#117—1462no—
497#117—1462no—
498#117—1462no—
499#117—1462no—
500#117—1468no—
501#117—1462no—
502#117—1462no—
503#117—1462no—
504#117—1462no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—1462no—
510C2×C4⋊C4—1462no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1462no—
514C2×C4⋊C4—1462no—
515C2×C4⋊C4C22×D7311yescharacteristic
516C2×C4⋊C4C22×D7311yescharacteristic
517C2×C4⋊C4C22×D7311yescharacteristic
518C2×C4⋊C4C22×D7311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1468no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C42—21no—
531C2×C42—1468no—
532C2×C42—1461no—
533C2×C42—1461no—
534C2×C42—1461no—
535C2×C42—1461no—
536C2×C42—1461no—
537#107—22no—
538#107—1462no—
539#107—1462no—
540#107—1462no—
541#106—22no—
542#106—1462no—
543#106—1462no—
544#106—1462no—
545C22⋊C8—734no—
546C22⋊C8—734no—
547C22⋊C8—734no—
548C22⋊C8C4×D7314yescomplemented
549#95—21no—
550#95—1461no—
551#95—1461no—
552#95—1461no—
553C24—2921no—
554C24—2921no—
555C24—734no—
556C24—731no—
557C24—731no—
558C24—1462no—
559C24—1462no—
560C24—1462no—
561C24—1462no—
562C24D4×D7311yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—2922no—
572C22×C4—2922no—
573C22×C4—2922no—
574C22×C4—2922no—
575C22×C4—731no—
576C22×C4—732no—
577C22×C4—732no—
578C22×C4—732no—
579C22×C4—732no—
580C22×C4—732no—
581C22×C4—732no—
582C22×C4—734no—
583C22×C4—731no—
584C22×C4—734no—
585C22×C4—734no—
586C22×C4—732no—
587C22×C4—732no—
588C22×C4—1464no—
589C22×C4—1464no—
590C22×C4—1462no—
591C22×C4—1462no—
592C22×C4—1468no—
593C22×C4—1468no—
594C22×C4—1468no—
595C22×C4—1468no—
596C22×C4—1462no—
597C22×C4—1462no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4—1461no—
605C22×C4—1461no—
606C22×C4—1461no—
607C22×C4—1461no—
608C22×C4C2×C4×D7312yes—
609C22×C4D4×D7311yescharacteristic
610C22×C4Q8×D7312yes—
611C22×C4C23×D7311yescharacteristic
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—732no—
617C2×C8—732no—
618C2×C8—1468no—
619C2×C8—1468no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8C2×C4×D7312yes—
625C2×C8C2×C4×D7312yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—732no—
633C4⋊C4—732no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4—1461no—
637C4⋊C4—1461no—
638C4⋊C4—1461no—
639C4⋊C4—1461no—
640C4⋊C4—1461no—
641C4⋊C4—1461no—
642C4⋊C4D4×D7312yes—
643C4⋊C4D4×D7312yes—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—2922no—
647C22⋊C4—2922no—
648C22⋊C4—2922no—
649C22⋊C4—2922no—
650C22⋊C4—2922no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C42—24no—
655C42—2922no—
656C42—2922no—
657C42—1464no—
658C42—1464no—
659C42—1464no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—2924no—
667C23—2924no—
668C23—2924no—
669C23—2924no—
670C23—2924no—
671C23—732no—
672C23—732no—
673C23—732no—
674C23—732no—
675C23—732no—
676C23—732no—
677C23—1468no—
678C23—1468no—
679C23—1461no—
680C23—1461no—
681C23—1461no—
682C23—1461no—
683C23—1461no—
684C23—1461no—
685C23—1461no—
686C23—1461no—
687C23C4⋊C4×D7312yes—
688C23C2×D4×D7311yescharacteristic
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—2928no—
708C2×C4—2928no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—2921no—
715C2×C4—2921no—
716C2×C4—2921no—
717C2×C4—2921no—
718C2×C4—2921no—
719C2×C4—732no—
720C2×C4—732no—
721C2×C4—732no—
722C2×C4—734no—
723C2×C4—734no—
724C2×C4—734no—
725C2×C4—734no—
726C2×C4—732no—
727C2×C4—1468no—
728C2×C4—1468no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1468no—
732C2×C4—1461no—
733C2×C4—1461no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4C4⋊C4×D7312yes—
739C2×C4C22×C4×D7311yescharacteristic
740C2×C4C2×D4×D7311yescharacteristic
741C2×C4C2×D4×D7311yescharacteristic
742C2×C4C2×Q8×D7311yescharacteristic
743C2×C4#41×D7311yescharacteristic
744C2×C4#41×D7311yescharacteristic
745C8—22no—
746C8—22no—
747C8—1462no—
748C8—1462no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—29216no—
757C22—734no—
758C22—734no—
759C22—1462no—
760C22—1462no—
761C22—1462no—
762C22—1462no—
763C22—1462no—
764C22—1462no—
765C22—1462no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22—1462no—
770C22—1462no—
771C22C2×C4⋊C4×D7311yescharacteristic
772C22#120×D7311yescharacteristic
773C22#123×D7311yescharacteristic
774C22#135×D7311yescharacteristic
775C22#135×D7311yescharacteristic
776C22#1798938311yescharacteristic
777C22#1798938611yescharacteristic
778C4—22no—
779C4—42no—
780C4—42no—
781C4—81no—
782C4—81no—
783C4—2922no—
784C4—2922no—
785C4—5841no—
786C4—5841no—
787C4—734no—
788C4—1462no—
789C4C4×D4×D7311yescharacteristic
790C4C4×D4×D7311yescharacteristic
791C4C22⋊Q8×D7311yescharacteristic
792C4C22⋊Q8×D7311yescharacteristic
793C2—42no—
794C2—1464no—
795C2—1464no—
796C2#385×D7311yescharacteristic
797C2#427×D7311yescharacteristic
798C2#2261851811yescharacteristic
799C2#2261914611yescharacteristic
800C2#2261915211yescharacteristic
801C2#2261984311yescharacteristic
802C2#2261984911yescharacteristic
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#20843
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×#17988624C2semidirect
3. C2×#17988622C2semidirect
6. #22610132C2semidirect
7. #22610130C2semidirect
8. #22610128C2semidirect
9. #22610125C2semidirect
10. #22610122C2semidirect
11. #22610120C2semidirect
12. #22610117C2semidirect
13. #22609646C2semidirect
14. #22609646C2semidirect
15. C73×#1854C2semidirect
34. C2×#14556525C22semidirect
35. C2×#14556524C22semidirect
36. C2×#14556524C22semidirect
37. C2×#14556523C22semidirect
38. C2×#14556522C22semidirect
39. C2×#14556522C22semidirect
43. C22⋊C8×D73C4semidirect
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×C8×D73C2×C4semidirect
85. C2×C8×D73C2×C4semidirect
129. C22⋊#10596831C2×C4semidirect
149. C22⋊C8×C73C2×C4semidirect
375. C2×D73#427semidirect
410. #1854D73semidirect
417. C73#20843semidirect
440. C2×#107C2×D73semidirect
444. C2×#106C2×D73semidirect
464. #340C2×D73semidirect
465. #340C2×D73semidirect
548. 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×#179886242
C2×#179886222
C2×C22⋊C8×D732
#226123132
#226101322
#226101302
#226101282
#226101252
#226101222
#226101202
#226101172
#226096462
C73×#18542
#2084373