Finite Group Databasebeta

← #33095117

Subgroups — #33095117

Order 18688.

1486 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic
2#22612314C211yesmaximal, characteristic, complemented
3#22610377C214yesmaximal, complemented
4#22610233C214yesmaximal, complemented
5#22610028C212yesmaximal, complemented
6#22609874C212yesmaximal, complemented
7C2×#407×C73C211yesmaximal, characteristic, complemented
8C22×#11924028C2211yescharacteristic
9#17989098—21no—
10#17989098—21no—
11#17989098—21no—
12#17989098—21no—
13#17989098C412yescomplemented
14#17989098C412yescomplemented
15#17989098C2212yes—
16#17989098C2212yes—
17C2×#14556574—21no—
18C2×#14556570C411yescharacteristic, complemented
19C2×#14556570C411yescharacteristic, complemented
20C2×#14556565C411yescharacteristic, complemented
21C2×#14556565C411yescharacteristic, complemented
22C2×#14556560—21no—
23C2×C4×C22⋊D73—21no—
24C2×C4×C22⋊D73—21no—
25C2×#14556550C2211yescharacteristic
26C2×#14556550C2212yescomplemented
27C2×#14556517C2218yescomplemented
28#17988450—21no—
29#17988447—21no—
30#17988447—21no—
31#17988443—21no—
32C4×C22⋊Dic73C2212yes—
33C4×C22⋊Dic73C2212yescomplemented
34#17988348C2218yescomplemented
35C24×C4×C73C2211yescharacteristic
36C22×M16×C73C2212yescomplemented
37#407×C73—21no—
38#407×C73—21no—
39#407×C73C2212yes—
40#407×C73C2212yescomplemented
41C2×C22⋊C8×C73—21no—
42C2×C22⋊C8×C73—21no—
43C2×#11924028—21no—
44C2×#11924028—21no—
45C2×#11924028—44no—
46C2×#11924028C2×C412yes—
47C2×#11924028C2312yes—
48C22×Dic146C2×C411yescharacteristic
49C22×D292C2×C411yescharacteristic
50C22×C22⋊D73—21no—
51C22×C22⋊D73—21no—
52C22×C22⋊D73—21no—
53C22×C4×D73—21no—
54#14556574—22no—
55#14556574—22no—
56#14556574—22no—
57#14556574—22no—
58#14556570—21no—
59#14556570—21no—
60#14556570—21no—
61#14556570—21no—
62#14556570C2×C412yes—
63#14556570C2×C412yes—
64#14556570C2×C412yes—
65#14556570C2×C412yes—
66#14556565—21no—
67#14556565—21no—
68#14556565—21no—
69#14556565—21no—
70#14556565C2×C412yes—
71#14556565C2×C412yes—
72#14556565C2×C412yes—
73#14556565C2×C412yes—
74#14556560—22no—
75#14556560—22no—
76#14556560—22no—
77#14556560—22no—
78C4×C22⋊D73—22no—
79C4×C22⋊D73—22no—
80C4×C22⋊D73—22no—
81C4×C22⋊D73—22no—
82C4×C22⋊D73—22no—
83C4×C22⋊D73—22no—
84C4×C22⋊D73—22no—
85C4×C22⋊D73—22no—
86#14556550—21no—
87#14556550—21no—
88#14556550—44no—
89#14556550C2×C412yes—
90#14556550C2312yes—
91C2×C4⋊Dic73—22no—
92C2×C4⋊Dic73C2×C411yescharacteristic
93C2×C4⋊Dic73C2×C411yescharacteristic
94C2×#11924007—21no—
95C2×#11924007—21no—
96C2×C22⋊Dic73—21no—
97C2×C22⋊Dic73—21no—
98C2×C22⋊Dic73—21no—
99C2×C22⋊Dic73—22no—
100C2×C22⋊Dic73—22no—
101C2×C22⋊Dic73—22no—
102C2×#11924005—21no—
103C2×#11924005—21no—
104C2×C4×Dic73—21no—
105C2×C4×Dic73C2314yes—
106#14556517—48no—
107#14556498—22no—
108#14556498—22no—
109C25×C73D411yescharacteristic
110C23×C4×C73—44no—
111C23×C4×C73C2×C411yescharacteristic
112C23×C4×C73C2×C411yescharacteristic
113C23×C4×C73C2×C411yescharacteristic
114C23×C4×C73C2×C411yescharacteristic
115C23×C4×C73D411yescharacteristic
116C23×C4×C73D411yescharacteristic
117C23×C4×C73D411yescharacteristic
118C23×C4×C73D411yescharacteristic
119C23×C4×C73D411yescharacteristic
120C23×C4×C73D411yescharacteristic
121C23×C4×C73D411yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C2×M16×C73—22no—
126C2×M16×C73—44no—
127C2×M16×C73C2314yes—
128C22×C8×C73—22no—
129C22⋊C8×C73—22no—
130C22⋊C8×C73—22no—
131C22⋊C8×C73—22no—
132C22⋊C8×C73—22no—
133C23×D73—21no—
134#11924028—28no—
135#11924028—44no—
136#11924028—44no—
137#11924028—44no—
138C2×Dic146—21no—
139C2×Dic146—42no—
140C2×Dic146C22×C412yes—
141C2×D292—21no—
142C2×D292—42no—
143C2×D292C22×C412yes—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C2×C22⋊D73—22no—
150C2×C22⋊D73—44no—
151C2×C22⋊D73—44no—
152C2×C22⋊D73—44no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—24no—
157C2×C4×D73—22no—
158C2×C4×D73—22no—
159C2×C4×D73—44no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—44no—
163C4⋊Dic73C22×C412yes—
164C4⋊Dic73C22×C412yes—
165#11924007—22no—
166#11924007—22no—
167#11924007—22no—
168#11924007—22no—
169C22⋊Dic73—22no—
170C22⋊Dic73—22no—
171C22⋊Dic73—22no—
172C22⋊Dic73—22no—
173C22⋊Dic73—22no—
174C22⋊Dic73—22no—
175C22⋊Dic73—44no—
176C22⋊Dic73—44no—
177C22⋊Dic73—44no—
178#11924005—22no—
179#11924005—22no—
180#11924005—22no—
181#11924005—22no—
182C4×Dic73—22no—
183C4×Dic73—22no—
184C4×Dic73—28no—
185C24×C73—42no—
186C24×C73—42no—
187C24×C73—42no—
188C24×C73C22⋊C411yescharacteristic
189C24×C73C22⋊C411yescharacteristic
190C24×C73C22⋊C411yescharacteristic
191C24×C73C22⋊C411yescharacteristic
192C24×C73C2×D411yescharacteristic
193C24×C73C2×D411yescharacteristic
194C24×C73C2×D411yescharacteristic
195C22×C4×C73—24no—
196C22×C4×C73—24no—
197C22×C4×C73—24no—
198C22×C4×C73—42no—
199C22×C4×C73—42no—
200C22×C4×C73—42no—
201C22×C4×C73—42no—
202C22×C4×C73—42no—
203C22×C4×C73—42no—
204C22×C4×C73—42no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73C22⋊C411yescharacteristic
210C22×C4×C73C22⋊C411yescharacteristic
211C22×C4×C73C22⋊C411yescharacteristic
212C22×C4×C73C22⋊C411yescharacteristic
213C22×C4×C73C22⋊C411yescharacteristic
214C22×C4×C73C22⋊C411yescharacteristic
215C22×C4×C73C22⋊C411yescharacteristic
216C22×C4×C73C22⋊C411yescharacteristic
217C22×C4×C73C22⋊C411yescharacteristic
218C22×C4×C73C22⋊C411yescharacteristic
219C22×C4×C73C22⋊C411yescharacteristic
220C22×C4×C73C22⋊C411yescharacteristic
221C22×C4×C73C22×C411yescharacteristic
222C22×C4×C73C22×C411yescharacteristic
223C22×C4×C73C22×C411yescharacteristic
224C22×C4×C73C22×C411yescharacteristic
225C22×C4×C73C22×C411yescharacteristic
226C22×C4×C73C22×C411yescharacteristic
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2411yescharacteristic
237M16×C73—28no—
238M16×C73—44no—
239C2×C8×C73—24no—
240C2×C8×C73—44no—
241C23×C73—22no—
242C23×C73—22no—
243C23×C73—22no—
244C23×C73—22no—
245C23×C73—22no—
246C23×C73—22no—
247C23×C73—22no—
248C23×C73—22no—
249C23×C73—22no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—416no—
263C23×C73C2×C22⋊C411yescharacteristic
264C23×C73C2×C22⋊C411yescharacteristic
265C23×C73C2×C22⋊C411yescharacteristic
266C23×C73C2×C22⋊C411yescharacteristic
267C23×C73C2×C22⋊C411yescharacteristic
268C23×C73C2×C22⋊C411yescharacteristic
269C23×C73C22×D411yescharacteristic
270C22×D73—22no—
271C22×D73—42no—
272C22×D73—42no—
273C22×D73—42no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
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—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
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×C73C2×C22⋊C411yescharacteristic
302C2×C4×C73C2×C22⋊C411yescharacteristic
303C2×C4×C73C2×C22⋊C411yescharacteristic
304C2×C4×C73C2×C22⋊C411yescharacteristic
305C2×C4×C73C2×C22⋊C411yescharacteristic
306C2×C4×C73C2×C22⋊C411yescharacteristic
307C2×C4×C73C23×C411yescharacteristic
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73H(5,𝔽2)14yes—
310C22⋊D73—44no—
311C22⋊D73—44no—
312C22⋊D73—44no—
313C22⋊D73—44no—
314C22⋊D73—44no—
315C22⋊D73—44no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73—44no—
323C2×Dic73—44no—
324C2×Dic73—44no—
325D292—24no—
326D292—42no—
327C4×D73—44no—
328C4×D73—44no—
329Dic146—24no—
330Dic146—42no—
331C8×C73—44no—
332C22×C73—21no—
333C22×C73—21no—
334C22×C73—21no—
335C22×C73—21no—
336C22×C73—21no—
337C22×C73—21no—
338C22×C73—21no—
339C22×C73—21no—
340C22×C73—21no—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—21no—
346C22×C73—21no—
347C22×C73—21no—
348C22×C73—21no—
349C22×C73—21no—
350C22×C73—44no—
351C22×C73—44no—
352C22×C73—44no—
353C22×C73—44no—
354C22×C73—44no—
355C22×C73—44no—
356C22×C73—44no—
357C22×C73#42112yes—
358C22×C73#42112yes—
359C22×C73C22×C22⋊C411yescharacteristic
360C22×C73#53412yes—
361C2×D73—42no—
362C2×D73—42no—
363C2×D73—42no—
364C2×D73—84no—
365C4×C73—21no—
366C4×C73—21no—
367C4×C73—21no—
368C4×C73—21no—
369C4×C73—21no—
370C4×C73—21no—
371C4×C73#51812yes—
372C4×C73#53412yes—
373Dic73—42no—
374Dic73—42no—
375Dic73—42no—
376Dic73—84no—
377#21774—731nomaximal, Sylow
378C2×C73—22no—
379C2×C73—22no—
380C2×C73—22no—
381C2×C73—41no—
382C2×C73—41no—
383C2×C73—41no—
384C2×C73—41no—
385C2×C73#230811yescharacteristic
386C2×C73C2×#42111yescharacteristic
387C2×C73C2×#42111yescharacteristic
388D73—82no—
389C2×#525—731no—
390C2×#407D7311yescharacteristic, complemented
391#2280—731no—
392#1897—734no—
393#1871—734no—
394#1826—732no—
395#1789—732no—
396C73#2177411yescharacteristic, complemented, Sylow
397C22×#41—731no—
398C24×C4C2×D7311yescharacteristic
399C22×M16C2×D7312yescomplemented
400#525—732no—
401#525—732no—
402#525—732no—
403#525—732no—
404#525—1461no—
405#525—1461no—
406#525—1461no—
407#525—1461no—
408C2×#123—1461no—
409C2×C22⋊Q8—731no—
410C2×C22⋊Q8—731no—
411C2×#121—731no—
412C2×#121—731no—
413C2×#120—1461no—
414C2×C4×D4—1461no—
415C2×C4×D4—1461no—
416C2×#117—732no—
417C2×#117—731no—
418C2×#104—738no—
419#407—21no—
420#407—21no—
421#407C2×D7312yes—
422#407C2×D7312yescomplemented
423C2×C22⋊C8—21no—
424C2×C22⋊C8—21no—
425#381—1461no—
426#380—1461no—
427#380—1461no—
428#379—1461no—
429C4×C22⋊C4—732no—
430C4×C22⋊C4—732no—
431#339—738no—
432C25D29211yescharacteristic
433C2×#41—2924no—
434C2×#41—732no—
435C2×#41—732no—
436C2×#41—1461no—
437C2×#41—1461no—
438C22×Q8—731no—
439C22×D4—731no—
440C22×D4—1461no—
441C22×D4—1461no—
442C22×D4—1461no—
443C23×C4—44no—
444C23×C4—1461no—
445C23×C4C4×D7311yescharacteristic
446C23×C4C4×D7311yescharacteristic
447C23×C4C4×D7311yescharacteristic
448C23×C4C4×D7311yescharacteristic
449C23×C4D29211yescharacteristic
450C23×C4D29211yescharacteristic
451C23×C4D29211yescharacteristic
452C23×C4C22⋊D7311yescharacteristic
453C23×C4C22⋊D7311yescharacteristic
454C23×C4C22⋊D7311yescharacteristic
455C23×C4C22⋊D7311yescharacteristic
456C23×C4C22×D7311yescharacteristic
457C23×C4C22×D7311yescharacteristic
458C23×C4C22×D7311yescharacteristic
459C2×M16—22no—
460C2×M16—44no—
461C2×M16C22×D7314yes—
462C22×C8—22no—
463#123—1462no—
464#123—1462no—
465#123—1462no—
466#123—1462no—
467C22⋊Q8—732no—
468C22⋊Q8—732no—
469C22⋊Q8—732no—
470C22⋊Q8—732no—
471C22⋊Q8—1461no—
472C22⋊Q8—1461no—
473C22⋊Q8—1461no—
474C22⋊Q8—1461no—
475#121—732no—
476#121—732no—
477#121—732no—
478#121—732no—
479#121—1461no—
480#121—1461no—
481#121—1461no—
482#121—1461no—
483#120—1462no—
484#120—1462no—
485#120—1462no—
486#120—1462no—
487C4×D4—1462no—
488C4×D4—1462no—
489C4×D4—1462no—
490C4×D4—1462no—
491C4×D4—1462no—
492C4×D4—1462no—
493C4×D4—1462no—
494C4×D4—1462no—
495#117—2924no—
496#117—732no—
497#117—732no—
498#117—1461no—
499#117—1461no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—1462no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C22⋊C4—1462no—
506C2×C22⋊C4—1462no—
507C2×C22⋊C4—1462no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C42—734no—
514C2×C42—1461no—
515#104—2928no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#95—1462no—
521#95—1462no—
522C24—42no—
523C24—42no—
524C24—42no—
525C24—1461no—
526C24#1192400511yescharacteristic
527C24#1192400511yescharacteristic
528C24#1192400511yescharacteristic
529C24#1192400511yescharacteristic
530C24C2×D29211yescharacteristic
531C24C2×D29211yescharacteristic
532C24C2×D29211yescharacteristic
533#41—2924no—
534#41—2924no—
535#41—2924no—
536#41—1468no—
537C2×Q8—2922no—
538C2×Q8—732no—
539C2×Q8—1461no—
540C2×D4—2922no—
541C2×D4—2924no—
542C2×D4—2924no—
543C2×D4—2924no—
544C2×D4—732no—
545C2×D4—1462no—
546C2×D4—1462no—
547C2×D4—1462no—
548C2×D4—1462no—
549C2×D4—1462no—
550C2×D4—1462no—
551C2×D4—1461no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—2924no—
567C22×C4—1464no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4#1192400511yescharacteristic
574C22×C4#1192400511yescharacteristic
575C22×C4#1192400511yescharacteristic
576C22×C4#1192400511yescharacteristic
577C22×C4#1192400511yescharacteristic
578C22×C4#1192400511yescharacteristic
579C22×C4#1192400511yescharacteristic
580C22×C4#1192400511yescharacteristic
581C22×C4#1192400511yescharacteristic
582C22×C4#1192400511yescharacteristic
583C22×C4#1192400511yescharacteristic
584C22×C4#1192400511yescharacteristic
585C22×C4C2×C4×D7311yescharacteristic
586C22×C4C2×C4×D7311yescharacteristic
587C22×C4C2×C4×D7311yescharacteristic
588C22×C4C2×C4×D7311yescharacteristic
589C22×C4C2×C4×D7311yescharacteristic
590C22×C4C2×C4×D7311yescharacteristic
591C22×C4C2×C22⋊D7311yescharacteristic
592C22×C4C2×C22⋊D7311yescharacteristic
593C22×C4C2×C22⋊D7311yescharacteristic
594C22×C4C2×C22⋊D7311yescharacteristic
595C22×C4C2×C22⋊D7311yescharacteristic
596C22×C4C2×C22⋊D7311yescharacteristic
597C22×C4C2×D29211yescharacteristic
598C22×C4C2×D29211yescharacteristic
599C22×C4C2×D29211yescharacteristic
600C22×C4C23×D7311yescharacteristic
601M16—28no—
602M16—44no—
603C2×C8—24no—
604C2×C8—44no—
605C4⋊C4—2924no—
606C4⋊C4—732no—
607C4⋊C4—732no—
608C4⋊C4—1462no—
609C4⋊C4—1462no—
610C4⋊C4—1462no—
611C4⋊C4—1462no—
612C4⋊C4—1461no—
613C4⋊C4—1461no—
614C22⋊C4—2924no—
615C22⋊C4—2924no—
616C22⋊C4—2924no—
617C22⋊C4—1462no—
618C22⋊C4—1462no—
619C22⋊C4—1462no—
620C22⋊C4—1462no—
621C22⋊C4—1462no—
622C22⋊C4—1462no—
623C22⋊C4—1462no—
624C22⋊C4—1462no—
625C22⋊C4—1462no—
626C22⋊C4—1462no—
627C42—1468no—
628C42—1462no—
629C42—1462no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—416no—
652C23—2922no—
653C23—2922no—
654C23—2922no—
655C23—1462no—
656C23C2×#1192400511yescharacteristic
657C23C2×#1192400511yescharacteristic
658C23C2×#1192400511yescharacteristic
659C23C2×#1192400511yescharacteristic
660C23C2×#1192400511yescharacteristic
661C23C2×#1192400511yescharacteristic
662C23C22×D29211yescharacteristic
663Q8—2922no—
664Q8—1464no—
665D4—2922no—
666D4—2924no—
667D4—2924no—
668D4—2924no—
669D4—2924no—
670D4—2924no—
671D4—2924no—
672D4—1464no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—2924no—
701C2×C4—2922no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—2924no—
705C2×C4—2924no—
706C2×C4—2924no—
707C2×C4—2924no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4C2×#1192400511yescharacteristic
712C2×C4C2×#1192400511yescharacteristic
713C2×C4C2×#1192400511yescharacteristic
714C2×C4C2×#1192400511yescharacteristic
715C2×C4C2×#1192400511yescharacteristic
716C2×C4C2×#1192400511yescharacteristic
717C2×C4C22×C4×D7311yescharacteristic
718C2×C4C22×C22⋊D7311yescharacteristic
719C2×C4#1455663614yes—
720C8—44no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—2922no—
747C22—2922no—
748C22—2922no—
749C22—5844no—
750C22#1798860312yes—
751C22#1798860312yes—
752C22C22×#1192400511yescharacteristic
753C22#1798914912yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—2922no—
761C4—2922no—
762C4—2922no—
763C4—5844no—
764C4#1798906012yes—
765C4#1798914612yes—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—41no—
772C2—41no—
773C2—5842no—
774C2#2261250611yescharacteristic
775C2C2×#1798860311yescharacteristic
776C2C2×#1798860311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#407×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC2×#17989098C2
cosocleC22×C4×C73C24
hypercenterC2×#407D73
hypocenterC73#21774
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #22612314C2semidirect
3. #22610377C2semidirect
4. #22610233C2semidirect
5. #22610028C2semidirect
6. #22609874C2semidirect
7. C2×#407×C73C2semidirect
13. #17989098C4semidirect
14. #17989098C4semidirect
18. C2×#14556570C4semidirect
19. C2×#14556570C4semidirect
20. C2×#14556565C4semidirect
21. C2×#14556565C4semidirect
26. C2×#14556550C22semidirect
27. C2×#14556517C22semidirect
33. C4×C22⋊Dic73C22semidirect
34. #17988348C22semidirect
36. C22×M16×C73C22semidirect
40. #407×C73C22semidirect
390. C2×#407D73semidirect
396. C73#21774semidirect
399. C22×M16C2×D73semidirect
422. #407C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890982
#226123142
#226103772
#226102332
#226100282
#226098742
C2×#407×C732
#2177473