Finite Group Databasebeta

← #33053264

Subgroups — #33053264

Order 18688.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic
2#22612314C211yesmaximal, characteristic, complemented
3#22608475C214yesmaximal, complemented
4#22608465C212yesmaximal, complemented
5#22608461C212yesmaximal, complemented
6#22608423C214yesmaximal, complemented
7C2×#407×C73C211yesmaximal, characteristic, complemented
8C22×#11924028C411yescharacteristic, complemented
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×#14556570C2211yescharacteristic
20C2×#14556565C411yescharacteristic, complemented
21C2×#14556565C2211yescharacteristic
22C2×#14556560—21no—
23C2×C4×C22⋊D73—21no—
24C2×C4×C22⋊D73—21no—
25C2×#14556550—21no—
26C2×#14556550C411yescharacteristic, complemented
27#17988450C2212yes—
28#17988447—21no—
29#17988447C2212yescomplemented
30#17988443—21no—
31C4×C22⋊Dic73—21no—
32C4×C22⋊Dic73C2212yescomplemented
33#17988325C2218yescomplemented
34#17988322C2218yescomplemented
35C24×C4×C73C2211yescharacteristic
36C22×M16×C73—21no—
37#407×C73—21no—
38#407×C73—21no—
39#407×C73C2212yes—
40#407×C73C2212yescomplemented
41C2×C22⋊C8×C73—21no—
42C2×C22⋊C8×C73C2212yescomplemented
43C2×#11924028—21no—
44C2×#11924028—21no—
45C2×#11924028—44no—
46C2×#11924028C2×C412yes—
47C2×#11924028C2×C412yes—
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#14556570C2312yes—
66#14556565—21no—
67#14556565—21no—
68#14556565—21no—
69#14556565—21no—
70#14556565C2×C412yes—
71#14556565C2×C412yes—
72#14556565C2×C412yes—
73#14556565C2312yes—
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#14556550C2×C412yes—
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×Dic73—22no—
106#14556498—22no—
107#14556498C2314yes—
108C25×C73D411yescharacteristic
109C23×C4×C73—44no—
110C23×C4×C73C2×C411yescharacteristic
111C23×C4×C73C2×C411yescharacteristic
112C23×C4×C73C2×C411yescharacteristic
113C23×C4×C73C2×C411yescharacteristic
114C23×C4×C73D411yescharacteristic
115C23×C4×C73D411yescharacteristic
116C23×C4×C73D411yescharacteristic
117C23×C4×C73D411yescharacteristic
118C23×C4×C73D411yescharacteristic
119C23×C4×C73D411yescharacteristic
120C23×C4×C73D411yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C2×M16×C73—22no—
125C2×M16×C73—22no—
126C2×M16×C73—44no—
127C22×C8×C73—22no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—22no—
130C22⋊C8×C73—22no—
131C22⋊C8×C73C2314yes—
132C23×D73—21no—
133#11924028—44no—
134#11924028—44no—
135#11924028—44no—
136#11924028—44no—
137C2×Dic146—21no—
138C2×Dic146—42no—
139C2×Dic146C22×C412yes—
140C2×D292—21no—
141C2×D292—42no—
142C2×D292C22×C412yes—
143C2×C22⋊D73—22no—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C2×C22⋊D73—44no—
150C2×C22⋊D73—44no—
151C2×C22⋊D73—44no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—24no—
156C2×C4×D73—22no—
157C2×C4×D73—22no—
158C2×C4×D73—44no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—44no—
162C4⋊Dic73C22×C412yes—
163C4⋊Dic73C22×C412yes—
164#11924007—22no—
165#11924007—22no—
166#11924007—22no—
167#11924007—22no—
168C22⋊Dic73—22no—
169C22⋊Dic73—22no—
170C22⋊Dic73—22no—
171C22⋊Dic73—22no—
172C22⋊Dic73—22no—
173C22⋊Dic73—22no—
174C22⋊Dic73—44no—
175C22⋊Dic73—44no—
176C22⋊Dic73—44no—
177#11924005—22no—
178#11924005—22no—
179#11924005—22no—
180#11924005—22no—
181C4×Dic73—22no—
182C4×Dic73—22no—
183C4×Dic73—44no—
184C24×C73—42no—
185C24×C73—42no—
186C24×C73—42no—
187C24×C73C22⋊C411yescharacteristic
188C24×C73C22⋊C411yescharacteristic
189C24×C73C22⋊C411yescharacteristic
190C24×C73C22⋊C411yescharacteristic
191C24×C73C2×D411yescharacteristic
192C24×C73C2×D411yescharacteristic
193C24×C73C2×D411yescharacteristic
194C22×C4×C73—24no—
195C22×C4×C73—24no—
196C22×C4×C73—24no—
197C22×C4×C73—42no—
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×C73C22⋊C411yescharacteristic
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×C73C2×D411yescharacteristic
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×C73C2411yescharacteristic
236M16×C73—44no—
237M16×C73—44no—
238C2×C8×C73—24no—
239C2×C8×C73—44no—
240C23×C73—22no—
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—41no—
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—416no—
262C23×C73C2×C22⋊C411yescharacteristic
263C23×C73C2×C22⋊C411yescharacteristic
264C23×C73C2×C22⋊C411yescharacteristic
265C23×C73C2×C22⋊C411yescharacteristic
266C23×C73C2×C22⋊C411yescharacteristic
267C23×C73C2×C22⋊C411yescharacteristic
268C23×C73C22×D411yescharacteristic
269C22×D73—22no—
270C22×D73—42no—
271C22×D73—42no—
272C22×D73—42no—
273C2×C4×C73—22no—
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—41no—
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#9914yes—
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
309C22⋊D73—44no—
310C22⋊D73—44no—
311C22⋊D73—44no—
312C22⋊D73—44no—
313C22⋊D73—44no—
314C22⋊D73—44no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—44no—
322C2×Dic73—44no—
323C2×Dic73—44no—
324D292—42no—
325D292—42no—
326C4×D73—44no—
327C4×D73—44no—
328Dic146—42no—
329Dic146—42no—
330C8×C73—44no—
331C22×C73—21no—
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—44no—
350C22×C73—44no—
351C22×C73—44no—
352C22×C73—44no—
353C22×C73—44no—
354C22×C73—44no—
355C22×C73—44no—
356C22×C73C2×#9912yes—
357C22×C73#42112yes—
358C22×C73C22×C22⋊C411yescharacteristic
359C22×C73#57512yes—
360C2×D73—42no—
361C2×D73—42no—
362C2×D73—42no—
363C2×D73—84no—
364C4×C73—21no—
365C4×C73—21no—
366C4×C73—21no—
367C4×C73—21no—
368C4×C73—21no—
369C4×C73—21no—
370C4×C73C2×#9912yes—
371C4×C73C2×#9912yes—
372Dic73—42no—
373Dic73—42no—
374Dic73—42no—
375Dic73—84no—
376#17559—731nomaximal, Sylow
377C2×C73—22no—
378C2×C73—22no—
379C2×C73—22no—
380C2×C73—41no—
381C2×C73—41no—
382C2×C73—41no—
383C2×C73—41no—
384C2×C73C22×#9911yescharacteristic
385C2×C73#289611yescharacteristic
386C2×C73C2×#42111yescharacteristic
387D73—82no—
388C2×#525—731no—
389C2×#407D7311yescharacteristic, complemented
390#2280—731no—
391#1513—734no—
392#1511—732no—
393#1510—732no—
394#1501—734no—
395C73#1755911yescharacteristic, complemented, Sylow
396C22×#41—731no—
397C24×C4C2×D7311yescharacteristic
398C22×M16—21no—
399#525—732no—
400#525—732no—
401#525—732no—
402#525—732no—
403#525—1461no—
404#525—1461no—
405#525—1461no—
406#525—1461no—
407C2×#123—1461no—
408C2×C22⋊Q8—731no—
409C2×C22⋊Q8—731no—
410C2×#121—731no—
411C2×#121—731no—
412C2×#120—1461no—
413C2×C4×D4—1461no—
414C2×C4×D4—1461no—
415C2×#117—731no—
416C2×#117—1461no—
417#407—21no—
418#407—21no—
419#407C2×D7312yes—
420#407C2×D7312yescomplemented
421C2×C22⋊C8—21no—
422C2×C22⋊C8C2×D7312yescomplemented
423#381—732no—
424#380—732no—
425#380—1461no—
426#379—1461no—
427C4×C22⋊C4—732no—
428C4×C22⋊C4—1461no—
429#328—738no—
430#327—738no—
431C25D29211yescharacteristic
432C2×#41—2924no—
433C2×#41—732no—
434C2×#41—732no—
435C2×#41—1461no—
436C2×#41—1461no—
437C22×Q8—731no—
438C22×D4—731no—
439C22×D4—1461no—
440C22×D4—1461no—
441C22×D4—1461no—
442C23×C4—44no—
443C23×C4—1461no—
444C23×C4C4×D7311yescharacteristic
445C23×C4C4×D7311yescharacteristic
446C23×C4C4×D7311yescharacteristic
447C23×C4C4×D7311yescharacteristic
448C23×C4D29211yescharacteristic
449C23×C4D29211yescharacteristic
450C23×C4D29211yescharacteristic
451C23×C4C22⋊D7311yescharacteristic
452C23×C4C22⋊D7311yescharacteristic
453C23×C4C22⋊D7311yescharacteristic
454C23×C4C22⋊D7311yescharacteristic
455C23×C4C22×D7311yescharacteristic
456C23×C4C22×D7311yescharacteristic
457C23×C4C22×D7311yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—44no—
461C22×C8—22no—
462#123—1462no—
463#123—1462no—
464#123—1462no—
465#123—1462no—
466C22⋊Q8—732no—
467C22⋊Q8—732no—
468C22⋊Q8—732no—
469C22⋊Q8—732no—
470C22⋊Q8—1461no—
471C22⋊Q8—1461no—
472C22⋊Q8—1461no—
473C22⋊Q8—1461no—
474#121—732no—
475#121—732no—
476#121—732no—
477#121—732no—
478#121—1461no—
479#121—1461no—
480#121—1461no—
481#121—1461no—
482#120—1462no—
483#120—1462no—
484#120—1462no—
485#120—1462no—
486C4×D4—1462no—
487C4×D4—1462no—
488C4×D4—1462no—
489C4×D4—1462no—
490C4×D4—1462no—
491C4×D4—1462no—
492C4×D4—1462no—
493C4×D4—1462no—
494#117—2924no—
495#117—732no—
496#117—732no—
497#117—1461no—
498#117—1461no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—1462no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C22⋊C4—1462no—
505C2×C22⋊C4—1462no—
506C2×C22⋊C4—1462no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C42—1462no—
513C2×C42—1461no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8C22×D7314yes—
518#95—734no—
519#95—1462no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—1461no—
524C24#1192400511yescharacteristic
525C24#1192400511yescharacteristic
526C24#1192400511yescharacteristic
527C24#1192400511yescharacteristic
528C24C2×D29211yescharacteristic
529C24C2×D29211yescharacteristic
530C24C2×D29211yescharacteristic
531#41—2924no—
532#41—2924no—
533#41—2924no—
534#41—2924no—
535C2×Q8—2922no—
536C2×Q8—732no—
537C2×Q8—1461no—
538C2×D4—2922no—
539C2×D4—2924no—
540C2×D4—2924no—
541C2×D4—2924no—
542C2×D4—732no—
543C2×D4—1462no—
544C2×D4—1462no—
545C2×D4—1462no—
546C2×D4—1462no—
547C2×D4—1462no—
548C2×D4—1462no—
549C2×D4—1461no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
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—2924no—
565C22×C4—1464no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4#1192400511yescharacteristic
572C22×C4#1192400511yescharacteristic
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×C4C2×C4×D7311yescharacteristic
584C22×C4C2×C4×D7311yescharacteristic
585C22×C4C2×C4×D7311yescharacteristic
586C22×C4C2×C4×D7311yescharacteristic
587C22×C4C2×C4×D7311yescharacteristic
588C22×C4C2×C4×D7311yescharacteristic
589C22×C4C2×C22⋊D7311yescharacteristic
590C22×C4C2×C22⋊D7311yescharacteristic
591C22×C4C2×C22⋊D7311yescharacteristic
592C22×C4C2×C22⋊D7311yescharacteristic
593C22×C4C2×C22⋊D7311yescharacteristic
594C22×C4C2×C22⋊D7311yescharacteristic
595C22×C4C2×D29211yescharacteristic
596C22×C4C2×D29211yescharacteristic
597C22×C4C2×D29211yescharacteristic
598C22×C4C23×D7311yescharacteristic
599M16—44no—
600M16—44no—
601C2×C8—24no—
602C2×C8—44no—
603C4⋊C4—2924no—
604C4⋊C4—732no—
605C4⋊C4—732no—
606C4⋊C4—1462no—
607C4⋊C4—1462no—
608C4⋊C4—1462no—
609C4⋊C4—1461no—
610C4⋊C4—1461no—
611C4⋊C4—1462no—
612C22⋊C4—2924no—
613C22⋊C4—2924no—
614C22⋊C4—2924no—
615C22⋊C4—1462no—
616C22⋊C4—1462no—
617C22⋊C4—1462no—
618C22⋊C4—1462no—
619C22⋊C4—1462no—
620C22⋊C4—1462no—
621C22⋊C4—1462no—
622C22⋊C4—1462no—
623C22⋊C4—1462no—
624C22⋊C4—1462no—
625C42—2924no—
626C42—1462no—
627C42—1462no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—2922no—
651C23—2922no—
652C23—2922no—
653C23—1462no—
654C23C2×#1192400511yescharacteristic
655C23C2×#1192400511yescharacteristic
656C23C2×#1192400511yescharacteristic
657C23C2×#1192400511yescharacteristic
658C23C2×#1192400511yescharacteristic
659C23C2×#1192400511yescharacteristic
660C23C22×D29211yescharacteristic
661Q8—2922no—
662Q8—2922no—
663D4—2922no—
664D4—2922no—
665D4—2924no—
666D4—2924no—
667D4—2924no—
668D4—2924no—
669D4—2924no—
670D4—2924no—
671C2×C4—22no—
672C2×C4—22no—
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—41no—
687C2×C4—41no—
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—2922no—
699C2×C4—2922no—
700C2×C4—2922no—
701C2×C4—2924no—
702C2×C4—2924no—
703C2×C4—2924no—
704C2×C4—2924no—
705C2×C4—2924no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4#1455650514yes—
710C2×C4C2×#1192400511yescharacteristic
711C2×C4C2×#1192400511yescharacteristic
712C2×C4C2×#1192400511yescharacteristic
713C2×C4C2×#1192400511yescharacteristic
714C2×C4C2×#1192400511yescharacteristic
715C2×C4C2×#1192400511yescharacteristic
716C2×C4C22×C4×D7311yescharacteristic
717C2×C4C22×C22⋊D7311yescharacteristic
718C8—44no—
719C22—21no—
720C22—21no—
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—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—2922no—
745C22—2922no—
746C22—2922no—
747C22—5844no—
748C22C2×#1455650512yes—
749C22#1798860312yes—
750C22C22×#1192400511yescharacteristic
751C22#1798938712yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—2922no—
759C4—2922no—
760C4—2922no—
761C4—5844no—
762C4C2×#1455650512yes—
763C4C2×#1455650512yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—5842no—
772C2C22×#1455650511yescharacteristic
773C2#2261845111yescharacteristic
774C2C2×#1798860311yescharacteristic
subgroupG/H
centerC2×C4C2×#11924005
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#407×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC2×#17989098C2
cosocleC22×C4×C73C24
hypercenterC2×#407D73
hypocenterC73#17559
LCSG ▷ C2×C4×C73 ▷ C22×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. #22608475C2semidirect
4. #22608465C2semidirect
5. #22608461C2semidirect
6. #22608423C2semidirect
7. C2×#407×C73C2semidirect
8. C22×#11924028C4semidirect
13. #17989098C4semidirect
14. #17989098C4semidirect
18. C2×#14556570C4semidirect
20. C2×#14556565C4semidirect
26. C2×#14556550C4semidirect
29. #17988447C22semidirect
32. C4×C22⋊Dic73C22semidirect
33. #17988325C22semidirect
34. #17988322C22semidirect
40. #407×C73C22semidirect
42. C2×C22⋊C8×C73C22semidirect
389. C2×#407D73semidirect
395. C73#17559semidirect
420. #407C2×D73semidirect
422. C2×C22⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890982
#226123142
#226084752
#226084652
#226084612
#226084232
C2×#407×C732
#1755973