Finite Group Databasebeta

← #33091684

Subgroups — #33091684

Order 18688.

1468 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×C4×#11924028C211yesmaximal, characteristic
2C2×#17988747C211yesmaximal, characteristic
3C2×#17988692C211yesmaximal, characteristic, complemented
4C2×#17988685C211yesmaximal, characteristic, complemented
5#22610275C211yesmaximal, characteristic, complemented
6#22610268C211yesmaximal, characteristic, complemented
7#22610244C211yesmaximal, characteristic, complemented
8#22610191C211yesmaximal, characteristic, complemented
9#22610184C211yesmaximal, characteristic, complemented
10#22610128C211yesmaximal, characteristic, complemented
11#22609869C211yesmaximal, characteristic
12#22609764C211yesmaximal, characteristic, complemented
13#22609759C211yesmaximal, characteristic, complemented
14#22609693C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C73C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C22×#11924018C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C4×#11924028—24no—
20C4×#11924028—24no—
21C2×C4×Dic146C2211yescharacteristic
22C2×C4×Dic146C2211yescharacteristic
23C2×C4×D292C2211yescharacteristic
24C2×C4×D292C2211yescharacteristic
25C2×C4×C22⋊D73—21no—
26C2×C4×C22⋊D73—21no—
27C2×#14556550C2211yescharacteristic
28C2×#14556548—21no—
29C2×C42×D73—21no—
30#17988747C418yescomplemented
31#17988692—24no—
32#17988685—24no—
33C2×#14556524C2211yescharacteristic
34C2×#14556522C2211yescharacteristic
35C2×#14556515C2211yescharacteristic
36C2×#14556515C2211yescharacteristic
37C2×#14556514C2211yescharacteristic
38C2×#14556514C2211yescharacteristic
39C2×#14556514C2211yescharacteristic
40C2×#14556511C2211yescharacteristic
41C2×#14556511C2211yescharacteristic
42C2×#14556511C2211yescharacteristic
43C2×C22⋊#10596831C2211yescharacteristic
44C2×C22⋊#10596831C2211yescharacteristic
45C2×#14556502C2211yescharacteristic
46C2×#14556502C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988342C2211yescharacteristic
52#17988342C2211yescharacteristic
53C2×C22⋊Q8×C73C2211yescharacteristic
54C2×C4×Q8×C73C2211yescharacteristic
55C22×C42×C73C2211yescharacteristic
56#391×C73C2211yescharacteristic
57#389×C73C2211yescharacteristic
58#387×C73—21no—
59#385×C73—21no—
60#380×C73C2211yescharacteristic
61C4×C4⋊C4×C73—21no—
62C4×C4⋊C4×C73C2211yescharacteristic
63C4×C22⋊C4×C73—21no—
64C2×#11924028—22no—
65C2×#11924028—22no—
66C2×#11924028—22no—
67C2×#11924028—22no—
68C2×#11924028—22no—
69C2×#11924028C2×C414yes—
70C22×Dic146C2311yescharacteristic
71C22×D292C2311yescharacteristic
72C22×C22⋊D73—21no—
73C22×C4×D73—21no—
74C22×C4×D73—21no—
75C22×C4×D73—21no—
76C2×#11924018—22no—
77C2×#11924018—22no—
78C2×#11924018C2×C414yescomplemented
79C2×#11924015—22no—
80C2×#11924015—22no—
81C2×#11924015C2×C414yescomplemented
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C4×Dic146—22no—
87C4×Dic146—22no—
88C4×Dic146—22no—
89C4×Dic146D414yes—
90C4×D292—22no—
91C4×D292—22no—
92C4×D292—22no—
93C4×D292D414yes—
94C4×C22⋊D73—28no—
95C4×C22⋊D73—28no—
96#14556550—22no—
97#14556550—22no—
98#14556548—28no—
99C2×C4⋊Dic73C2311yescharacteristic
100C2×C4⋊Dic73C2311yescharacteristic
101C2×#11924007—21no—
102C2×#11924007—21no—
103C2×C22⋊Dic73—21no—
104C2×#11924005—21no—
105C2×#11924005—21no—
106C2×C4×Dic73—21no—
107C2×C4×Dic73—21no—
108C2×C4×Dic73—21no—
109C42×D73—28no—
110#14556524—22no—
111#14556522—22no—
112#14556515—22no—
113#14556515—22no—
114#14556514—22no—
115#14556514—22no—
116#14556514C2×C414yescomplemented
117#14556511—22no—
118#14556511—22no—
119#14556511C2×C414yescomplemented
120C22⋊#10596831—22no—
121C22⋊#10596831C2×C414yescomplemented
122#14556502—22no—
123#14556502—22no—
124C22×Q8×C73C2311yescharacteristic
125C23×C4×C73D411yescharacteristic
126C23×C4×C73D411yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C22⋊Q8×C73—22no—
129C22⋊Q8×C73C2×C414yescomplemented
130C4×Q8×C73—22no—
131C4×Q8×C73—22no—
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73—21no—
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C22⋊C4×C73—21no—
139C2×C22⋊C4×C73—21no—
140C2×C42×C73—22no—
141C2×C42×C73—22no—
142C2×C42×C73—21no—
143C2×C42×C73—21no—
144C2×C42×C73D411yescharacteristic
145C2×C42×C73D411yescharacteristic
146C2×C42×C73C2311yescharacteristic
147C2×C42×C73C2311yescharacteristic
148#95×C73—21no—
149#95×C73—21no—
150#95×C73—21no—
151#95×C73—21no—
152#95×C73—21no—
153C23×D73—21no—
154#11924028—28no—
155#11924028—28no—
156#11924028—28no—
157#11924028—28no—
158C2×Dic146—21no—
159C2×Dic146—21no—
160C2×Dic146—21no—
161C2×Dic146C22×C412yes—
162C2×Dic146C2×D412yes—
163C2×Dic146#4112yes—
164C2×D292—21no—
165C2×D292—21no—
166C2×D292—21no—
167C2×D292C22×C412yes—
168C2×D292C2×D412yes—
169C2×D292#4112yes—
170C2×C22⋊D73—24no—
171C2×C22⋊D73—24no—
172C2×C22⋊D73—24no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C2×C4×D73—24no—
177C2×C4×D73—24no—
178C2×C4×D73—24no—
179C2×C4×D73—24no—
180C2×C4×D73—24no—
181C2×C4×D73—42no—
182C2×C4×D73—42no—
183C2×C4×D73—42no—
184C2×C4×D73—42no—
185#11924018—28no—
186#11924015—28no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831C22×C412yes—
198C2×#10596831C22×C412yes—
199C4⋊Dic73—21no—
200C4⋊Dic73—21no—
201C4⋊Dic73C2×D412yes—
202C4⋊Dic73C2×D412yes—
203#11924007—24no—
204#11924007—24no—
205C22⋊Dic73—24no—
206#11924005—24no—
207#11924005—24no—
208C4×Dic73—24no—
209C4×Dic73—24no—
210C4×Dic73—24no—
211C24×C73C2×D411yescharacteristic
212C2×Q8×C73—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73—21no—
215C2×Q8×C73—21no—
216C2×Q8×C73—21no—
217C2×Q8×C73C22×C412yes—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—41no—
230C22×C4×C73—41no—
231C22×C4×C73—41no—
232C22×C4×C73C22×C412yes—
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2×D411yescharacteristic
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73#4112yes—
239C22×C4×C73C2411yescharacteristic
240C4⋊C4×C73—24no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—42no—
247C4⋊C4×C73—42no—
248C4⋊C4×C73C22×C412yes—
249C22⋊C4×C73—24no—
250C22⋊C4×C73—42no—
251C42×C73—22no—
252C42×C73—22no—
253C42×C73—21no—
254C42×C73—21no—
255C42×C73—42no—
256C42×C73—42no—
257C42×C73C2×D412yes—
258C42×C73C2×D412yes—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73C4×D412yes—
266C23×C73C22×D411yescharacteristic
267C22×D73—22no—
268C22×D73—22no—
269C22×D73—22no—
270C22×D73—41no—
271C22×D73—41no—
272C22×D73—41no—
273C22×D73—41no—
274Q8×C73—22no—
275Q8×C73—22no—
276Q8×C73—41no—
277Q8×C73—41no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—44no—
296C2×C4×C73—44no—
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×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73C4×D412yes—
308C2×C4×C73#12012yes—
309C2×C4×C73#12012yes—
310C2×C4×C73#13712yes—
311C2×C4×C73C23×C411yescharacteristic
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4111yescharacteristic
315C2×C4×C73C2×#4111yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C22⋊D73—216no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327D292—22no—
328D292—22no—
329D292—22no—
330D292C4×D414yes—
331C4×D73—216no—
332C4×D73—48no—
333C4×D73—48no—
334Dic146—22no—
335Dic146—22no—
336Dic146—22no—
337Dic146C4×D414yes—
338#10596831—22no—
339#10596831—22no—
340#10596831—41no—
341#10596831—41no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73C2×C4×D411yescharacteristic
350C22×C73C2×#12011yescharacteristic
351C22×C73#52511yescharacteristic
352C22×C73C2×#13711yescharacteristic
353C22×C73#57511yescharacteristic
354C22×C73#57511yescharacteristic
355C22×C73#57511yescharacteristic
356C2×D73—24no—
357C2×D73—42no—
358C2×D73—42no—
359C2×D73—42no—
360C2×D73—42no—
361C2×D73—42no—
362C2×D73—42no—
363C4×C73—22no—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—22no—
367C4×C73—42no—
368C4×C73—41no—
369C4×C73—42no—
370C4×C73—81no—
371C4×C73—81no—
372C4×C73C2×C4×D411yescharacteristic
373C4×C73C2×C4×D411yescharacteristic
374C4×C73#52511yescharacteristic
375C4×C73#52511yescharacteristic
376Dic73—24no—
377Dic73—42no—
378Dic73—42no—
379#21457—731nomaximal, Sylow
380C2×C73—42no—
381C2×C73C4×#12011yescharacteristic
382C2×C73#294311yescharacteristic
383C2×C73C4×#13711yescharacteristic
384C2×C73#300511yescharacteristic
385C2×C73#300711yescharacteristic
386C2×C73#311111yescharacteristic
387C2×C73#311611yescharacteristic
388D73—44no—
389C2×C4×#41—731no—
390C2×#452—731no—
391C2×#441—731no—
392C2×#440—731no—
393C4×C22⋊Q8D7311yescharacteristic, complemented
394#1878—731no—
395#1877—731no—
396#1873—731no—
397#1864—731no—
398#1863—731no—
399#1854—731no—
400#1788—731no—
401#1763—731no—
402#1762—731no—
403#1749—731no—
404C73#2145711yescharacteristic, complemented, Sylow
405C22×#41—731no—
406C22×Q16—731no—
407C22×SD16—731no—
408C2×C22⋊Q8C2×D7311yescharacteristic
409C4×#41—1464no—
410C4×#41—1464no—
411C2×C4×Q8—731no—
412C2×C4×Q8—731no—
413C2×C4×Q8C2×D7311yescharacteristic
414C2×C4×D4—731no—
415C2×C4×D4—731no—
416C2×C4×D4—1461no—
417C2×C4×D4—1461no—
418C2×#117—731no—
419C2×#117—1461no—
420C22×C42—1461no—
421C22×C42C2×D7311yescharacteristic
422#452—738no—
423#441—1464no—
424#440—1464no—
425C2×#107—731no—
426C2×#106—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×C22⋊C8—731no—
436C2×C22⋊C8—731no—
437C2×#97—731no—
438C2×#97—731no—
439#391C2×D7311yescharacteristic
440#389C2×D7311yescharacteristic
441#387—21no—
442#385—21no—
443#380C2×D7311yescharacteristic
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2×D7311yescharacteristic
446C4×C22⋊C4—21no—
447#340—731no—
448#340—731no—
449#340—731no—
450#340—731no—
451#336—731no—
452#336—731no—
453C2×#41—734no—
454C2×#41—1462no—
455C2×#41—1462no—
456C2×#41—1462no—
457C2×#41—1462no—
458C2×#41—1462no—
459C22×Q8—731no—
460C22×Q8C22×D7311yescharacteristic
461C22×D4—731no—
462C22×D4—1461no—
463C23×C4—1461no—
464C23×C4—1461no—
465C23×C4—1461no—
466C23×C4C22⋊D7311yescharacteristic
467C23×C4C22⋊D7311yescharacteristic
468C23×C4C22×D7311yescharacteristic
469C2×Q16—734no—
470C2×Q16—1462no—
471C2×Q16—1462no—
472C2×SD16—734no—
473C2×SD16—1462no—
474C2×SD16—1462no—
475C22×C8—731no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—731no—
479C22⋊Q8—22no—
480C22⋊Q8C4×D7314yescomplemented
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—734no—
484C4×Q8—1462no—
485C4×Q8—1462no—
486C4×Q8—1462no—
487C4×D4—734no—
488C4×D4—1462no—
489C4×D4—1462no—
490C4×D4—1468no—
491C4×D4—1468no—
492C4×D4—1462no—
493#117—1468no—
494#117—1462no—
495#117—1462no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4C22×D7311yescharacteristic
504C2×C4⋊C4C22×D7311yescharacteristic
505C2×C4⋊C4C22×D7311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—1468no—
516C2×C42—1461no—
517C2×C42—1461no—
518C2×C42—1461no—
519C2×C42C22⋊D7311yescharacteristic
520C2×C42C22⋊D7311yescharacteristic
521C2×C42C22×D7311yescharacteristic
522C2×C42C22×D7311yescharacteristic
523#107—1462no—
524#106—1462no—
525#103—734no—
526#103—1462no—
527#103—1462no—
528#103—1462no—
529#103—1462no—
530#102—734no—
531#102—1462no—
532#102—1462no—
533C22⋊C8—734no—
534C22⋊C8—1462no—
535#97—1462no—
536#97—1462no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542C24—1461no—
543C24C2×C22⋊D7311yescharacteristic
544#41—1468no—
545#41—1468no—
546#41—1468no—
547#41—1468no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—732no—
554C2×Q8—732no—
555C2×Q8—732no—
556C2×Q8—1461no—
557C2×Q8—1461no—
558C2×Q8—1461no—
559C2×Q8C2×C4×D7312yes—
560C2×D4—732no—
561C2×D4—732no—
562C2×D4—732no—
563C2×D4—1464no—
564C2×D4—1464no—
565C2×D4—1464no—
566C2×D4—1461no—
567C2×D4—1461no—
568C2×D4—1461no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—2922no—
584C22×C4—2922no—
585C22×C4—2922no—
586C22×C4—2922no—
587C22×C4—1464no—
588C22×C4—1464no—
589C22×C4—1464no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1464no—
593C22×C4—1461no—
594C22×C4—1464no—
595C22×C4C2×C4×D7312yes—
596C22×C4C2×C22⋊D7311yescharacteristic
597C22×C4C2×C22⋊D7311yescharacteristic
598C22×C4C2×C22⋊D7311yescharacteristic
599C22×C4C2×C22⋊D7311yescharacteristic
600C22×C4C2×C22⋊D7311yescharacteristic
601C22×C4#1192402812yes—
602C22×C4C23×D7311yescharacteristic
603Q16—1468no—
604SD16—1468no—
605C2×C8—732no—
606C2×C8—732no—
607C2×C8—1461no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1461no—
630C4⋊C4—1461no—
631C4⋊C4C2×C4×D7312yes—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C42—1464no—
644C42—1464no—
645C42—1464no—
646C42D4×D7312yes—
647C42D4×D7312yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—2921no—
655C23—2921no—
656C23—2921no—
657C23—2921no—
658C23—1462no—
659C23—1462no—
660C23—1462no—
661C23C4×C22⋊D7312yes—
662C23C22×C22⋊D7311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—734no—
668Q8—1462no—
669Q8—1462no—
670Q8—1462no—
671D4—734no—
672D4—14616no—
673D4—1462no—
674D4—1462no—
675D4—1462no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—41no—
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—2928no—
706C2×C4—2928no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—14616no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4C4×C22⋊D7312yes—
718C2×C4#1455655912yes—
719C2×C4#1455655912yes—
720C2×C4#1455662212yes—
721C2×C4C22×C4×D7311yescharacteristic
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4C2×D4×D7311yescharacteristic
724C2×C4#41×D7311yescharacteristic
725C2×C4#41×D7311yescharacteristic
726C2×C4C2×#1192402811yescharacteristic
727C8—2921no—
728C8—2921no—
729C8—1462no—
730C8—1462no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—2922no—
739C22—2922no—
740C22—2922no—
741C22—2922no—
742C22—2922no—
743C22—2922no—
744C22—1464no—
745C22C2×C4×C22⋊D7311yescharacteristic
746C22C2×#1455655911yescharacteristic
747C22#1798909411yescharacteristic
748C22C2×#1455662211yescharacteristic
749C22#1798938511yescharacteristic
750C22#1798938511yescharacteristic
751C22#1798938511yescharacteristic
752C4—22no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—41no—
757C4—42no—
758C4—42no—
759C4—81no—
760C4—81no—
761C4—2922no—
762C4—2922no—
763C4—1464no—
764C4C4×D4×D7311yescharacteristic
765C4C4×D4×D7311yescharacteristic
766C4#1798909611yescharacteristic
767C4#1798909611yescharacteristic
768C2—42no—
769C2—2924no—
770C2C4×#1455655911yescharacteristic
771C2#2261872911yescharacteristic
772C2C4×#1455662211yescharacteristic
773C2#2261917111yescharacteristic
774C2#2261918911yescharacteristic
775C2#2262003411yescharacteristic
776C2#2262008711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×C22⋊Q8×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenterC4×C22⋊Q8D73
hypocenterC73#21457
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#17988692C2semidirect
4. C2×#17988685C2semidirect
5. #22610275C2semidirect
6. #22610268C2semidirect
7. #22610244C2semidirect
8. #22610191C2semidirect
9. #22610184C2semidirect
10. #22610128C2semidirect
12. #22609764C2semidirect
13. #22609759C2semidirect
14. #22609693C2semidirect
15. C4×C22⋊Q8×C73C2semidirect
30. #17988747C4semidirect
78. C2×#11924018C2×C4semidirect
81. C2×#11924015C2×C4semidirect
116. #14556514C2×C4semidirect
119. #14556511C2×C4semidirect
121. C22⋊#10596831C2×C4semidirect
129. C22⋊Q8×C73C2×C4semidirect
393. C4×C22⋊Q8D73semidirect
404. C73#21457semidirect
480. C22⋊Q8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#119240282
C2×#179887472
C2×#179886922
C2×#179886852
#226102752
#226102682
#226102442
#226101912
#226101842
#226101282
#226098692
#226097642
#226097592
#226096932
C4×C22⋊Q8×C732
#2145773