Finite Group Databasebeta

← C4×#17988730 #33091595

Subgroups — C4×#17988730 #33091595

Order 18688.

1564 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×C4×#11924028C211yesmaximal, characteristic, complemented
2C2×#17988730C211yesmaximal, characteristic
3C2×C4×#11924016C211yesmaximal, characteristic, complemented
4C2×C4×#11924013C211yesmaximal, characteristic, complemented
5#22610289C211yesmaximal, characteristic, complemented
6#22610282C211yesmaximal, characteristic, complemented
7#22610254C211yesmaximal, characteristic, complemented
8#22610191C211yesmaximal, characteristic, complemented
9#22610184C211yesmaximal, characteristic, complemented
10#22610128C211yesmaximal, characteristic, complemented
11#22609869C211yesmaximal, characteristic, complemented
12C4×#14556514C211yesmaximal, characteristic, complemented
13C4×#14556511C211yesmaximal, characteristic, complemented
14C4×C22⋊#10596831C211yesmaximal, characteristic, complemented
15C4×#121×C73C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C22×#11924013C2211yescharacteristic
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#17988730C418yesdirect product factor
31C4×#11924016—24no—
32C4×#11924013—24no—
33C2×#14556524C2211yescharacteristic
34C2×#14556522C2211yescharacteristic
35C2×#14556514C2211yescharacteristic
36C2×#14556514C2211yescharacteristic
37C2×#14556514C2211yescharacteristic
38C2×#14556512C2211yescharacteristic
39C2×#14556512C2211yescharacteristic
40C2×#14556511C2211yescharacteristic
41C2×#14556511C2211yescharacteristic
42C2×#14556511C2211yescharacteristic
43C2×C22⋊#10596831C2211yescharacteristic
44C2×C22⋊#10596831C2211yescharacteristic
45C2×C4×#10596831C2211yescharacteristic
46C2×C4×#10596831C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988342C2211yescharacteristic
52#17988342C2211yescharacteristic
53C2×#121×C73C2211yescharacteristic
54C2×C4×D4×C73—21no—
55C2×C4×D4×C73C2211yescharacteristic
56C22×C42×C73C2211yescharacteristic
57#390×C73C2211yescharacteristic
58#389×C73C2211yescharacteristic
59#388×C73—21no—
60#386×C73—21no—
61#380×C73C2211yescharacteristic
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×C414yescomplemented
70C22×Dic146C2311yescharacteristic
71C22×D292C2311yescharacteristic
72C22×C22⋊D73—21no—
73C22×C4×D73—21no—
74C22×C4×D73—21no—
75C22×C4×D73—21no—
76C2×#11924016—22no—
77C2×#11924016—22no—
78C2×#11924016C2×C414yescomplemented
79C2×#11924013—22no—
80C2×#11924013—22no—
81C2×#11924013C2×C414yescomplemented
82C22×#10596831C2311yescharacteristic
83C22×#10596831C2311yescharacteristic
84C22×#10596831C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C4×Dic146—22no—
87C4×Dic146—22no—
88C4×Dic146—22no—
89C4×Dic146D414yescomplemented
90C4×D292—22no—
91C4×D292—22no—
92C4×D292—22no—
93C4×D292D414yescomplemented
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#14556514—22no—
113#14556514—22no—
114#14556514C2×C414yescomplemented
115#14556512—22no—
116#14556512—22no—
117#14556511—22no—
118#14556511—22no—
119#14556511C2×C414yescomplemented
120C22⋊#10596831—22no—
121C22⋊#10596831C2×C414yescomplemented
122C4×#10596831—22no—
123C4×#10596831—22no—
124C22×D4×C73—21no—
125C22×D4×C73C2311yescharacteristic
126C23×C4×C73—21no—
127C23×C4×C73D411yescharacteristic
128C23×C4×C73D411yescharacteristic
129C23×C4×C73C2311yescharacteristic
130#121×C73—22no—
131#121×C73C2×C414yescomplemented
132C4×D4×C73—22no—
133C4×D4×C73—22no—
134C4×D4×C73—44no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140C2×C22⋊C4×C73—21no—
141C2×C22⋊C4×C73—21no—
142C2×C22⋊C4×C73—21no—
143C2×C22⋊C4×C73—21no—
144C2×C42×C73—22no—
145C2×C42×C73—22no—
146C2×C42×C73—21no—
147C2×C42×C73D411yescharacteristic
148C2×C42×C73D411yescharacteristic
149C2×C42×C73C2311yescharacteristic
150C2×C42×C73C2311yescharacteristic
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C23×D73—21no—
155#11924028—28no—
156#11924028—28no—
157#11924028—28no—
158#11924028—28no—
159C2×Dic146—21no—
160C2×Dic146—21no—
161C2×Dic146—21no—
162C2×Dic146C22×C412yes—
163C2×Dic146C2×D412yes—
164C2×Dic146#4112yes—
165C2×D292—21no—
166C2×D292—21no—
167C2×D292—21no—
168C2×D292C22×C412yes—
169C2×D292C2×D412yes—
170C2×D292#4112yes—
171C2×C22⋊D73—24no—
172C2×C22⋊D73—24no—
173C2×C22⋊D73—24no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C2×C4×D73—24no—
178C2×C4×D73—24no—
179C2×C4×D73—24no—
180C2×C4×D73—24no—
181C2×C4×D73—24no—
182C2×C4×D73—42no—
183C2×C4×D73—42no—
184C2×C4×D73—42no—
185C2×C4×D73—42no—
186#11924016—28no—
187#11924013—28no—
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×#10596831—21no—
198C2×#10596831C22×C412yes—
199C2×#10596831C22×C412yes—
200C4⋊Dic73—21no—
201C4⋊Dic73—21no—
202C4⋊Dic73C2×D412yes—
203C4⋊Dic73C2×D412yes—
204#11924007—24no—
205#11924007—24no—
206C22⋊Dic73—24no—
207#11924005—24no—
208#11924005—24no—
209C4×Dic73—24no—
210C4×Dic73—24no—
211C4×Dic73—24no—
212C24×C73—21no—
213C24×C73C2×D411yescharacteristic
214C2×D4×C73—24no—
215C2×D4×C73—21no—
216C2×D4×C73—21no—
217C2×D4×C73—21no—
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—42no—
221C2×D4×C73—42no—
222C2×D4×C73C22×C412yes—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—41no—
236C22×C4×C73—42no—
237C22×C4×C73—42no—
238C22×C4×C73—42no—
239C22×C4×C73C22×C412yes—
240C22×C4×C73C2×D411yescharacteristic
241C22×C4×C73C2×D411yescharacteristic
242C22×C4×C73C2×D411yescharacteristic
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73#4112yes—
246C22×C4×C73C2411yescharacteristic
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—42no—
253C4⋊C4×C73C22×C412yes—
254C22⋊C4×C73—24no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C42×C73—22no—
260C42×C73—22no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—42no—
264C42×C73C2×D412yes—
265C42×C73C2×D412yes—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—22no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73C4×D412yes—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—41no—
285C22×D73—41no—
286C22×D73—41no—
287C22×D73—41no—
288D4×C73—22no—
289D4×C73—22no—
290D4×C73—48no—
291D4×C73—41no—
292D4×C73—41no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—44no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—44no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—84no—
318C2×C4×C73C4×D412yes—
319C2×C4×C73#12012yes—
320C2×C4×C73#12012yes—
321C2×C4×C73#13512yes—
322C2×C4×C73#13512yes—
323C2×C4×C73AGL(1,ℤ/8)12yes—
324C2×C4×C73C23×C411yescharacteristic
325C2×C4×C73C22×D411yescharacteristic
326C2×C4×C73C22×D411yescharacteristic
327C2×C4×C73C2×#4111yescharacteristic
328C2×C4×C73C2×#4111yescharacteristic
329C2×C4×C73C2×#4111yescharacteristic
330C22⋊D73—216no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—41no—
337C2×Dic73—41no—
338C2×Dic73—41no—
339C2×Dic73—41no—
340D292—22no—
341D292—22no—
342D292—22no—
343D292C4×D414yescomplemented
344C4×D73—216no—
345C4×D73—48no—
346C4×D73—48no—
347Dic146—22no—
348Dic146—22no—
349Dic146—22no—
350Dic146C4×D414yescomplemented
351#10596831—22no—
352#10596831—22no—
353#10596831—41no—
354#10596831—41no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73—81no—
368C22×C73—81no—
369C22×C73C2×C4×D411yescharacteristic
370C22×C73C2×#12011yescharacteristic
371C22×C73#52511yescharacteristic
372C22×C73C2×#13511yescharacteristic
373C22×C73C2×#13511yescharacteristic
374C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C73#57511yescharacteristic
376C2×D73—24no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C2×D73—42no—
383C4×C73—22no—
384C4×C73—22no—
385C4×C73—22no—
386C4×C73—42no—
387C4×C73—41no—
388C4×C73—81no—
389C4×C73—81no—
390C4×C73#44914yescomplemented
391C4×C73C2×C4×D411yescharacteristic
392C4×C73C2×C4×D411yescharacteristic
393C4×C73#52511yescharacteristic
394C4×C73#52511yescharacteristic
395Dic73—24no—
396Dic73—42no—
397Dic73—42no—
398C4×#449—731nomaximal, Sylow
399C2×C73—42no—
400C2×C73—82no—
401C2×C73C4×#12011yescharacteristic
402C2×C73C4×#13511yescharacteristic
403C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
404C2×C73C2×#44911yescharacteristic
405C2×C73#300211yescharacteristic
406C2×C73#310211yescharacteristic
407C2×C73#310611yescharacteristic
408D73—44no—
409C2×C4×#41—731no—
410C2×#449—731no—
411C2×C4×SD16—731no—
412C2×C4×D8—731no—
413C4×#121D7311yescharacteristic, complemented
414#1880—731no—
415#1879—731no—
416#1875—731no—
417#1864—731no—
418#1863—731no—
419#1854—731no—
420#1788—731no—
421C4×#103—731no—
422C4×#102—731no—
423C4×C22⋊C8—731no—
424C73C4×#44911yescharacteristic, complemented, Sylow
425C22×#41—731no—
426C22×SD16—731no—
427C22×D8—731no—
428C2×#121C2×D7311yescharacteristic
429C4×#41—1464no—
430C4×#41—1464no—
431C2×C4×Q8—731no—
432C2×C4×Q8—731no—
433C2×C4×D4—21no—
434C2×C4×D4—731no—
435C2×C4×D4—731no—
436C2×C4×D4—1461no—
437C2×C4×D4—1461no—
438C2×C4×D4C2×D7311yescharacteristic
439C2×#117—731no—
440C2×#117—1461no—
441C22×C42—1461no—
442C22×C42C2×D7311yescharacteristic
443#449—738no—
444C4×SD16—1464no—
445C4×D8—1464no—
446C2×#107—731no—
447C2×#106—731no—
448C2×#103—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#102—731no—
452C2×#102—731no—
453C2×#102—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8—731no—
458C2×C4×C8—731no—
459C2×C4×C8—731no—
460#390C2×D7311yescharacteristic
461#389C2×D7311yescharacteristic
462#388—21no—
463#386—21no—
464#380C2×D7311yescharacteristic
465C4×C4⋊C4C2×D7311yescharacteristic
466C4×C22⋊C4—21no—
467#340—731no—
468#340—731no—
469#340—731no—
470#340—731no—
471#336—731no—
472#336—731no—
473C2×#41—734no—
474C2×#41—1462no—
475C2×#41—1462no—
476C2×#41—1462no—
477C2×#41—1462no—
478C2×#41—1462no—
479C22×Q8—731no—
480C22×D4—21no—
481C22×D4—731no—
482C22×D4—1461no—
483C22×D4C22×D7311yescharacteristic
484C23×C4—21no—
485C23×C4—1461no—
486C23×C4—1461no—
487C23×C4—1461no—
488C23×C4C22⋊D7311yescharacteristic
489C23×C4C22⋊D7311yescharacteristic
490C23×C4C22×D7311yescharacteristic
491C2×SD16—734no—
492C2×SD16—1462no—
493C2×SD16—1462no—
494C2×D8—734no—
495C2×D8—1462no—
496C2×D8—1462no—
497C22×C8—731no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8—731no—
501#121—22no—
502#121C4×D7314yescomplemented
503C4×Q8—734no—
504C4×Q8—1462no—
505C4×Q8—1462no—
506C4×Q8—1462no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—44no—
510C4×D4—734no—
511C4×D4—1462no—
512C4×D4—1462no—
513C4×D4—1468no—
514C4×D4—1468no—
515C4×D4—1462no—
516#117—1468no—
517#117—1462no—
518#117—1462no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4C22×D7311yescharacteristic
525C2×C4⋊C4C22×D7311yescharacteristic
526C2×C4⋊C4C22×D7311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—21no—
538C2×C42—1468no—
539C2×C42—1461no—
540C2×C42—1461no—
541C2×C42—1461no—
542C2×C42C22⋊D7311yescharacteristic
543C2×C42C22⋊D7311yescharacteristic
544C2×C42C22×D7311yescharacteristic
545C2×C42C22×D7311yescharacteristic
546#107—1462no—
547#106—1462no—
548#103—734no—
549#103—1462no—
550#103—1462no—
551#102—734no—
552#102—1462no—
553#102—1462no—
554#102—1462no—
555#102—1462no—
556C22⋊C8—734no—
557C22⋊C8—1462no—
558C4×C8—1462no—
559C4×C8—1462no—
560#95—21no—
561#95—21no—
562#95—21no—
563C24—21no—
564C24—1461no—
565C24C2×C22⋊D7311yescharacteristic
566#41—1468no—
567#41—1468no—
568#41—1468no—
569#41—1468no—
570C2×Q8—732no—
571C2×Q8—732no—
572C2×Q8—732no—
573C2×Q8—1461no—
574C2×Q8—1461no—
575C2×Q8—1461no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—732no—
585C2×D4—732no—
586C2×D4—732no—
587C2×D4—1464no—
588C2×D4—1464no—
589C2×D4—1464no—
590C2×D4—1461no—
591C2×D4—1461no—
592C2×D4—1461no—
593C2×D4C2×C4×D7312yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—2922no—
611C22×C4—2922no—
612C22×C4—2922no—
613C22×C4—2922no—
614C22×C4—1464no—
615C22×C4—1464no—
616C22×C4—1464no—
617C22×C4—1461no—
618C22×C4—1461no—
619C22×C4—1464no—
620C22×C4—1461no—
621C22×C4—1464no—
622C22×C4C2×C4×D7312yes—
623C22×C4C2×C22⋊D7311yescharacteristic
624C22×C4C2×C22⋊D7311yescharacteristic
625C22×C4C2×C22⋊D7311yescharacteristic
626C22×C4C2×C22⋊D7311yescharacteristic
627C22×C4C2×C22⋊D7311yescharacteristic
628C22×C4#1192402812yes—
629C22×C4C23×D7311yescharacteristic
630SD16—1468no—
631D8—1468no—
632C2×C8—732no—
633C2×C8—732no—
634C2×C8—1461no—
635C2×C8—1461no—
636C2×C8—1461no—
637C2×C8—1461no—
638C2×C8—1461no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—732no—
651C4⋊C4—732no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1461no—
655C4⋊C4—1461no—
656C4⋊C4C2×C4×D7312yes—
657C22⋊C4—24no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C22⋊C4—1464no—
665C42—22no—
666C42—22no—
667C42—21no—
668C42—21no—
669C42—42no—
670C42—1464no—
671C42—1464no—
672C42—1464no—
673C42D4×D7312yes—
674C42D4×D7312yes—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—2921no—
689C23—2921no—
690C23—2921no—
691C23—2921no—
692C23—1462no—
693C23—1462no—
694C23—1462no—
695C23C4×C22⋊D7312yes—
696C23C22×C22⋊D7311yescharacteristic
697Q8—734no—
698Q8—1462no—
699Q8—1462no—
700Q8—1462no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—734no—
707D4—14616no—
708D4—1462no—
709D4—1462no—
710D4—1462no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—84no—
736C2×C4—2928no—
737C2×C4—2921no—
738C2×C4—2921no—
739C2×C4—2921no—
740C2×C4—2921no—
741C2×C4—2928no—
742C2×C4—14616no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1462no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4C4×C22⋊D7312yes—
749C2×C4#1455655912yes—
750C2×C4#1455655912yes—
751C2×C4#1455661112yes—
752C2×C4#1455661112yes—
753C2×C4#1455661712yes—
754C2×C4C22×C4×D7311yescharacteristic
755C2×C4C2×D4×D7311yescharacteristic
756C2×C4C2×D4×D7311yescharacteristic
757C2×C4#41×D7311yescharacteristic
758C2×C4#41×D7311yescharacteristic
759C2×C4C2×#1192402811yescharacteristic
760C8—2921no—
761C8—2921no—
762C8—1462no—
763C8—1462no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—2922no—
779C22—2922no—
780C22—2922no—
781C22—2922no—
782C22—2922no—
783C22—2922no—
784C22—1464no—
785C22C2×C4×C22⋊D7311yescharacteristic
786C22C2×#1455655911yescharacteristic
787C22#1798909411yescharacteristic
788C22C2×#1455661111yescharacteristic
789C22C2×#1455661111yescharacteristic
790C22C2×#1455661711yescharacteristic
791C22#1798938511yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—2922no—
800C4—2922no—
801C4—1464no—
802C4#1798873014yesdirect product factor
803C4C4×D4×D7311yescharacteristic
804C4C4×D4×D7311yescharacteristic
805C4#1798909611yescharacteristic
806C4#1798909611yescharacteristic
807C2—42no—
808C2—82no—
809C2—2924no—
810C2C4×#1455655911yescharacteristic
811C2C4×#1455661111yescharacteristic
812C2C4×#1455661711yescharacteristic
813C2C2×#1798873011yescharacteristic
814C2#2261914711yescharacteristic
815C2#2261994311yescharacteristic
816C2#2261998511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×#121×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988730C2
cosocleC22×C4×C73C24
hypercenterC4×#121D73
hypocenterC73C4×#449
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11924028C2semidirect
3. C2×C4×#11924016C2semidirect
4. C2×C4×#11924013C2semidirect
5. #22610289C2semidirect
6. #22610282C2semidirect
7. #22610254C2semidirect
8. #22610191C2semidirect
9. #22610184C2semidirect
10. #22610128C2semidirect
11. #22609869C2semidirect
12. C4×#14556514C2semidirect
13. C4×#14556511C2semidirect
14. C4×C22⋊#10596831C2semidirect
15. C4×#121×C73C2semidirect
30. #17988730C4direct (N × H)
69. C2×#11924028C2×C4semidirect
78. C2×#11924016C2×C4semidirect
81. C2×#11924013C2×C4semidirect
89. C4×Dic146D4semidirect
93. C4×D292D4semidirect
114. #14556514C2×C4semidirect
119. #14556511C2×C4semidirect
121. C22⋊#10596831C2×C4semidirect
131. #121×C73C2×C4semidirect
343. D292C4×D4semidirect
350. Dic146C4×D4semidirect
390. C4×C73#449semidirect
413. C4×#121D73semidirect
424. C73C4×#449semidirect
502. #121C4×D73semidirect
802. C4#17988730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#119240282
C2×#179887302
C2×C4×#119240162
C2×C4×#119240132
#226102892
#226102822
#226102542
#226101912
#226101842
#226101282
#226098692
C4×#145565142
C4×#145565112
C4×C22⋊#105968312
C4×#121×C732
C4×#44973