Finite Group Databasebeta

← C2×#22621668 #33961245

Subgroups — C2×#22621668 #33961245

Order 18688.

2794 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556611C211yesmaximal, characteristic, complemented
2C23×#11924018C211yesmaximal, characteristic, complemented
3C2×#17989246C211yesmaximal, characteristic, complemented
4#22621668C2116yesmaximal, direct product factor
5C2×#17988969C211yesmaximal, characteristic, complemented
6C2×#17988826C211yesmaximal, characteristic, complemented
7C2×#17988821C211yesmaximal, characteristic, complemented
8C2×#17988809C211yesmaximal, characteristic, complemented
9C2×#17988806C211yesmaximal, characteristic, complemented
10C2×#17988749C211yesmaximal, characteristic, complemented
11C2×#17988747C211yesmaximal, characteristic, complemented
12C2×#17988726C211yesmaximal, characteristic, complemented
13C2×#17988725C211yesmaximal, characteristic, complemented
14C2×C4×#11924018C211yesmaximal, characteristic, complemented
15C2×D4×#10596831C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C2×#14556611—28no—
20C2×#14556611C2218yescomplemented
21C22×#11924018—28no—
22C22×#11924018C2211yescharacteristic
23C22×#11924018C2211yescharacteristic
24C22×#11924018C2211yescharacteristic
25C22×#11924018C2211yescharacteristic
26C22×#11924018C2218yescomplemented
27C22×#11924016C2211yescharacteristic
28C22×#11924016C2211yescharacteristic
29C22×#11924015C2211yescharacteristic
30C22×#11924015C2211yescharacteristic
31C22×#11924013C2211yescharacteristic
32C23×#10596831C2211yescharacteristic
33C23×#10596831C2211yescharacteristic
34#17989246—24no—
35#17989246C2218yescomplemented
36C2×#14556579C2211yescharacteristic
37C2×#14556577—21no—
38C2×#14556570C2211yescharacteristic
39C2×#14556569—21no—
40C2×#14556565C2211yescharacteristic
41C2×#14556563—21no—
42C2×C4×Dic146C2211yescharacteristic
43C2×#14556551—21no—
44#17988969C2218yescomplemented
45#17988826C2218yescomplemented
46#17988821C2218yescomplemented
47#17988809C2218yescomplemented
48#17988806C2218yescomplemented
49#17988749C2218yescomplemented
50#17988747C2218yescomplemented
51#17988726C2218yescomplemented
52#17988725C2218yescomplemented
53C4×#11924018C2218yescomplemented
54D4×#10596831C2218yescomplemented
55C2×#14556524C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556515C2211yescharacteristic
58C2×#14556515C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556512C2211yescharacteristic
62C2×#14556511C2211yescharacteristic
63C2×C22⋊#10596831C2211yescharacteristic
64C2×C22⋊#10596831C2211yescharacteristic
65C2×C4×#10596831C2211yescharacteristic
66C22×#41×C73C2211yescharacteristic
67C23×Q8×C73C2211yescharacteristic
68#548×C73—24no—
69#548×C73C2218yescomplemented
70C2×#124×C73—21no—
71C2×#124×C73C2211yescharacteristic
72C2×C22⋊Q8×C73—21no—
73C2×C22⋊Q8×C73C2211yescharacteristic
74C2×#121×C73—21no—
75C2×#121×C73C2211yescharacteristic
76C2×C4×Q8×C73C2211yescharacteristic
77C2×C4×D4×C73—21no—
78C2×C4×D4×C73C2211yescharacteristic
79C2×#11924028—24no—
80C2×#11924028—22no—
81C2×#11924028—42no—
82C2×#11924028C2314yes—
83C22×Dic146—24no—
84C22×Dic146—22no—
85C22×Dic146—21no—
86C22×Dic146—42no—
87C22×Dic146C2311yescharacteristic
88C22×Dic146C2314yes—
89C22×Dic146C2311yescharacteristic
90C22×D292C2311yescharacteristic
91C22×C22⋊D73—21no—
92C22×C22⋊D73—21no—
93C23×Dic73—21no—
94C22×C4×D73—21no—
95#14556611—232no—
96C2×#11924018—24no—
97C2×#11924018—232no—
98C2×#11924018—24no—
99C2×#11924018—24no—
100C2×#11924018D418yescomplemented
101C2×#11924018C2314yes—
102C2×#11924018C2314yes—
103C2×#11924018C2314yes—
104C2×#11924018C2314yes—
105C2×#11924016—24no—
106C2×#11924016—42no—
107C2×#11924016C2314yes—
108C2×#11924016C2314yes—
109C2×#11924015—24no—
110C2×#11924015—42no—
111C2×#11924015C2314yes—
112C2×#11924015C2314yes—
113C2×#11924013—24no—
114C2×#11924013C2314yes—
115C22×#10596831—24no—
116C22×#10596831—24no—
117C22×#10596831C2311yescharacteristic
118C22×#10596831C2311yescharacteristic
119C22×#10596831C2314yes—
120C22×#10596831C2314yes—
121C22×#10596831C2311yescharacteristic
122C22×#10596831C2311yescharacteristic
123#14556579—22no—
124#14556579C2314yes—
125#14556577—28no—
126#14556570—22no—
127#14556570C2314yes—
128#14556569—28no—
129#14556565—22no—
130#14556565C2314yes—
131#14556563—28no—
132C4×Dic146—22no—
133C4×Dic146C2314yes—
134#14556551—28no—
135C2×C4⋊Dic73C2311yescharacteristic
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×C22⋊Dic73—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×C4×Dic73—21no—
143#14556524C2314yes—
144C4⋊#10596831C2314yes—
145#14556515C2314yes—
146#14556515C2314yes—
147#14556514C2314yes—
148#14556514C2314yes—
149#14556512C2314yes—
150#14556511C2314yes—
151C22⋊#10596831C2314yes—
152C22⋊#10596831C2314yes—
153C4×#10596831C2314yes—
154C2×#41×C73—22no—
155C2×#41×C73—24no—
156C2×#41×C73—42no—
157C2×#41×C73C2314yes—
158C22×Q8×C73—21no—
159C22×Q8×C73—22no—
160C22×Q8×C73—24no—
161C22×Q8×C73—42no—
162C22×Q8×C73C2311yescharacteristic
163C22×Q8×C73C2314yes—
164C22×Q8×C73C2311yescharacteristic
165C22×D4×C73—21no—
166C22×D4×C73—21no—
167C22×D4×C73D411yescharacteristic
168C22×D4×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73—21no—
171C23×C4×C73C2311yescharacteristic
172C23×C4×C73C2311yescharacteristic
173#124×C73—28no—
174#124×C73—22no—
175#124×C73C2314yes—
176C22⋊Q8×C73—22no—
177C22⋊Q8×C73—28no—
178C22⋊Q8×C73C2314yes—
179#121×C73—28no—
180#121×C73—22no—
181#121×C73C2314yes—
182C4×Q8×C73—22no—
183C4×Q8×C73C2314yes—
184C4×D4×C73—28no—
185C4×D4×C73D414yes—
186C4×D4×C73C2314yes—
187C2×C4⋊C4×C73—21no—
188C2×C4⋊C4×C73—21no—
189C2×C4⋊C4×C73D411yescharacteristic
190C2×C4⋊C4×C73C2311yescharacteristic
191C2×C22⋊C4×C73—21no—
192C2×C22⋊C4×C73—21no—
193C2×C22⋊C4×C73—21no—
194C2×C22⋊C4×C73—21no—
195C2×C22⋊C4×C73D411yescharacteristic
196C2×C22⋊C4×C73D411yescharacteristic
197C2×C42×C73—21no—
198C2×C42×C73C2311yescharacteristic
199C23×D73—21no—
200#11924028—28no—
201#11924028—44no—
202#11924028—48no—
203C2×Dic146—21no—
204C2×Dic146—22no—
205C2×Dic146—22no—
206C2×Dic146—22no—
207C2×Dic146—28no—
208C2×Dic146—24no—
209C2×Dic146—21no—
210C2×Dic146—44no—
211C2×Dic146—48no—
212C2×Dic146—44no—
213C2×Dic146C2×D414yes—
214C2×Dic146C2412yes—
215C2×Dic146C2412yes—
216C2×D292—22no—
217C2×D292—22no—
218C2×D292—21no—
219C2×D292C2412yes—
220C2×C22⋊D73—24no—
221C2×C22⋊D73—24no—
222C2×C22⋊D73—44no—
223C2×C22⋊D73—44no—
224C22×Dic73—21no—
225C22×Dic73—21no—
226C22×Dic73—21no—
227C22×Dic73—24no—
228C22×Dic73—44no—
229C2×C4×D73—24no—
230C2×C4×D73—44no—
231#11924018—28no—
232#11924018—28no—
233#11924018—28no—
234#11924018C2×D4116yescomplemented
235#11924016—28no—
236#11924016—44no—
237#11924015—28no—
238#11924015—44no—
239#11924013—28no—
240C2×#10596831—22no—
241C2×#10596831—22no—
242C2×#10596831—22no—
243C2×#10596831—28no—
244C2×#10596831—28no—
245C2×#10596831C2×D414yes—
246C2×#10596831C2412yes—
247C2×#10596831C2412yes—
248C2×#10596831C2412yes—
249C2×#10596831C2412yes—
250C4⋊Dic73—21no—
251C4⋊Dic73C2412yes—
252#11924007—24no—
253#11924007—24no—
254C22⋊Dic73—24no—
255#11924005—24no—
256#11924005—24no—
257#11924005—24no—
258C4×Dic73—24no—
259C24×C73—21no—
260C24×C73C2×D411yescharacteristic
261C24×C73C2×D411yescharacteristic
262#41×C73—28no—
263#41×C73—44no—
264#41×C73—48no—
265C2×Q8×C73—21no—
266C2×Q8×C73—24no—
267C2×Q8×C73—21no—
268C2×Q8×C73—22no—
269C2×Q8×C73—28no—
270C2×Q8×C73—22no—
271C2×Q8×C73—22no—
272C2×Q8×C73—44no—
273C2×Q8×C73—44no—
274C2×Q8×C73—48no—
275C2×Q8×C73C2×D414yes—
276C2×Q8×C73C2412yes—
277C2×Q8×C73C2412yes—
278C2×D4×C73—24no—
279C2×D4×C73—24no—
280C2×D4×C73—24no—
281C2×D4×C73—22no—
282C2×D4×C73—21no—
283C2×D4×C73—22no—
284C2×D4×C73—44no—
285C2×D4×C73—44no—
286C2×D4×C73C2×D414yes—
287C2×D4×C73C2412yes—
288C22×C4×C73—21no—
289C22×C4×C73—22no—
290C22×C4×C73—22no—
291C22×C4×C73—22no—
292C22×C4×C73—22no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—24no—
296C22×C4×C73—24no—
297C22×C4×C73—44no—
298C22×C4×C73—44no—
299C22×C4×C73C2×D411yescharacteristic
300C22×C4×C73C2×D411yescharacteristic
301C22×C4×C73C2×D411yescharacteristic
302C22×C4×C73C2×D411yescharacteristic
303C22×C4×C73C2×D412yes—
304C22×C4×C73C2×D412yes—
305C22×C4×C73C2412yes—
306C22×C4×C73C2412yes—
307C22×C4×C73C2411yescharacteristic
308C4⋊C4×C73—24no—
309C4⋊C4×C73—24no—
310C4⋊C4×C73—21no—
311C4⋊C4×C73C2×D414yes—
312C4⋊C4×C73C2412yes—
313C22⋊C4×C73—24no—
314C22⋊C4×C73—24no—
315C22⋊C4×C73—24no—
316C22⋊C4×C73—24no—
317C22⋊C4×C73C2×D414yes—
318C22⋊C4×C73C2×D414yes—
319C42×C73—24no—
320C42×C73C2×D412yes—
321C42×C73C2412yes—
322C23×C73—22no—
323C23×C73—22no—
324C23×C73—22no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—22no—
328C23×C73—42no—
329C23×C73—42no—
330C23×C73—42no—
331C23×C73#13514yescomplemented
332C23×C73C22×D412yes—
333C23×C73C22×D412yes—
334C23×C73C22×D411yescharacteristic
335C22×D73—22no—
336C22×D73—42no—
337C22×D73—42no—
338C22×D73—42no—
339Q8×C73—24no—
340Q8×C73—22no—
341Q8×C73—22no—
342Q8×C73—22no—
343Q8×C73—48no—
344Q8×C73—42no—
345Q8×C73C22×D414yes—
346D4×C73—28no—
347D4×C73—22no—
348D4×C73—22no—
349D4×C73—48no—
350D4×C73—48no—
351D4×C73—42no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—24no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—24no—
359C2×C4×C73—24no—
360C2×C4×C73—22no—
361C2×C4×C73—22no—
362C2×C4×C73—22no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—22no—
366C2×C4×C73—48no—
367C2×C4×C73—48no—
368C2×C4×C73—42no—
369C2×C4×C73—42no—
370C2×C4×C73C22×D412yes—
371C2×C4×C73C22×D412yes—
372C2×C4×C73C22×D412yes—
373C2×C4×C73C22×D412yes—
374C2×C4×C73C22×D412yes—
375C2×C4×C73C22×D411yescharacteristic
376C2×C4×C73H(5,𝔽2)12yes—
377C2×C4×C73C2511yescharacteristic
378C22⋊D73—48no—
379C22⋊D73—48no—
380C2×Dic73—24no—
381C2×Dic73—22no—
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—48no—
385C2×Dic73—42no—
386C2×Dic73—42no—
387D292—22no—
388D292—22no—
389D292—42no—
390C4×D73—48no—
391Dic146—24no—
392Dic146—22no—
393Dic146—22no—
394Dic146—22no—
395Dic146—48no—
396Dic146—42no—
397Dic146C22×D414yes—
398#10596831—22no—
399#10596831—22no—
400#10596831—22no—
401#10596831C22×D414yes—
402C22×C73—22no—
403C22×C73—28no—
404C22×C73—22no—
405C22×C73—22no—
406C22×C73—22no—
407C22×C73—22no—
408C22×C73—44no—
409C22×C73—42no—
410C22×C73—42no—
411C22×C73—42no—
412C22×C73—84no—
413C22×C73D4212yes—
414C22×C73C2×#13512yes—
415C22×C73C2×#13514yescomplemented
416C22×C73#57812yes—
417C22×C73C23×D411yescharacteristic
418C2×D73—42no—
419C2×D73—42no—
420C2×D73—42no—
421C2×D73—84no—
422C4×C73—22no—
423C4×C73—22no—
424C4×C73—24no—
425C4×C73—22no—
426C4×C73—22no—
427C4×C73—42no—
428C4×C73—42no—
429C4×C73D4212yes—
430C4×C73C23×D411yescharacteristic
431C4×C73C2×H(5,𝔽2)11yescharacteristic
432Dic73—24no—
433Dic73—42no—
434Dic73—42no—
435C2×#3285—731nomaximal, Sylow
436C2×C73—24no—
437C2×C73—42no—
438C2×C73—82no—
439C2×C73#328514yescomplemented
440C2×C73C2×D4211yescharacteristic
441C2×C73C22×#13511yescharacteristic
442C2×C73C2×#57811yescharacteristic
443D73—82no—
444C22×#135—731no—
445C23×Q16—731no—
446C2×#548—731no—
447C2×#548D7311yescharacteristic, complemented
448#3285—7316no—
449C2×#495—731no—
450C2×#467—731no—
451C2×#466—731no—
452C2×#464—731no—
453C2×#464—731no—
454C2×#452—731no—
455C2×#452—731no—
456C2×#448—731no—
457C2×#448—731no—
458C2×C4×Q16—731no—
459C2×C8×D4—731no—
460C73C2×#328511yescharacteristic, complemented, Sylow
461C22×#41—731no—
462C22×#41C2×D7311yescharacteristic
463C23×Q8—731no—
464C23×Q8C2×D7311yescharacteristic
465C2×#135—738no—
466C2×#135—1468no—
467C22×Q16—731no—
468C22×Q16—731no—
469C22×Q16—731no—
470C22×Q16—731no—
471C22×Q16—738no—
472C22×Q16—1468no—
473C22×SD16—731no—
474C22×SD16—731no—
475C22×SD16—731no—
476C22×SD16—731no—
477C22×D8—731no—
478C23×C8—731no—
479C23×C8—731no—
480#548—24no—
481#548—738no—
482#548—1464no—
483#548C2×D7318yescomplemented
484C2×#124—21no—
485C2×#124—731no—
486C2×#124—1461no—
487C2×#124C2×D7311yescharacteristic
488C2×C22⋊Q8—21no—
489C2×C22⋊Q8—731no—
490C2×C22⋊Q8—1461no—
491C2×C22⋊Q8C2×D7311yescharacteristic
492C2×#121—21no—
493C2×#121—731no—
494C2×#121—1461no—
495C2×#121C2×D7311yescharacteristic
496C2×C4×Q8—731no—
497C2×C4×Q8C2×D7311yescharacteristic
498C2×C4×D4—21no—
499C2×C4×D4—1461no—
500C2×C4×D4C2×D7311yescharacteristic
501#495—738no—
502#467—738no—
503#466—738no—
504#464—738no—
505#464—738no—
506#452—738no—
507#452—738no—
508#448—738no—
509#448—738no—
510C4×Q16—738no—
511C8×D4—738no—
512C2×#107—731no—
513C2×C4⋊C8—731no—
514C2×#103—731no—
515C2×#103—731no—
516C2×#103—731no—
517C2×#103—731no—
518C2×#102—731no—
519C2×#102—731no—
520C2×C22⋊C8—731no—
521C2×C22⋊C8—731no—
522C2×C4×C8—731no—
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—2922no—
527C2×#41—734no—
528C2×#41—1464no—
529C2×#41—1462no—
530C2×#41C22×D7314yes—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—24no—
534C22×Q8—42no—
535C22×Q8—2922no—
536C22×Q8—734no—
537C22×Q8—731no—
538C22×Q8—731no—
539C22×Q8—1464no—
540C22×Q8—1461no—
541C22×Q8—1462no—
542C22×Q8C22×D7311yescharacteristic
543C22×Q8C22×D7314yes—
544C22×Q8C22×D7311yescharacteristic
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—731no—
548C22×D4—1461no—
549C22×D4—1461no—
550C22×D4C22⋊D7311yescharacteristic
551C22×D4C22×D7311yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—1461no—
555C23×C4—1461no—
556C23×C4C22×D7311yescharacteristic
557C23×C4C22×D7311yescharacteristic
558#135—14632no—
559C2×Q16—738no—
560C2×Q16—734no—
561C2×Q16—734no—
562C2×Q16—734no—
563C2×Q16—734no—
564C2×Q16—1464no—
565C2×Q16—14632no—
566C2×Q16—1464no—
567C2×Q16—1464no—
568C2×SD16—2922no—
569C2×SD16—2922no—
570C2×SD16—734no—
571C2×SD16—734no—
572C2×SD16—734no—
573C2×SD16—734no—
574C2×SD16—1464no—
575C2×SD16—1464no—
576C2×D8—734no—
577C2×D8—1464no—
578C22×C8—731no—
579C22×C8—731no—
580C22×C8—731no—
581C22×C8—734no—
582C22×C8—734no—
583C22×C8—731no—
584C22×C8—1464no—
585C22×C8—1464no—
586#124—28no—
587#124—22no—
588#124—734no—
589#124—1468no—
590#124—1462no—
591#124C22×D7314yes—
592C22⋊Q8—22no—
593C22⋊Q8—28no—
594C22⋊Q8—734no—
595C22⋊Q8—1462no—
596C22⋊Q8—1468no—
597C22⋊Q8C22×D7314yes—
598#121—28no—
599#121—22no—
600#121—734no—
601#121—1468no—
602#121—1462no—
603#121C22×D7314yes—
604C4×Q8—22no—
605C4×Q8—734no—
606C4×Q8—1462no—
607C4×Q8C22×D7314yes—
608C4×D4—28no—
609C4×D4—1468no—
610C4×D4C22⋊D7314yes—
611C4×D4C22×D7314yes—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—731no—
615C2×C4⋊C4—1461no—
616C2×C4⋊C4—1461no—
617C2×C4⋊C4C22⋊D7311yescharacteristic
618C2×C4⋊C4C22×D7311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—1461no—
624C2×C22⋊C4—1461no—
625C2×C22⋊C4—1461no—
626C2×C22⋊C4—1461no—
627C2×C22⋊C4C22⋊D7311yescharacteristic
628C2×C22⋊C4C22⋊D7311yescharacteristic
629C2×C42—21no—
630C2×C42—1461no—
631C2×C42C22×D7311yescharacteristic
632#107—734no—
633C4⋊C8—734no—
634#103—734no—
635#103—734no—
636#103—734no—
637#103—734no—
638#102—734no—
639#102—734no—
640C22⋊C8—734no—
641C22⋊C8—734no—
642C4×C8—734no—
643C24—21no—
644C24—1461no—
645C24C2×C22⋊D7311yescharacteristic
646C24C2×C22⋊D7311yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—2928no—
651#41—2924no—
652#41—1468no—
653C2×Q8—21no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—28no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—48no—
663C2×Q8—2928no—
664C2×Q8—2924no—
665C2×Q8—2924no—
666C2×Q8—734no—
667C2×Q8—732no—
668C2×Q8—732no—
669C2×Q8—1468no—
670C2×Q8—1462no—
671C2×Q8—1462no—
672C2×Q8—1461no—
673C2×Q8—1464no—
674C2×Q8—1461no—
675C2×Q8—1462no—
676C2×Q8D4×D7314yes—
677C2×Q8C23×D7312yes—
678C2×Q8C23×D7312yes—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—2924no—
688C2×D4—2924no—
689C2×D4—732no—
690C2×D4—1464no—
691C2×D4—1464no—
692C2×D4—1462no—
693C2×D4—1461no—
694C2×D4—1462no—
695C2×D4C2×C22⋊D7314yes—
696C2×D4C23×D7312yes—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—24no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—2924no—
709C22×C4—2924no—
710C22×C4—1464no—
711C22×C4—1461no—
712C22×C4—1461no—
713C22×C4—1464no—
714C22×C4—1461no—
715C22×C4C2×C22⋊D7312yes—
716C22×C4C2×C22⋊D7312yes—
717C22×C4C2×C22⋊D7311yescharacteristic
718C22×C4C2×C22⋊D7311yescharacteristic
719C22×C4C2×C22⋊D7311yescharacteristic
720C22×C4C2×C22⋊D7311yescharacteristic
721C22×C4C23×D7312yes—
722C22×C4C23×D7312yes—
723C22×C4C23×D7311yescharacteristic
724Q16—7316no—
725Q16—1468no—
726Q16—1468no—
727Q16—1468no—
728SD16—2924no—
729SD16—2924no—
730SD16—1468no—
731SD16—1468no—
732D8—1468no—
733C2×C8—734no—
734C2×C8—732no—
735C2×C8—732no—
736C2×C8—732no—
737C2×C8—732no—
738C2×C8—1468no—
739C2×C8—1468no—
740C2×C8—1462no—
741C2×C8—1462no—
742C2×C8—1462no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—21no—
746C4⋊C4—732no—
747C4⋊C4—1464no—
748C4⋊C4—1464no—
749C4⋊C4—1461no—
750C4⋊C4C2×C22⋊D7314yes—
751C4⋊C4C23×D7312yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—1464no—
757C22⋊C4—1464no—
758C22⋊C4—1464no—
759C22⋊C4—1464no—
760C22⋊C4C2×C22⋊D7314yes—
761C22⋊C4C2×C22⋊D7314yes—
762C42—24no—
763C42—1464no—
764C42C2×C22⋊D7312yes—
765C42C23×D7312yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—2922no—
776C23—2922no—
777C23—2922no—
778C23—1462no—
779C23#1455661114yescomplemented
780C23C22×C22⋊D7312yes—
781C23C22×C22⋊D7312yes—
782C23C22×C22⋊D7311yescharacteristic
783Q8—22no—
784Q8—24no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—42no—
789Q8—2928no—
790Q8—2922no—
791Q8—734no—
792Q8—1462no—
793Q8—1462no—
794Q8—1462no—
795Q8—1464no—
796Q8C2×D4×D7314yes—
797D4—28no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—42no—
803D4—2928no—
804D4—2928no—
805D4—2922no—
806D4—1462no—
807D4—1462no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—48no—
823C2×C4—48no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—2928no—
827C2×C4—2922no—
828C2×C4—2922no—
829C2×C4—2928no—
830C2×C4—1462no—
831C2×C4—1462no—
832C2×C4—1462no—
833C2×C4—1464no—
834C2×C4C2×D4×D7312yes—
835C2×C4C22×C22⋊D7312yes—
836C2×C4C22×C22⋊D7312yes—
837C2×C4C22×C22⋊D7312yes—
838C2×C4C22×C22⋊D7312yes—
839C2×C4C22×C22⋊D7311yescharacteristic
840C2×C4#1455663612yes—
841C2×C4C24×D7311yescharacteristic
842C8—734no—
843C8—1462no—
844C8—1462no—
845C8—1462no—
846C22—22no—
847C22—22no—
848C22—28no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—2922no—
858C22—2922no—
859C22—2922no—
860C22—5844no—
861C22D4×C22⋊D7312yes—
862C22C2×#1455661112yes—
863C22C2×#1455661114yescomplemented
864C22#1798940212yes—
865C22C23×C22⋊D7311yescharacteristic
866C4—22no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—2922no—
874C4—2922no—
875C4—1464no—
876C4D4×C22⋊D7312yes—
877C4C22×D4×D7311yescharacteristic
878C4C2×#1455663611yescharacteristic
879C2—24no—
880C2—42no—
881C2—82no—
882C2—5842no—
883C2#2262166814yesdirect product factor
884C2C2×D4×C22⋊D7311yescharacteristic
885C2C22×#1455661111yescharacteristic
886C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#548×C73C2
socleC23×C73C22×D4
hypercenterC2×#548D73
hypocenterC73C2×#3285
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556611C2semidirect
2. C23×#11924018C2semidirect
3. C2×#17989246C2semidirect
4. #22621668C2direct (N × H)
5. C2×#17988969C2semidirect
6. C2×#17988826C2semidirect
7. C2×#17988821C2semidirect
8. C2×#17988809C2semidirect
9. C2×#17988806C2semidirect
10. C2×#17988749C2semidirect
11. C2×#17988747C2semidirect
12. C2×#17988726C2semidirect
13. C2×#17988725C2semidirect
14. C2×C4×#11924018C2semidirect
15. C2×D4×#10596831C2semidirect
16. C2×#548×C73C2semidirect
20. C2×#14556611C22semidirect
26. C22×#11924018C22semidirect
35. #17989246C22semidirect
44. #17988969C22semidirect
45. #17988826C22semidirect
46. #17988821C22semidirect
47. #17988809C22semidirect
48. #17988806C22semidirect
49. #17988749C22semidirect
50. #17988747C22semidirect
51. #17988726C22semidirect
52. #17988725C22semidirect
53. C4×#11924018C22semidirect
54. D4×#10596831C22semidirect
69. #548×C73C22semidirect
100. C2×#11924018D4semidirect
234. #11924018C2×D4semidirect
331. C23×C73#135semidirect
415. C22×C73C2×#135semidirect
439. C2×C73#3285semidirect
447. C2×#548D73semidirect
460. C73C2×#3285semidirect
483. #548C2×D73semidirect
779. C23#14556611semidirect
863. C22C2×#14556611semidirect
883. C2#22621668direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566112
C23×#119240182
C2×#179892462
#226216682
C2×#179889692
C2×#179888262
C2×#179888212
C2×#179888092
C2×#179888062
C2×#179887492
C2×#179887472
C2×#179887262
C2×#179887252
C2×C4×#119240182
C2×D4×#105968312
C2×#548×C732
C2×#328573