Finite Group Databasebeta

← C2×#22622827 #33966458

Subgroups — C2×#22622827 #33966458

Order 18688.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989293C211yesmaximal, characteristic, complemented
2C2×#17989252C211yesmaximal, characteristic, complemented
3#22622827C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988984C211yesmaximal, characteristic, complemented
6C2×#17988890C211yesmaximal, characteristic, complemented
7C2×#17988884C211yesmaximal, characteristic, complemented
8C2×#17988876C211yesmaximal, characteristic, complemented
9C2×#17988876C211yesmaximal, characteristic, complemented
10C2×#17988874C211yesmaximal, characteristic, complemented
11C2×#17988866C211yesmaximal, characteristic, complemented
12C2×#17988715C211yesmaximal, characteristic, complemented
13C2×#17988700C211yesmaximal, characteristic
14C2×#17988698C211yesmaximal, characteristic
15C2×#17988669C211yesmaximal, characteristic
16C2×#501×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73—21no—
18C22×D584C2211yescharacteristic
19#17989293—24no—
20#17989293C2218yescomplemented
21#17989252—24no—
22#17989252C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556582C2211yescharacteristic
27C2×#14556571—21no—
28C2×#14556569—21no—
29C2×#14556569—21no—
30C2×#14556569—21no—
31C2×#14556569—21no—
32C2×#14556567—21no—
33C2×C4×Dic146C2211yescharacteristic
34C2×C4×D292C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×#14556553C2211yescharacteristic
38C2×#14556553C2211yescharacteristic
39C2×#14556553C2211yescharacteristic
40C2×C4⋊C4×D73—21no—
41#17988995C2218yescomplemented
42#17988984C2218yescomplemented
43#17988890C2218yescomplemented
44#17988884C2218yescomplemented
45#17988876C2218yescomplemented
46#17988876C2218yescomplemented
47#17988874C2218yescomplemented
48#17988866C2218yescomplemented
49#17988715C2218yescomplemented
50#17988700C2218yes—
51#17988698C2218yes—
52#17988669C2218yes—
53C2×#14556524C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×C4⋊#10596831C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#501×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×#106×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C2×Q8×D73—28no—
82C2×Q8×D73—48no—
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C2×D584Q818yescomplemented
92C2×D584C2314yes—
93C22×#10596831C2311yescharacteristic
94C22×#10596831C2311yescharacteristic
95#14556590—22no—
96#14556590—22no—
97#14556590—22no—
98#14556590C2314yes—
99#14556590C2314yes—
100#14556590C2314yes—
101#14556582—22no—
102#14556582C2314yes—
103#14556571—28no—
104#14556569—28no—
105#14556569—28no—
106#14556569—28no—
107#14556569—28no—
108#14556567—28no—
109C4×Dic146D414yes—
110C4×Dic146C2314yes—
111C4×D292—22no—
112C4×D292—22no—
113C4×D292C2314yes—
114C4×D292C2314yes—
115#14556553—22no—
116#14556553—22no—
117#14556553—22no—
118#14556553—22no—
119#14556553C2314yes—
120#14556553C2314yes—
121#14556553C2314yes—
122#14556553C2314yes—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73D411yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C4⋊C4×D73—28no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73C2311yescharacteristic
141C2×C4×Dic73C2311yescharacteristic
142#14556524C2314yes—
143#14556523C2314yes—
144#14556522C2314yes—
145#14556522C2314yes—
146#14556522C2314yes—
147C4⋊#10596831C2314yes—
148#14556520C2314yes—
149#14556520C2314yes—
150#14556513C2314yes—
151#14556513C2314yes—
152#14556511C2314yes—
153#14556511C2314yes—
154#14556511C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157C8×Dic73C2314yes—
158C22×Q8×C73—21no—
159C22×C8×C73C2311yescharacteristic
160C22×C8×C73C2311yescharacteristic
161C4⋊Q8×C73—22no—
162C4⋊Q8×C73C2314yes—
163#125×C73—22no—
164#125×C73C2314yes—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C42×C73C2311yescharacteristic
173#107×C73C2314yes—
174#107×C73C2314yes—
175#106×C73C2314yes—
176#106×C73C2314yes—
177#97×C73C2314yes—
178C23×D73—21no—
179C23×D73—21no—
180C2×Dic146—24no—
181C2×Dic146—24no—
182C2×Dic146—24no—
183C2×Dic146—24no—
184C2×Dic146—44no—
185C2×Dic146—44no—
186C2×Dic146—82no—
187C2×Dic146C2×D414yes—
188Q8×D73—432no—
189C2×D292—21no—
190C2×D292—21no—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292C2×Q814yes—
194C2×D292C2×Q814yescomplemented
195C2×D292C2412yes—
196C2×D292C2412yes—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C22×Dic73C2×D411yescharacteristic
203C2×C4×D73—24no—
204C2×C4×D73—24no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—24no—
209C2×C4×D73—44no—
210C2×C4×D73—44no—
211C2×C4×D73—44no—
212C2×C4×D73—44no—
213C2×C4×D73—82no—
214C2×C4×D73—82no—
215D584C2×Q8116yescomplemented
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—24no—
223C4⋊Dic73C2×D414yes—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007C2×D414yes—
231#11924007C2×D414yes—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238C4×Dic73C2×D412yes—
239C4×Dic73C2×D412yes—
240C4×Dic73C2412yes—
241C4×Dic73C2412yes—
242C2×Q8×C73—24no—
243C2×Q8×C73—44no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2411yescharacteristic
251C2×C8×C73—22no—
252C2×C8×C73C2×Q814yescomplemented
253C2×C8×C73C2412yes—
254C2×C8×C73C2412yes—
255C4⋊C4×C73—24no—
256C4⋊C4×C73—24no—
257C4⋊C4×C73—24no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73C2412yes—
263C4⋊C4×C73C2412yes—
264C4⋊C4×C73C2412yes—
265C4⋊C4×C73C2412yes—
266C42×C73C2×D412yes—
267C42×C73C2412yes—
268C23×C73C22×D411yescharacteristic
269C22×D73—24no—
270C22×D73—24no—
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—42no—
274C22×D73—42no—
275C22×D73—42no—
276C22×D73—42no—
277Q8×C73—48no—
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—42no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73C22×D412yes—
289C2×C4×C73C22×D412yes—
290C2×C4×C73C22×D411yescharacteristic
291C2×C4×C73C22×Q812yes—
292C2×C4×C732−1+412yes—
293C2×C4×C73C2511yescharacteristic
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—42no—
300C2×Dic73—42no—
301C2×Dic73AGL(1,ℤ/8)14yes—
302C2×Dic73C22×D412yes—
303C2×Dic73C22×D412yes—
304C2×Dic73C22×D412yes—
305C2×Dic73C22×D412yes—
306D292—24no—
307D292—24no—
308D292—22no—
309D292—22no—
310D292C22×Q814yes—
311D292C22×Q814yescomplemented
312C4×D73—48no—
313C4×D73—48no—
314C4×D73—48no—
315C4×D73—48no—
316C4×D73—84no—
317C4×D73—84no—
318Dic146—28no—
319Dic146—48no—
320Dic146—48no—
321Dic146—84no—
322C8×C73—22no—
323C8×C73C22×Q814yescomplemented
324#10596831—22no—
325#10596831—22no—
326C22×C73D4×Q812yes—
327C22×C73C2×AGL(1,ℤ/8)12yes—
328C22×C73#57712yes—
329C22×C73C23×D411yescharacteristic
330C2×D73—24no—
331C2×D73—24no—
332C2×D73—48no—
333C2×D73—48no—
334C2×D73—42no—
335C2×D73—42no—
336C2×D73—42no—
337C2×D73—42no—
338C4×C73—22no—
339C4×C73—22no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73D4×Q812yes—
345C4×C73C23×Q811yescharacteristic
346C4×C73C2×2−1+411yescharacteristic
347Dic73—22no—
348Dic73—22no—
349Dic73—22no—
350Dic73—42no—
351Dic73—42no—
352Dic73C2×AGL(1,ℤ/8)14yes—
353C2×#3384—731nomaximal, Sylow
354C2×C73#338414yescomplemented
355C2×C73C2×D4×Q811yescharacteristic
356C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
357C2×C73C2×#57711yescharacteristic
358D73—44no—
359D73—44no—
360C2×#554—731no—
361C2×D4×Q8—731no—
362#3384—7316no—
363C2×#501—731no—
364C2×#501D7311yescharacteristic, complemented
365C2×#498—731no—
366C2×#478—731no—
367C2×#478—731no—
368C2×#476—731no—
369C2×#476—731no—
370C2×#476—731no—
371C2×#474—731no—
372C2×#446—731no—
373C2×#442—731no—
374C2×#442—731no—
375C2×C4×D8—731no—
376C73C2×#338411yescharacteristic, complemented, Sylow
377C23×Q8—1461no—
378C22×D8—731no—
379#554—738no—
380#554—1464no—
381D4×Q8—738no—
382D4×Q8—1464no—
383C2×C4⋊Q8—731no—
384C2×C4⋊Q8—731no—
385C2×C4⋊Q8—731no—
386C2×C4⋊Q8C2×D7311yescharacteristic
387C2×#125—731no—
388C2×#125C2×D7311yescharacteristic
389C2×C22⋊Q8—1461no—
390C2×C22⋊Q8—1461no—
391C2×C22⋊Q8—1461no—
392C2×C22⋊Q8—1461no—
393C2×C22⋊Q8—1461no—
394C2×C22⋊Q8—1461no—
395C2×C4×Q8—731no—
396C2×C4×D4—731no—
397C2×C4×D4—731no—
398C2×C4×D4—731no—
399C2×C4×D4—731no—
400C2×C4×D4—731no—
401C2×C4×D4—731no—
402C22×C4⋊C4—1461no—
403#501—738no—
404#501C2×D7318yescomplemented
405#498—738no—
406#478—738no—
407#478—738no—
408#476—738no—
409#476—738no—
410#476—738no—
411#474—738no—
412#446—738no—
413#442—738no—
414#442—738no—
415C4×D8—738no—
416C2×#107—731no—
417C2×#107C2×D7311yescharacteristic
418C2×#107C2×D7311yescharacteristic
419C2×#106—731no—
420C2×#106—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×#106C2×D7311yescharacteristic
424C2×#106C2×D7311yescharacteristic
425C2×C4⋊C8—731no—
426C2×C4⋊C8—731no—
427C2×C4⋊C8—731no—
428C2×#102—731no—
429C2×#102—731no—
430C2×#102—731no—
431C2×#102—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#97—731no—
435C2×#97C2×D7311yescharacteristic
436C2×C4×C8—731no—
437C22×Q8—21no—
438C22×Q8—2928no—
439C22×Q8—731no—
440C22×Q8—1461no—
441C22×Q8—1461no—
442C22×Q8—1461no—
443C22×Q8—1468no—
444C22×D4—731no—
445C22×D4—731no—
446C23×C4—1461no—
447C23×C4—1461no—
448C23×C4—1461no—
449C23×C4—1461no—
450C23×C4—1461no—
451C23×C4—1461no—
452C2×D8—738no—
453C2×D8—734no—
454C22×C8—731no—
455C22×C8—731no—
456C22×C8C22×D7311yescharacteristic
457C22×C8C22×D7311yescharacteristic
458C4⋊Q8—22no—
459C4⋊Q8—734no—
460C4⋊Q8—734no—
461C4⋊Q8—734no—
462C4⋊Q8—1462no—
463C4⋊Q8—1462no—
464C4⋊Q8—1462no—
465C4⋊Q8C22×D7314yes—
466#125—22no—
467#125—734no—
468#125—1462no—
469#125C22×D7314yes—
470C22⋊Q8—1468no—
471C22⋊Q8—1468no—
472C22⋊Q8—1468no—
473C22⋊Q8—1468no—
474C22⋊Q8—1468no—
475C22⋊Q8—1468no—
476C4×Q8—734no—
477C4×Q8—734no—
478C4×D4—734no—
479C4×D4—734no—
480C4×D4—734no—
481C4×D4—734no—
482C4×D4—734no—
483C4×D4—734no—
484C4×D4—1462no—
485C4×D4—1462no—
486C4×D4—1462no—
487C4×D4—1462no—
488C4×D4—1462no—
489C4×D4—1462no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—731no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—1468no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4C22×D7311yescharacteristic
505C2×C4⋊C4C22×D7311yescharacteristic
506C2×C4⋊C4C22×D7311yescharacteristic
507C2×C4⋊C4C22×D7311yescharacteristic
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C42—731no—
515C2×C42—731no—
516C2×C42C22×D7311yescharacteristic
517#107—734no—
518#107C22×D7314yes—
519#107C22×D7314yes—
520#106—734no—
521#106—734no—
522#106—734no—
523#106—734no—
524#106C22×D7314yes—
525#106C22×D7314yes—
526C4⋊C8—734no—
527C4⋊C8—734no—
528C4⋊C8—734no—
529#102—734no—
530#102—734no—
531#102—734no—
532#102—734no—
533#102—734no—
534#102—734no—
535#97—734no—
536#97C22×D7314yes—
537C4×C8—734no—
538C24—1461no—
539C24—1461no—
540C2×Q8—24no—
541C2×Q8—44no—
542C2×Q8—2924no—
543C2×Q8—2924no—
544C2×Q8—29232no—
545C2×Q8—5842no—
546C2×Q8—734no—
547C2×Q8—1464no—
548C2×Q8—1464no—
549C2×Q8—1464no—
550C2×Q8—1464no—
551C2×D4—734no—
552C2×D4—734no—
553C2×D4—732no—
554C2×D4—732no—
555C2×D4—1461no—
556C2×D4—1461no—
557C2×D4—1462no—
558C2×D4—1462no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—2924no—
564C22×C4—2924no—
565C22×C4—2924no—
566C22×C4—2924no—
567C22×C4—5842no—
568C22×C4—5842no—
569C22×C4—731no—
570C22×C4—731no—
571C22×C4—731no—
572C22×C4—731no—
573C22×C4—1464no—
574C22×C4—1464no—
575C22×C4—1464no—
576C22×C4—1464no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1464no—
580C22×C4—1464no—
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584D8—7316no—
585C2×C8—22no—
586C2×C8—732no—
587C2×C8—732no—
588C2×C8—1462no—
589C2×C8—1462no—
590C2×C8Q8×D7314yescomplemented
591C2×C8C23×D7312yes—
592C2×C8C23×D7312yes—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—734no—
601C4⋊C4—734no—
602C4⋊C4—734no—
603C4⋊C4—732no—
604C4⋊C4—732no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1461no—
611C4⋊C4—1461no—
612C4⋊C4C23×D7312yes—
613C4⋊C4C23×D7312yes—
614C4⋊C4C23×D7312yes—
615C4⋊C4C23×D7312yes—
616C22⋊C4—1464no—
617C22⋊C4—1464no—
618C22⋊C4—1464no—
619C22⋊C4—1464no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C42—732no—
623C42—732no—
624C42—732no—
625C42—732no—
626C42D4×D7312yes—
627C42C23×D7312yes—
628C23—2922no—
629C23—2922no—
630C23—2922no—
631C23—2922no—
632C23—1462no—
633C23—1462no—
634C23—1464no—
635C23—1464no—
636C23C2×D4×D7311yescharacteristic
637Q8—48no—
638Q8—2928no—
639Q8—2928no—
640Q8—5844no—
641Q8—1468no—
642D4—734no—
643D4—734no—
644D4—1462no—
645D4—1462no—
646D4—1464no—
647D4—1464no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—2928no—
659C2×C4—2928no—
660C2×C4—2928no—
661C2×C4—2928no—
662C2×C4—2922no—
663C2×C4—2922no—
664C2×C4—5844no—
665C2×C4—5844no—
666C2×C4—732no—
667C2×C4—734no—
668C2×C4—732no—
669C2×C4—732no—
670C2×C4—732no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4C2×D4×D7312yes—
677C2×C4C2×D4×D7312yes—
678C2×C4C2×D4×D7311yescharacteristic
679C2×C4C2×Q8×D7312yes—
680C2×C4#1455663912yes—
681C2×C4C24×D7311yescharacteristic
682C8—22no—
683C8—1462no—
684C8—1462no—
685C8C2×Q8×D7314yescomplemented
686C22—2928no—
687C22—2928no—
688C22—2922no—
689C22—2922no—
690C22—2922no—
691C22—2922no—
692C22—1464no—
693C22—1464no—
694C22#1798925212yes—
695C22AGL(1,ℤ/8)×D7312yes—
696C22#1798939612yes—
697C22C22×D4×D7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—2922no—
705C4—2922no—
706C4—734no—
707C4—1462no—
708C4—1462no—
709C4—1462no—
710C4#1798925212yes—
711C4C22×Q8×D7311yescharacteristic
712C4C2×#1455663911yescharacteristic
713C2—2924no—
714C2—2924no—
715C2#2262282714yesdirect product factor
716C2C2×#1798925211yescharacteristic
717C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
718C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#501×C73C2
socleC23×C73C22×D4
prime radicalC22×D584C22
hypercenterC2×#501D73
hypocenterC73C2×#3384
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#17989293C2semidirect
2. C2×#17989252C2semidirect
3. #22622827C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988984C2semidirect
6. C2×#17988890C2semidirect
7. C2×#17988884C2semidirect
8. C2×#17988876C2semidirect
9. C2×#17988876C2semidirect
10. C2×#17988874C2semidirect
11. C2×#17988866C2semidirect
12. C2×#17988715C2semidirect
16. C2×#501×C73C2semidirect
20. #17989293C22semidirect
22. #17989252C22semidirect
41. #17988995C22semidirect
42. #17988984C22semidirect
43. #17988890C22semidirect
44. #17988884C22semidirect
45. #17988876C22semidirect
46. #17988876C22semidirect
47. #17988874C22semidirect
48. #17988866C22semidirect
49. #17988715C22semidirect
71. #501×C73C22semidirect
91. C2×D584Q8semidirect
194. C2×D292C2×Q8semidirect
215. D584C2×Q8semidirect
252. C2×C8×C73C2×Q8semidirect
311. D292C22×Q8semidirect
323. C8×C73C22×Q8semidirect
354. C2×C73#3384semidirect
364. C2×#501D73semidirect
376. C73C2×#3384semidirect
404. #501C2×D73semidirect
590. C2×C8Q8×D73semidirect
685. C8C2×Q8×D73semidirect
715. C2#22622827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892932
C2×#179892522
#226228272
C2×#179889952
C2×#179889842
C2×#179888902
C2×#179888842
C2×#179888762
C2×#179888742
C2×#179888662
C2×#179887152
C2×#179887002
C2×#179886982
C2×#179886692
C2×#501×C732
C2×#338473