Finite Group Databasebeta

← C2×#22619759 #33953540

Subgroups — C2×#22619759 #33953540

Order 18688.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989217C211yesmaximal, characteristic, complemented
2C2×#17989059C211yesmaximal, characteristic
3#22619759C2116yesmaximal, direct product factor
4C2×#17988890C211yesmaximal, characteristic, complemented
5C2×#17988885C211yesmaximal, characteristic, complemented
6C2×#17988884C211yesmaximal, characteristic, complemented
7C2×#17988877C211yesmaximal, characteristic, complemented
8C2×#17988876C211yesmaximal, characteristic, complemented
9C2×#17988868C211yesmaximal, characteristic, complemented
10C2×#17988865C211yesmaximal, characteristic, complemented
11C2×#17988626C211yesmaximal, characteristic, complemented
12C2×#17988624C211yesmaximal, characteristic, complemented
13C2×#17988612C211yesmaximal, characteristic, complemented
14C2×#17988590C211yesmaximal, characteristic
15C2×#102×D73C211yesmaximal, characteristic
16C2×#478×C73C211yesmaximal, characteristic, complemented
17C22×D4×D73C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#17989217—24no—
21#17989217C2218yescomplemented
22C2×#14556591C2211yescharacteristic, complemented
23C2×#14556590—21no—
24C2×#14556590C2211yescharacteristic, complemented
25C2×#14556582C2211yescharacteristic, complemented
26C2×#14556581—21no—
27C2×#14556571—21no—
28C2×#14556569—21no—
29#17989059—24no—
30#17989059C2218yes—
31C2×C4×D292C2211yescharacteristic
32C2×D4×Dic73C2211yescharacteristic
33C2×#14556553C2211yescharacteristic
34C2×C4×C22⋊D73—21no—
35C2×#14556551—21no—
36C2×#14556549C2211yescharacteristic
37C2×#14556549C2211yescharacteristic
38C2×#14556548C2211yescharacteristic
39C2×C4⋊C4×D73C2211yescharacteristic
40C22×#11924005—21no—
41C2×C22⋊C4×D73—21no—
42#17988890C2218yescomplemented
43#17988885C2218yescomplemented
44#17988884C2218yescomplemented
45#17988877C2218yescomplemented
46#17988876C2218yescomplemented
47#17988868C2218yescomplemented
48#17988865C2218yescomplemented
49#17988626C2218yescomplemented
50#17988624C2218yescomplemented
51C2×#14556525C2211yescharacteristic, complemented
52C2×#14556525C2211yescharacteristic, complemented
53C2×#14556524C2211yescharacteristic, complemented
54C2×#14556522C2211yescharacteristic, complemented
55C2×#14556522C2211yescharacteristic, complemented
56C2×#14556522C2211yescharacteristic, complemented
57#17988612C2218yescomplemented
58C2×C4⋊#10596831C2211yescharacteristic, complemented
59C2×#14556520C2211yescharacteristic, complemented
60C2×#14556520C2211yescharacteristic, complemented
61#17988590C2218yes—
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556511C2211yescharacteristic
68#102×D73C2218yes—
69C2×#125×C73C2211yescharacteristic, complemented
70C2×C4×D4×C73C2211yescharacteristic
71#478×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic, complemented
73C2×#106×C73C2211yescharacteristic, complemented
74C2×C4⋊C8×C73C2211yescharacteristic, complemented
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C24×D73—21no—
78C22×Dic146—21no—
79C22×Dic146—21no—
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C2×D4×D73—22no—
83C2×D4×D73—24no—
84C2×D4×D73Q818yescomplemented
85C2×D4×D73C2314yes—
86C23×Dic73—21no—
87C22×C4×D73—21no—
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73C2311yescharacteristic
91C2×#11924011—24no—
92C2×#11924011C2314yes—
93C22×#10596831C2311yescharacteristic
94C22×#10596831C2311yescharacteristic
95C2×C8×D73—24no—
96C2×C8×D73C2314yes—
97#14556591—22no—
98#14556591C2314yescomplemented
99#14556590—28no—
100#14556590—22no—
101#14556590C2314yescomplemented
102#14556582—22no—
103#14556582C2314yescomplemented
104#14556581—28no—
105#14556571—28no—
106#14556569—28no—
107C4×D292—22no—
108C4×D292C2314yes—
109D4×Dic73—22no—
110D4×Dic73C2314yes—
111#14556553—22no—
112#14556553C2314yes—
113C4×C22⋊D73—28no—
114#14556551—28no—
115#14556549—22no—
116#14556549—22no—
117#14556549C2314yes—
118#14556549C2314yes—
119#14556548D414yes—
120#14556548C2314yes—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007D411yescharacteristic
130C2×#11924007D411yescharacteristic
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C2×C22⋊Dic73—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—28no—
138C2×#11924005—21no—
139C2×#11924005D411yescharacteristic
140C2×#11924005D411yescharacteristic
141C22⋊C4×D73—28no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yescomplemented
146#14556525C2314yescomplemented
147#14556524C2314yescomplemented
148#14556522C2314yescomplemented
149#14556522C2314yescomplemented
150#14556522C2314yescomplemented
151C4⋊#10596831C2314yescomplemented
152#14556520C2314yescomplemented
153#14556520C2314yescomplemented
154#14556513C2314yes—
155#14556513C2314yes—
156#14556512C2314yes—
157#14556512C2314yes—
158#14556511C2314yes—
159#14556511C2314yes—
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164#125×C73—22no—
165#125×C73C2314yescomplemented
166C4×D4×C73—22no—
167C4×D4×C73C2314yes—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C22⋊C4×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#107×C73C2314yescomplemented
176#106×C73C2314yescomplemented
177C4⋊C8×C73C2314yescomplemented
178#102×C73C2314yes—
179#102×C73C2314yes—
180C23×D73—21no—
181C23×D73—28no—
182C23×D73—24no—
183C23×D73—82no—
184C23×D73—82no—
185C23×D73C2×D411yescharacteristic
186C2×Dic146—24no—
187C2×Dic146—24no—
188C2×Dic146—82no—
189C2×Dic146—82no—
190C2×D292—21no—
191C2×D292—22no—
192C2×D292C2×Q814yes—
193C2×D292C2412yes—
194C2×C22⋊D73—28no—
195C2×C22⋊D73—24no—
196D4×D73—216no—
197D4×D73—28no—
198D4×D73C2×Q8116yescomplemented
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—24no—
203C22×Dic73—82no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—24no—
208C2×C4×D73—24no—
209C2×C4×D73—24no—
210C2×C4×D73—82no—
211C2×C4×D73—82no—
212C2×C4×D73—82no—
213C2×C4×D73C2×D412yes—
214C2×C4×D73C2×Q814yes—
215C2×C4×D73#4114yes—
216C2×C4×D73C2412yes—
217#11924011—28no—
218C2×#10596831—22no—
219C2×#10596831—22no—
220C2×#10596831C2412yes—
221C2×#10596831C2412yes—
222C8×D73—28no—
223C4⋊Dic73—21no—
224C4⋊Dic73—24no—
225C4⋊Dic73—21no—
226C4⋊Dic73—21no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2412yes—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007C2×D414yes—
235#11924007C2×D414yes—
236C22⋊Dic73—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005C2×D414yes—
242#11924005C2×D414yes—
243C4×Dic73—24no—
244C4×Dic73—24no—
245C4×Dic73C2×D412yes—
246C4×Dic73C2412yes—
247C24×C73—21no—
248C2×D4×C73—21no—
249C2×D4×C73—22no—
250C2×D4×C73C2×Q814yes—
251C2×D4×C73C2412yes—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—24no—
256C22×C4×C73—82no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2411yescharacteristic
260C2×C8×C73—22no—
261C2×C8×C73—22no—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—24no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73C2412yes—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C22⋊C4×C73—24no—
273C42×C73C2×D412yes—
274C42×C73C2412yes—
275C23×C73—24no—
276C23×C73—22no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73C22×D411yescharacteristic
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—24no—
283C22×D73—22no—
284C22×D73—216no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—816no—
288C22×D73—84no—
289C22×D73—84no—
290C22×D73C22⋊Q814yes—
291C22×D73C22×D412yes—
292D4×C73—24no—
293D4×C73—22no—
294D4×C73C22×Q814yes—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73—84no—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C22×Q812yes—
308C2×C4×C73C2×#4112yes—
309C2×C4×C73C2511yescharacteristic
310C22⋊D73—216no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—84no—
320C2×Dic73C22⋊Q814yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324D292—24no—
325D292—22no—
326D292C22×Q814yes—
327C4×D73—84no—
328C4×D73—84no—
329C4×D73—84no—
330C4×D73C22⋊Q818yes—
331C4×D73C22×Q814yes—
332C4×D73C2×#4114yes—
333Dic146—84no—
334Dic146—84no—
335C8×C73—22no—
336C8×C73—22no—
337#10596831—22no—
338#10596831—22no—
339C22×C73—24no—
340C22×C73—48no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73C2×C22⋊Q812yes—
344C22×C73#57612yes—
345C22×C73#57712yes—
346C22×C73C23×D411yescharacteristic
347C2×D73—28no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—24no—
351C2×D73—48no—
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—816no—
355C2×D73C2×C22⋊Q814yes—
356C4×C73—22no—
357C4×C73—22no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73C2×C22⋊Q812yes—
362C4×C73C23×Q811yescharacteristic
363C4×C73C22×#4111yescharacteristic
364Dic73—22no—
365Dic73—22no—
366Dic73—42no—
367Dic73—42no—
368Dic73—42no—
369Dic73C2×C22⋊Q814yes—
370C2×#3081—731nomaximal, Sylow
371C2×C73—44no—
372C2×C73#308114yescomplemented
373C2×C73C22×C22⋊Q811yescharacteristic
374C2×C73C2×#57611yescharacteristic
375C2×C73C2×#57711yescharacteristic
376D73—24no—
377D73—44no—
378C2×#544—731no—
379C2×#518—731no—
380#3081—7316no—
381C2×#478—731no—
382C2×#478—731no—
383C2×#478—731no—
384C2×#478D7311yescharacteristic, complemented
385C2×#476—731no—
386C2×#476—731no—
387C2×#474—731no—
388C2×#474—731no—
389C2×#428—731no—
390C2×#427—731no—
391C2×#424—731no—
392C2×#418—731no—
393C22×#102—731no—
394C73C2×#308111yescharacteristic, complemented, Sylow
395C23×D4—731no—
396C22×M16—731no—
397C23×C8—731no—
398#544—738no—
399#544—1464no—
400C2×C4⋊Q8—731no—
401C2×C4⋊Q8—731no—
402C2×C4⋊Q8—1461no—
403C2×#125—731no—
404C2×#125—1461no—
405C2×#125C2×D7311yescharacteristic, complemented
406C2×C22⋊Q8—1461no—
407C2×C22⋊Q8—1461no—
408#518—738no—
409#518—1464no—
410C2×C4×D4—731no—
411C2×C4×D4—731no—
412C2×C4×D4—731no—
413C2×C4×D4—1461no—
414C2×C4×D4—1461no—
415C2×C4×D4C2×D7311yescharacteristic
416C2×#117—731no—
417C2×#117—731no—
418C2×#117—731no—
419C22×C4⋊C4—731no—
420C22×C22⋊C4—1461no—
421C22×C22⋊C4—1461no—
422#478—738no—
423#478—738no—
424#478—738no—
425#478C2×D7318yescomplemented
426#476—738no—
427#476—738no—
428#474—738no—
429#474—738no—
430#428—738no—
431#427—738no—
432C2×#107—731no—
433C2×#107—731no—
434C2×#107—731no—
435C2×#107C2×D7311yescharacteristic, complemented
436C2×#106—731no—
437C2×#106—731no—
438C2×#106—731no—
439C2×#106C2×D7311yescharacteristic, complemented
440#424—738no—
441C2×C4⋊C8—731no—
442C2×C4⋊C8—731no—
443C2×C4⋊C8—731no—
444C2×C4⋊C8C2×D7311yescharacteristic, complemented
445#418—738no—
446C2×#102—731no—
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102—738no—
453C2×#102C2×D7311yescharacteristic
454C2×#102C2×D7311yescharacteristic
455C25—1461no—
456C22×Q8—1461no—
457C22×Q8—1461no—
458C22×D4—738no—
459C22×D4—734no—
460C22×D4—731no—
461C22×D4—1462no—
462C22×D4—1464no—
463C22×D4—1461no—
464C22×D4C22×D7311yescharacteristic
465C23×C4—21no—
466C23×C4—731no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4—1461no—
470C23×C4—1461no—
471C2×M16—734no—
472C2×M16—1464no—
473C22×C8—731no—
474C22×C8—731no—
475C22×C8—734no—
476C22×C8—1464no—
477C22×C8C22×D7311yescharacteristic
478C22×C8C22×D7311yescharacteristic
479C4⋊Q8—734no—
480C4⋊Q8—734no—
481C4⋊Q8—1462no—
482C4⋊Q8—1468no—
483C4⋊Q8—1462no—
484#125—22no—
485#125—734no—
486#125—1462no—
487#125—1468no—
488#125C22×D7314yescomplemented
489C22⋊Q8—1468no—
490C22⋊Q8—1468no—
491C4×D4—22no—
492C4×D4—734no—
493C4×D4—734no—
494C4×D4—734no—
495C4×D4—1462no—
496C4×D4—1462no—
497C4×D4—1468no—
498C4×D4—1468no—
499C4×D4—1462no—
500C4×D4C22×D7314yes—
501#117—734no—
502#117—734no—
503#117—734no—
504#117—734no—
505#117—1462no—
506#117—1462no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—734no—
515C2×C4⋊C4—1462no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4C22×D7311yescharacteristic
522C2×C4⋊C4C22×D7311yescharacteristic
523C2×C4⋊C4C22×D7311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—1468no—
528C2×C22⋊C4—1468no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C42—731no—
535C2×C42—1461no—
536C2×C42—1461no—
537C2×C42C22×D7311yescharacteristic
538#107—734no—
539#107—734no—
540#107—734no—
541#107C22×D7314yescomplemented
542#106—734no—
543#106—734no—
544#106—734no—
545#106C22×D7314yescomplemented
546C4⋊C8—734no—
547C4⋊C8—734no—
548C4⋊C8—734no—
549C4⋊C8C22×D7314yescomplemented
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102—734no—
555#102—734no—
556#102C22×D7314yes—
557#102C22×D7314yes—
558C24—21no—
559C24—5842no—
560C24—5842no—
561C24—731no—
562C24—1464no—
563C24—1468no—
564C24—1461no—
565C2×Q8—5842no—
566C2×Q8—5842no—
567C2×Q8—1464no—
568C2×Q8—1464no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—7316no—
572C2×D4—734no—
573C2×D4—732no—
574C2×D4—1468no—
575C2×D4—14616no—
576C2×D4—1464no—
577C2×D4—1468no—
578C2×D4—1461no—
579C2×D4—1462no—
580C2×D4Q8×D7314yes—
581C2×D4C23×D7312yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—5842no—
588C22×C4—5842no—
589C22×C4—5842no—
590C22×C4—5842no—
591C22×C4—731no—
592C22×C4—732no—
593C22×C4—734no—
594C22×C4—734no—
595C22×C4—732no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—1464no—
599C22×C4—1464no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1464no—
604C22×C4—1464no—
605C22×C4D4×D7311yescharacteristic
606C22×C4D4×D7311yescharacteristic
607C22×C4C23×D7311yescharacteristic
608M16—1468no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—732no—
612C2×C8—732no—
613C2×C8—1468no—
614C2×C8—1462no—
615C2×C8—1462no—
616C2×C8C23×D7312yes—
617C2×C8C23×D7312yes—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—734no—
624C4⋊C4—734no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—732no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1461no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C4⋊C4—1464no—
636C4⋊C4C23×D7312yes—
637C4⋊C4C23×D7312yes—
638C4⋊C4C23×D7312yes—
639C22⋊C4—24no—
640C22⋊C4—734no—
641C22⋊C4—734no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C42—732no—
648C42—732no—
649C42—1464no—
650C42—1464no—
651C42D4×D7312yes—
652C42C23×D7312yes—
653C23—22no—
654C23—24no—
655C23—42no—
656C23—42no—
657C23—2922no—
658C23—2922no—
659C23—58416no—
660C23—5844no—
661C23—5844no—
662C23—732no—
663C23—734no—
664C23—14616no—
665C23—1462no—
666C23—1464no—
667C23—1462no—
668C23—1462no—
669C23C2×D4×D7311yescharacteristic
670Q8—5844no—
671Q8—5844no—
672D4—22no—
673D4—24no—
674D4—734no—
675D4—14616no—
676D4—1462no—
677D4—1464no—
678D4C2×Q8×D7314yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—2922no—
689C2×C4—2922no—
690C2×C4—2922no—
691C2×C4—5844no—
692C2×C4—5844no—
693C2×C4—5844no—
694C2×C4—5844no—
695C2×C4—732no—
696C2×C4—734no—
697C2×C4—734no—
698C2×C4—734no—
699C2×C4—738no—
700C2×C4—732no—
701C2×C4—732no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4C2×D4×D7312yes—
708C2×C4C2×D4×D7312yes—
709C2×C4C2×D4×D7311yescharacteristic
710C2×C4C2×Q8×D7312yes—
711C2×C4#41×D7312yes—
712C2×C4C24×D7311yescharacteristic
713C8—22no—
714C8—22no—
715C8—1462no—
716C8—1462no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—2928no—
722C22—2922no—
723C22—2922no—
724C22—58416no—
725C22—734no—
726C22—1464no—
727C22—1468no—
728C22—1462no—
729C22—1462no—
730C22C22⋊Q8×D7312yes—
731C22#1798938912yes—
732C22#1798939712yes—
733C22C22×D4×D7311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—2922no—
740C4—2922no—
741C4—2922no—
742C4—734no—
743C4—1462no—
744C4—1462no—
745C4C22⋊Q8×D7312yes—
746C4C22×Q8×D7311yescharacteristic
747C4C2×#41×D7311yescharacteristic
748C2—44no—
749C2—2924no—
750C2—1464no—
751C2#2261975914yesdirect product factor
752C2C2×C22⋊Q8×D7311yescharacteristic
753C2C2×#1798938911yescharacteristic
754C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#478×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×D73C22
hypercenterC2×#478D73
hypocenterC73C2×#3081
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#17989217C2semidirect
3. #22619759C2direct (N × H)
4. C2×#17988890C2semidirect
5. C2×#17988885C2semidirect
6. C2×#17988884C2semidirect
7. C2×#17988877C2semidirect
8. C2×#17988876C2semidirect
9. C2×#17988868C2semidirect
10. C2×#17988865C2semidirect
11. C2×#17988626C2semidirect
12. C2×#17988624C2semidirect
13. C2×#17988612C2semidirect
16. C2×#478×C73C2semidirect
21. #17989217C22semidirect
22. C2×#14556591C22semidirect
24. C2×#14556590C22semidirect
25. C2×#14556582C22semidirect
42. #17988890C22semidirect
43. #17988885C22semidirect
44. #17988884C22semidirect
45. #17988877C22semidirect
46. #17988876C22semidirect
47. #17988868C22semidirect
48. #17988865C22semidirect
49. #17988626C22semidirect
50. #17988624C22semidirect
51. C2×#14556525C22semidirect
52. C2×#14556525C22semidirect
53. C2×#14556524C22semidirect
54. C2×#14556522C22semidirect
55. C2×#14556522C22semidirect
56. C2×#14556522C22semidirect
57. #17988612C22semidirect
58. C2×C4⋊#10596831C22semidirect
59. C2×#14556520C22semidirect
60. C2×#14556520C22semidirect
69. C2×#125×C73C22semidirect
71. #478×C73C22semidirect
72. C2×#107×C73C22semidirect
73. C2×#106×C73C22semidirect
74. C2×C4⋊C8×C73C22semidirect
84. C2×D4×D73Q8semidirect
98. #14556591C23semidirect
101. #14556590C23semidirect
103. #14556582C23semidirect
145. #14556525C23semidirect
146. #14556525C23semidirect
147. #14556524C23semidirect
148. #14556522C23semidirect
149. #14556522C23semidirect
150. #14556522C23semidirect
151. C4⋊#10596831C23semidirect
152. #14556520C23semidirect
153. #14556520C23semidirect
165. #125×C73C23semidirect
175. #107×C73C23semidirect
176. #106×C73C23semidirect
177. C4⋊C8×C73C23semidirect
198. D4×D73C2×Q8semidirect
372. C2×C73#3081semidirect
384. C2×#478D73semidirect
394. C73C2×#3081semidirect
405. C2×#125C2×D73semidirect
425. #478C2×D73semidirect
435. C2×#107C2×D73semidirect
439. C2×#106C2×D73semidirect
444. C2×C4⋊C8C2×D73semidirect
488. #125C22×D73semidirect
541. #107C22×D73semidirect
545. #106C22×D73semidirect
549. C4⋊C8C22×D73semidirect
751. C2#22619759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892172
C2×#179890592
#226197592
C2×#179888902
C2×#179888852
C2×#179888842
C2×#179888772
C2×#179888762
C2×#179888682
C2×#179888652
C2×#179886262
C2×#179886242
C2×#179886122
C2×#179885902
C2×#102×D732
C2×#478×C732
C2×#308173