Finite Group Databasebeta

← C2×#22622661 #33965684

Subgroups — C2×#22622661 #33965684

Order 18688.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989313C211yesmaximal, characteristic, complemented
2C2×#17989258C211yesmaximal, characteristic
3#22622661C2116yesmaximal, direct product factor
4C2×#17988952C211yesmaximal, characteristic, complemented
5C2×#17988950C211yesmaximal, characteristic, complemented
6C2×#17988932C211yesmaximal, characteristic, complemented
7C2×#17988890C211yesmaximal, characteristic, complemented
8C2×#17988887C211yesmaximal, characteristic, complemented
9C2×#17988866C211yesmaximal, characteristic, complemented
10C2×#17988787C211yesmaximal, characteristic, complemented
11C2×#17988785C211yesmaximal, characteristic, complemented
12C2×#17988785C211yesmaximal, characteristic, complemented
13C2×#17988715C211yesmaximal, characteristic, complemented
14C2×#17988690C211yesmaximal, characteristic, complemented
15C2×#17988672C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×#11924015C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20#17989313—24no—
21#17989313C2218yescomplemented
22#17989258—24no—
23#17989258C2218yes—
24C2×#14556590—21no—
25C2×#14556590C2211yescharacteristic
26C2×#14556588C2211yescharacteristic
27C2×#14556587C2211yescharacteristic
28C2×#14556587C2211yescharacteristic
29C2×#14556583—21no—
30C2×#14556583C2211yescharacteristic
31C2×#14556582—21no—
32C2×#14556582C2211yescharacteristic
33C2×#14556565—21no—
34C2×#14556564—21no—
35C2×#14556564—21no—
36C2×Q8×Dic73C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×C4×Dic146—21no—
39C2×C4×Dic146C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×#14556553C2211yescharacteristic
42#17988952C2218yescomplemented
43#17988950C2218yescomplemented
44#17988932C2218yescomplemented
45#17988890C2218yescomplemented
46#17988887C2218yescomplemented
47#17988866C2218yescomplemented
48#17988787C2218yescomplemented
49#17988785C2218yescomplemented
50#17988785C2218yescomplemented
51#17988715C2218yescomplemented
52#17988690C2218yescomplemented
53#17988672C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556513C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C22×D292—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73—21no—
88C22×C22⋊D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C2×#11924015—24no—
92C2×#11924015—24no—
93C2×#11924015C2314yes—
94C2×#11924015C2314yes—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97#14556590—28no—
98#14556590—22no—
99#14556590C2314yes—
100#14556588—22no—
101#14556588C2314yes—
102#14556587—22no—
103#14556587—22no—
104#14556587C2314yes—
105#14556587C2314yes—
106#14556583—28no—
107#14556583—22no—
108#14556583C2314yes—
109#14556582—28no—
110#14556582—22no—
111#14556582C2314yes—
112#14556565—28no—
113#14556564—28no—
114#14556564—28no—
115Q8×Dic73—22no—
116Q8×Dic73—22no—
117Q8×Dic73C2314yes—
118Q8×Dic73C2314yes—
119C4×Dic146—28no—
120C4×Dic146D414yes—
121C4×Dic146C2314yes—
122#14556553—22no—
123#14556553—22no—
124#14556553C2314yes—
125#14556553C2314yes—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73D411yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007D411yescharacteristic
137C2×#11924007D411yescharacteristic
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73C2311yescharacteristic
143C2×C4×Dic73C2311yescharacteristic
144#14556524C2314yes—
145#14556522C2314yes—
146C4⋊#10596831C2314yes—
147#14556520C2314yes—
148#14556520C2314yes—
149#14556513C2314yes—
150#14556513C2314yes—
151#14556513C2314yes—
152#14556513C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155#14556511C2314yes—
156#14556511C2314yes—
157#14556501C2314yes—
158C8×Dic73C2314yes—
159C22×Q8×C73C2311yescharacteristic
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C2×SD16×C73—24no—
163C2×SD16×C73C2314yes—
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166C4×Q8×C73—22no—
167C4×Q8×C73C2314yes—
168C4×D4×C73—22no—
169C4×D4×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C22⋊C4×C73—21no—
174C2×C42×C73—21no—
175C2×C42×C73C2311yescharacteristic
176#107×C73C2314yes—
177#103×C73C2314yes—
178#102×C73C2314yes—
179#97×C73C2314yes—
180C23×D73—21no—
181C23×D73—21no—
182#11924028—432no—
183C2×Dic146—24no—
184C2×Dic146—24no—
185C2×Dic146—44no—
186C2×Dic146C2×D414yes—
187C2×D292—22no—
188C2×D292—22no—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—21no—
192C2×D292—21no—
193C2×D292—24no—
194C2×D292—24no—
195C2×D292—44no—
196C2×D292—82no—
197C2×D292C2412yes—
198C2×D292C2412yes—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—44no—
204C2×C22⋊D73—44no—
205C2×C22⋊D73—82no—
206C2×C22⋊D73—82no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C22×Dic73C2×D411yescharacteristic
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—44no—
216C2×C4×D73—44no—
217#11924015—28no—
218#11924015—28no—
219C2×#10596831—22no—
220C2×#10596831—22no—
221C2×#10596831C2412yes—
222C2×#10596831C2412yes—
223C4⋊Dic73—21no—
224C4⋊Dic73—21no—
225C4⋊Dic73—24no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2×D414yes—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007C2×D414yes—
236#11924007C2×D414yes—
237#11924005—24no—
238#11924005—24no—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73C2×D412yes—
242C4×Dic73C2×D412yes—
243C4×Dic73C2412yes—
244C4×Dic73C2412yes—
245C24×C73—21no—
246C2×Q8×C73—21no—
247C2×Q8×C73—22no—
248C2×Q8×C73#4114yescomplemented
249C2×Q8×C73C2412yes—
250C2×D4×C73—21no—
251C2×D4×C73—22no—
252C2×D4×C73—22no—
253C2×D4×C73C2412yes—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—24no—
258C22×C4×C73—44no—
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2411yescharacteristic
262SD16×C73—28no—
263C2×C8×C73—22no—
264C2×C8×C73—22no—
265C2×C8×C73C2412yes—
266C2×C8×C73C2412yes—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C22⋊C4×C73—24no—
273C42×C73—24no—
274C42×C73C2×D412yes—
275C42×C73C2412yes—
276C23×C73—22no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—42no—
284C22×D73—42no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73—42no—
289Q8×C73—24no—
290Q8×C73—22no—
291Q8×C73C2×#4114yescomplemented
292D4×C73—22no—
293D4×C73—22no—
294D4×C73—42no—
295C2×C4×C73—24no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—48no—
302C2×C4×C73—42no—
303C2×C4×C73—42no—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C2×#4112yes—
308C2×C4×C732−1+412yes—
309C2×C4×C73C2511yescharacteristic
310C22⋊D73—48no—
311C22⋊D73—48no—
312C22⋊D73—84no—
313C22⋊D73—84no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73AGL(1,ℤ/8)14yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C2×Dic73C22×D412yes—
325C2×Dic73C22×D412yes—
326D292—22no—
327D292—22no—
328D292—22no—
329D292—22no—
330D292—48no—
331D292—42no—
332D292—42no—
333D292—84no—
334C4×D73—48no—
335C4×D73—48no—
336Dic146—28no—
337Dic146—48no—
338C8×C73—22no—
339C8×C73—22no—
340#10596831—22no—
341#10596831—22no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—84no—
346C22×C73#54812yes—
347C22×C73C2×AGL(1,ℤ/8)12yes—
348C22×C73#57712yes—
349C22×C73C23×D411yescharacteristic
350C2×D73—42no—
351C2×D73—42no—
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—84no—
357C2×D73—84no—
358C4×C73—24no—
359C4×C73—22no—
360C4×C73—22no—
361C4×C73—42no—
362C4×C73—42no—
363C4×C73#54812yes—
364C4×C73C22×#4111yescharacteristic
365C4×C73C2×2−1+411yescharacteristic
366Dic73—22no—
367Dic73—22no—
368Dic73—22no—
369Dic73—42no—
370Dic73—42no—
371Dic73C2×AGL(1,ℤ/8)14yes—
372C2×#3368—731nomaximal, Sylow
373C2×C73—82no—
374C2×C73#336814yescomplemented
375C2×C73C2×#54811yescharacteristic
376C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
377C2×C73C2×#57711yescharacteristic
378D73—82no—
379D73—82no—
380C2×#557—731no—
381C2×#550—731no—
382#3368—7316no—
383C2×#490—731no—
384C2×#490—731no—
385C2×#486—731no—
386C2×#478—731no—
387C2×#478—731no—
388C2×#474—731no—
389C2×#460—731no—
390C2×#460—731no—
391C2×#460—731no—
392C2×#446—731no—
393C2×#440—731no—
394C2×#440D7311yescharacteristic, complemented
395C2×C4×SD16—731no—
396C73C2×#336811yescharacteristic, complemented, Sylow
397C22×#41—1461no—
398C22×SD16—731no—
399C22×SD16—731no—
400C22×SD16C2×D7311yescharacteristic
401#557—738no—
402#557—1464no—
403#550—738no—
404#550—1464no—
405C2×C4⋊Q8—731no—
406C2×C4⋊Q8—1461no—
407C2×#127—731no—
408C2×#127—731no—
409C2×#127—731no—
410C2×#125—731no—
411C2×#125—731no—
412C2×#125—1461no—
413C2×#125—1461no—
414C2×#121—1461no—
415C2×#121—1461no—
416C2×#121—1461no—
417C2×C4×Q8—731no—
418C2×C4×Q8—731no—
419C2×C4×Q8—731no—
420C2×C4×Q8—1461no—
421C2×C4×Q8C2×D7311yescharacteristic
422C2×C4×D4—731no—
423C2×C4×D4—731no—
424C2×C4×D4C2×D7311yescharacteristic
425#490—738no—
426#490—738no—
427#486—738no—
428#478—738no—
429#478—738no—
430#474—738no—
431#460—738no—
432#460—738no—
433#460—738no—
434#446—738no—
435#440—738no—
436#440C2×D7318yescomplemented
437C4×SD16—738no—
438C2×#107—731no—
439C2×#107C2×D7311yescharacteristic
440C2×#106—731no—
441C2×C4⋊C8—731no—
442C2×C4⋊C8—731no—
443C2×C4⋊C8—731no—
444C2×#103C2×D7311yescharacteristic
445C2×#102—731no—
446C2×#102—731no—
447C2×#102—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102—731no—
453C2×#102C2×D7311yescharacteristic
454C2×#97—731no—
455C2×#97C2×D7311yescharacteristic
456C2×C4×C8—731no—
457C2×#41—2928no—
458C2×#41—1468no—
459C22×Q8—731no—
460C22×Q8—1461no—
461C22×Q8C22×D7311yescharacteristic
462C22×D4—731no—
463C22×D4—731no—
464C22×D4—1461no—
465C22×D4—1461no—
466C22×D4—1461no—
467C22×D4—1461no—
468C22×D4—1461no—
469C22×D4—1461no—
470C22×D4C22×D7311yescharacteristic
471C23×C4—21no—
472C23×C4—1461no—
473C23×C4—1461no—
474C2×SD16—24no—
475C2×SD16—734no—
476C2×SD16—734no—
477C2×SD16—1464no—
478C2×SD16—1464no—
479C2×SD16C22×D7314yes—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8C22×D7311yescharacteristic
483C22×C8C22×D7311yescharacteristic
484C4⋊Q8—734no—
485C4⋊Q8—1462no—
486C4⋊Q8—1468no—
487#127—734no—
488#127—734no—
489#127—734no—
490#127—1462no—
491#127—1462no—
492#127—1462no—
493#125—734no—
494#125—734no—
495#125—1468no—
496#125—1462no—
497#125—1468no—
498#125—1462no—
499#121—1468no—
500#121—1468no—
501#121—1468no—
502C4×Q8—22no—
503C4×Q8—734no—
504C4×Q8—734no—
505C4×Q8—734no—
506C4×Q8—734no—
507C4×Q8—1468no—
508C4×Q8—1462no—
509C4×Q8—1462no—
510C4×Q8C22×D7314yes—
511C4×D4—22no—
512C4×D4—734no—
513C4×D4—734no—
514C4×D4—1462no—
515C4×D4—1462no—
516C4×D4C22×D7314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4C22×D7311yescharacteristic
531C2×C4⋊C4C22×D7311yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C42—21no—
536C2×C42—731no—
537C2×C42—731no—
538C2×C42—1461no—
539C2×C42—1461no—
540C2×C42C22×D7311yescharacteristic
541#107—734no—
542#107C22×D7314yes—
543#106—734no—
544C4⋊C8—734no—
545C4⋊C8—734no—
546C4⋊C8—734no—
547#103C22×D7314yes—
548#102—734no—
549#102—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102—734no—
555#102—734no—
556#102C22×D7314yes—
557#97—734no—
558#97C22×D7314yes—
559C4×C8—734no—
560C24—21no—
561C24—1461no—
562C24—1461no—
563#41—29232no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—2924no—
567C2×Q8—734no—
568C2×Q8—1464no—
569C2×Q8—1464no—
570C2×Q8#1192402814yescomplemented
571C2×Q8C23×D7312yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—2924no—
576C2×D4—2924no—
577C2×D4—2924no—
578C2×D4—5842no—
579C2×D4—5842no—
580C2×D4—5842no—
581C2×D4—732no—
582C2×D4—732no—
583C2×D4—1464no—
584C2×D4—1464no—
585C2×D4—1464no—
586C2×D4—1464no—
587C2×D4—1461no—
588C2×D4—1461no—
589C2×D4—1464no—
590C2×D4—1464no—
591C2×D4—1462no—
592C2×D4—1462no—
593C2×D4—1462no—
594C2×D4—1462no—
595C2×D4C23×D7312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—2924no—
602C22×C4—2924no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—1464no—
608C22×C4—1464no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4D4×D7311yescharacteristic
612C22×C4D4×D7311yescharacteristic
613C22×C4C23×D7311yescharacteristic
614SD16—28no—
615SD16—1468no—
616SD16—1468no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—732no—
620C2×C8—732no—
621C2×C8—1462no—
622C2×C8—1462no—
623C2×C8C23×D7312yes—
624C2×C8C23×D7312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—734no—
629C4⋊C4—734no—
630C4⋊C4—734no—
631C4⋊C4—732no—
632C4⋊C4—732no—
633C4⋊C4—1464no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4—1464no—
637C4⋊C4—1464no—
638C4⋊C4—1464no—
639C4⋊C4—1464no—
640C4⋊C4—1461no—
641C4⋊C4—1461no—
642C4⋊C4C23×D7312yes—
643C4⋊C4C23×D7312yes—
644C22⋊C4—24no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C42—24no—
648C42—732no—
649C42—732no—
650C42—732no—
651C42—732no—
652C42—1464no—
653C42—1464no—
654C42D4×D7312yes—
655C42C23×D7312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—2922no—
661C23—2922no—
662C23—2922no—
663C23—2922no—
664C23—2922no—
665C23—2922no—
666C23—1462no—
667C23—1462no—
668C23C2×D4×D7311yescharacteristic
669Q8—22no—
670Q8—24no—
671Q8—2928no—
672Q8—1468no—
673Q8C2×#1192402814yescomplemented
674D4—22no—
675D4—22no—
676D4—42no—
677D4—2928no—
678D4—2928no—
679D4—2928no—
680D4—2922no—
681D4—2922no—
682D4—5844no—
683D4—5844no—
684D4—5844no—
685D4—1462no—
686D4—1462no—
687D4—1462no—
688D4—1462no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—2928no—
699C2×C4—2928no—
700C2×C4—2922no—
701C2×C4—2922no—
702C2×C4—732no—
703C2×C4—734no—
704C2×C4—732no—
705C2×C4—732no—
706C2×C4—732no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4C2×D4×D7312yes—
713C2×C4C2×D4×D7312yes—
714C2×C4C2×D4×D7311yescharacteristic
715C2×C4C2×#1192402812yes—
716C2×C4#1455663812yes—
717C2×C4C24×D7311yescharacteristic
718C8—22no—
719C8—22no—
720C8—1462no—
721C8—1462no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2922no—
727C22—2922no—
728C22—2922no—
729C22—2922no—
730C22—2922no—
731C22—2922no—
732C22—5844no—
733C22—5844no—
734C22#1798924612yes—
735C22AGL(1,ℤ/8)×D7312yes—
736C22#1798939612yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—2922no—
744C4—2922no—
745C4—734no—
746C4—1462no—
747C4—1462no—
748C4—1462no—
749C4#1798924612yes—
750C4C22×#1192402811yescharacteristic
751C4C2×#1455663811yescharacteristic
752C2—82no—
753C2—5842no—
754C2—5842no—
755C2#2262266114yesdirect product factor
756C2C2×#1798924611yescharacteristic
757C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
758C2C2×#1798939611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989258C2
hypercenterC2×#440D73
hypocenterC73C2×#3368
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#17989313C2semidirect
3. #22622661C2direct (N × H)
4. C2×#17988952C2semidirect
5. C2×#17988950C2semidirect
6. C2×#17988932C2semidirect
7. C2×#17988890C2semidirect
8. C2×#17988887C2semidirect
9. C2×#17988866C2semidirect
10. C2×#17988787C2semidirect
11. C2×#17988785C2semidirect
12. C2×#17988785C2semidirect
13. C2×#17988715C2semidirect
14. C2×#17988690C2semidirect
15. C2×#17988672C2semidirect
16. C2×#440×C73C2semidirect
21. #17989313C22semidirect
42. #17988952C22semidirect
43. #17988950C22semidirect
44. #17988932C22semidirect
45. #17988890C22semidirect
46. #17988887C22semidirect
47. #17988866C22semidirect
48. #17988787C22semidirect
49. #17988785C22semidirect
50. #17988785C22semidirect
51. #17988715C22semidirect
52. #17988690C22semidirect
53. #17988672C22semidirect
72. #440×C73C22semidirect
248. C2×Q8×C73#41semidirect
291. Q8×C73C2×#41semidirect
374. C2×C73#3368semidirect
394. C2×#440D73semidirect
396. C73C2×#3368semidirect
436. #440C2×D73semidirect
570. C2×Q8#11924028semidirect
673. Q8C2×#11924028semidirect
755. C2#22622661direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893132
C2×#179892582
#226226612
C2×#179889522
C2×#179889502
C2×#179889322
C2×#179888902
C2×#179888872
C2×#179888662
C2×#179887872
C2×#179887852
C2×#179887152
C2×#179886902
C2×#179886722
C2×#440×C732
C2×#336873