Finite Group Databasebeta

← C2×#22622348 #33964473

Subgroups — C2×#22622348 #33964473

Order 18688.

1982 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×#17989301C211yesmaximal, characteristic, complemented
2C2×#17989300C211yesmaximal, characteristic, complemented
3#22622348C2116yesmaximal, direct product factor
4C2×#17988991C211yesmaximal, characteristic, complemented
5C2×#17988914C211yesmaximal, characteristic, complemented
6C2×#17988912C211yesmaximal, characteristic, complemented
7C2×#17988909C211yesmaximal, characteristic, complemented
8C2×#17988876C211yesmaximal, characteristic, complemented
9C2×#17988875C211yesmaximal, characteristic, complemented
10C2×#17988822C211yesmaximal, characteristic, complemented
11C2×#17988821C211yesmaximal, characteristic, complemented
12C2×#17988667C211yesmaximal, characteristic, complemented
13C2×#17988650C211yesmaximal, characteristic, complemented
14C2×#17988623C211yesmaximal, characteristic, complemented
15C2×#17988622C211yesmaximal, characteristic, complemented
16C2×#482×C73C211yesmaximal, characteristic, complemented
17C22×#11924013C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#17989301—24no—
21#17989301C2218yescomplemented
22#17989300—24no—
23#17989300C2218yescomplemented
24C2×#14556590C2211yescharacteristic
25C2×#14556590C2211yescharacteristic
26C2×#14556579—21no—
27C2×#14556578—21no—
28C2×#14556577—21no—
29C2×#14556577—21no—
30C2×#14556566C2211yescharacteristic
31C2×#14556565C2211yescharacteristic
32C2×#14556564—21no—
33C2×#14556563—21no—
34C2×#14556562C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×C4×C22⋊D73C2211yescharacteristic
38C2×#14556550C2211yescharacteristic
39C2×#14556549C2211yescharacteristic
40C2×#14556549C2211yescharacteristic
41C2×#14556548—21no—
42C2×#14556547—21no—
43#17988991C2218yescomplemented
44#17988914C2218yescomplemented
45#17988912C2218yescomplemented
46#17988909C2218yescomplemented
47#17988876C2218yescomplemented
48#17988875C2218yescomplemented
49#17988822C2218yescomplemented
50#17988821C2218yescomplemented
51#17988667C2218yescomplemented
52#17988650C2218yescomplemented
53#17988623C2218yescomplemented
54#17988622C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556522C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×#121×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71#482×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×D292—21no—
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C22×C22⋊D73—21no—
83C22×C22⋊D73D411yescharacteristic
84C23×Dic73—21no—
85C22×C4×D73—21no—
86C22×C4×D73C2311yescharacteristic
87C2×#11924013—24no—
88C2×#11924013C2314yes—
89C22×#10596831—24no—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2314yes—
92C22×#10596831C2311yescharacteristic
93C2×C8×D73—24no—
94C2×C8×D73C2314yes—
95#14556590—22no—
96#14556590—22no—
97#14556590C2314yes—
98#14556590C2314yes—
99#14556579—28no—
100#14556578—28no—
101#14556577—28no—
102#14556577—28no—
103#14556566—22no—
104#14556566C2314yes—
105#14556565—22no—
106#14556565C2314yes—
107#14556564—28no—
108#14556563—28no—
109#14556562—22no—
110#14556562C2314yes—
111D4×Dic73—22no—
112D4×Dic73C2314yes—
113#14556553—22no—
114#14556553C2314yes—
115C4×C22⋊D73D414yes—
116C4×C22⋊D73C2314yes—
117#14556550—22no—
118#14556550C2314yes—
119#14556549—22no—
120#14556549—22no—
121#14556549C2314yes—
122#14556549C2314yes—
123#14556548—28no—
124#14556547—28no—
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007D411yescharacteristic
131C2×C22⋊Dic73—21no—
132C2×C22⋊Dic73—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73D411yescharacteristic
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005D411yescharacteristic
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556524C2314yes—
147#14556524C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556513C2314yes—
154#14556513C2314yes—
155#14556512C2314yes—
156#14556511C2314yes—
157#14556503C2314yes—
158C8×Dic73C2314yes—
159C22×D4×C73—21no—
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164#121×C73—22no—
165#121×C73C2314yes—
166#117×C73—22no—
167#117×C73C2314yes—
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C42×C73—21no—
174#107×C73C2314yes—
175#106×C73C2314yes—
176#102×C73C2314yes—
177#102×C73C2314yes—
178C22⋊C8×C73C2314yes—
179C23×D73—21no—
180C23×D73C2×D411yescharacteristic
181C2×Dic146—24no—
182C2×Dic146—24no—
183C2×Dic146—82no—
184C2×Dic146—82no—
185C2×D292—22no—
186C2×D292—22no—
187C2×D292—21no—
188C2×D292—24no—
189C2×D292—82no—
190C2×D292C2412yes—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—82no—
195C2×C22⋊D73—82no—
196C2×C22⋊D73C2×D414yes—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—24no—
201C22×Dic73—44no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×C4×D73—22no—
206C2×C4×D73—22no—
207C2×C4×D73—24no—
208C2×C4×D73—44no—
209C2×C4×D73C2×D412yes—
210C2×C4×D73C2412yes—
211#11924013—28no—
212C2×#10596831—22no—
213C2×#10596831—28no—
214C2×#10596831#4114yes—
215C2×#10596831C2412yes—
216C2×#10596831C2412yes—
217C8×D73—28no—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223C4⋊Dic73C2412yes—
224#11924007—24no—
225#11924007—24no—
226#11924007C2×D414yes—
227C22⋊Dic73—24no—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73C2×D414yes—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005C2×D414yes—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73—24no—
240C4×Dic73C2×D412yes—
241C4×Dic73C2412yes—
242C24×C73—21no—
243C24×C73C2×D411yescharacteristic
244C2×D4×C73—24no—
245C2×D4×C73—21no—
246C2×D4×C73—22no—
247C2×D4×C73—22no—
248C2×D4×C73—82no—
249C2×D4×C73C2412yes—
250C22×C4×C73—22no—
251C22×C4×C73—22no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2×D412yes—
257C22×C4×C73C2412yes—
258C22×C4×C73C2411yescharacteristic
259C2×C8×C73—22no—
260C2×C8×C73—22no—
261C2×C8×C73C2412yes—
262C2×C8×C73C2412yes—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C42×C73—24no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—42no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73C22×D412yes—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73C22×D412yes—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—42no—
292D4×C73—84no—
293C2×C4×C73—22no—
294C2×C4×C73—24no—
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×C73C22×D412yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C2×#4112yes—
306C2×C4×C732−1+412yes—
307C2×C4×C73C2511yescharacteristic
308C22⋊D73—28no—
309C22⋊D73—84no—
310C22⋊D73—84no—
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—48no—
320C2×Dic73#13514yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324D292—22no—
325D292—22no—
326D292—42no—
327D292—84no—
328C4×D73—24no—
329C4×D73—22no—
330C4×D73—22no—
331C4×D73—48no—
332Dic146—84no—
333Dic146—84no—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831C2×#4114yes—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—44no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—84no—
346C22×C73#54712yes—
347C22×C73C2×#13512yes—
348C22×C73#57612yes—
349C22×C73C23×D411yescharacteristic
350C2×D73—22no—
351C2×D73—22no—
352C2×D73—22no—
353C2×D73—44no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—42no—
357C2×D73—84no—
358C4×C73—22no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73#54712yes—
363C4×C73C22×#4111yescharacteristic
364C4×C73C2×2−1+411yescharacteristic
365Dic73—22no—
366Dic73—22no—
367Dic73—42no—
368Dic73—42no—
369Dic73—42no—
370Dic73C2×#13514yes—
371C2×#3341—731nomaximal, Sylow
372C2×C73—42no—
373C2×C73—82no—
374C2×C73#334114yescomplemented
375C2×C73C2×#54711yescharacteristic
376C2×C73C22×#13511yescharacteristic
377C2×C73C2×#57611yescharacteristic
378D73—42no—
379D73—82no—
380C2×#555—731no—
381C2×#555—731no—
382#3341—7316no—
383C2×#500—731no—
384C2×#482—731no—
385C2×#482—731no—
386C2×#482—731no—
387C2×#482D7311yescharacteristic, complemented
388C2×#476—731no—
389C2×#476—731no—
390C2×#466—731no—
391C2×#466—731no—
392C2×C4×D8—731no—
393C2×C8×D4—731no—
394C2×#427—731no—
395C2×#427—731no—
396C73C2×#334111yescharacteristic, complemented, Sylow
397C22×D8—731no—
398C23×C8—731no—
399C23×C8—731no—
400#555—738no—
401#555—738no—
402#555—1464no—
403#555—1464no—
404C2×C4⋊Q8—731no—
405C2×C4⋊Q8—731no—
406C2×#124—1461no—
407C2×#124—1461no—
408C2×#124—1461no—
409C2×#124—1461no—
410C2×#121—731no—
411C2×#121—731no—
412C2×#121—731no—
413C2×#121—1461no—
414C2×#121—1461no—
415C2×#121C2×D7311yescharacteristic
416C2×C4×D4—731no—
417C2×C4×D4—731no—
418C2×C4×D4—731no—
419C2×#117—731no—
420C2×#117—731no—
421C2×#117—731no—
422C2×#117—1461no—
423C2×#117—1461no—
424C2×#117C2×D7311yescharacteristic
425#500—738no—
426#482—738no—
427#482—738no—
428#482—738no—
429#482C2×D7318yescomplemented
430#476—738no—
431#476—738no—
432#466—738no—
433#466—738no—
434C4×D8—738no—
435C8×D4—738no—
436#427—738no—
437#427—738no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#107—731no—
442C2×#107C2×D7311yescharacteristic
443C2×#106—731no—
444C2×#106—731no—
445C2×#106—731no—
446C2×#106C2×D7311yescharacteristic
447C2×C4⋊C8—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102C2×D7311yescharacteristic
453C2×#102C2×D7311yescharacteristic
454C2×C22⋊C8—731no—
455C2×C22⋊C8C2×D7311yescharacteristic
456C2×C4×C8—731no—
457C22×Q8—1461no—
458C22×Q8—1461no—
459C22×D4—21no—
460C22×D4—731no—
461C22×D4—731no—
462C22×D4—1461no—
463C22×D4—1461no—
464C22×D4—1461no—
465C22×D4C22×D7311yescharacteristic
466C23×C4—731no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4C22×D7311yescharacteristic
470C2×D8—734no—
471C2×D8—1464no—
472C22×C8—731no—
473C22×C8—731no—
474C22×C8—734no—
475C22×C8—734no—
476C22×C8—1464no—
477C22×C8—1464no—
478C22×C8C22×D7311yescharacteristic
479C22×C8C22×D7311yescharacteristic
480C4⋊Q8—734no—
481C4⋊Q8—734no—
482C4⋊Q8—1462no—
483C4⋊Q8—1462no—
484#124—1468no—
485#124—1468no—
486#124—1468no—
487#124—1468no—
488#121—22no—
489#121—734no—
490#121—734no—
491#121—734no—
492#121—1468no—
493#121—1462no—
494#121—1462no—
495#121—1468no—
496#121—1462no—
497#121C22×D7314yes—
498C4×D4—734no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1462no—
503C4×D4—1462no—
504#117—22no—
505#117—734no—
506#117—734no—
507#117—734no—
508#117—1468no—
509#117—1468no—
510#117—1462no—
511#117—1462no—
512#117—1462no—
513#117C22×D7314yes—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C4⋊C4C22×D7311yescharacteristic
522C2×C4⋊C4C22×D7311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C42—21no—
536C2×C42—731no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42—1461no—
540#107—734no—
541#107—734no—
542#107—734no—
543#107—734no—
544#107C22×D7314yes—
545#106—734no—
546#106—734no—
547#106—734no—
548#106C22×D7314yes—
549C4⋊C8—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102C22×D7314yes—
555#102C22×D7314yes—
556C22⋊C8—734no—
557C22⋊C8C22×D7314yes—
558C4×C8—734no—
559C24—21no—
560C24—731no—
561C24—1461no—
562C24D4×D7311yescharacteristic
563C2×Q8—5842no—
564C2×Q8—5842no—
565C2×Q8—1464no—
566C2×Q8—1464no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—82no—
572C2×D4—5842no—
573C2×D4—5842no—
574C2×D4—5842no—
575C2×D4—734no—
576C2×D4—732no—
577C2×D4—1464no—
578C2×D4—1464no—
579C2×D4—1464no—
580C2×D4—1464no—
581C2×D4—1461no—
582C2×D4—1462no—
583C2×D4—1462no—
584C2×D4C23×D7312yes—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—2924no—
591C22×C4—2924no—
592C22×C4—731no—
593C22×C4—731no—
594C22×C4—731no—
595C22×C4—732no—
596C22×C4—732no—
597C22×C4—1464no—
598C22×C4—1464no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4D4×D7312yes—
605C22×C4D4×D7311yescharacteristic
606C22×C4C23×D7312yes—
607C22×C4C23×D7311yescharacteristic
608D8—1468no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—734no—
612C2×C8—732no—
613C2×C8—732no—
614C2×C8—1468no—
615C2×C8—1468no—
616C2×C8—1462no—
617C2×C8C23×D7312yes—
618C2×C8C23×D7312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—734no—
623C4⋊C4—732no—
624C4⋊C4—732no—
625C4⋊C4—732no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1461no—
629C4⋊C4—1461no—
630C4⋊C4—1461no—
631C4⋊C4C23×D7312yes—
632C4⋊C4C23×D7312yes—
633C4⋊C4C23×D7312yes—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—734no—
637C22⋊C4—734no—
638C22⋊C4—1464no—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C42—24no—
647C42—732no—
648C42—732no—
649C42—1464no—
650C42—1464no—
651C42—1464no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—2922no—
660C23—2922no—
661C23—2922no—
662C23—732no—
663C23—1462no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23C2×D4×D7312yes—
668C23C2×D4×D7311yescharacteristic
669Q8—5844no—
670Q8—5844no—
671D4—22no—
672D4—22no—
673D4—42no—
674D4—84no—
675D4—2922no—
676D4—5844no—
677D4—5844no—
678D4—5844no—
679D4—1468no—
680D4—1462no—
681D4—1462no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—2928no—
693C2×C4—2922no—
694C2×C4—2922no—
695C2×C4—2922no—
696C2×C4—2928no—
697C2×C4—732no—
698C2×C4—734no—
699C2×C4—732no—
700C2×C4—732no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1464no—
709C2×C4C2×D4×D7312yes—
710C2×C4C2×D4×D7311yescharacteristic
711C2×C4#41×D7312yes—
712C2×C4#1455663812yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—22no—
716C8—734no—
717C8—1462no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2924no—
727C22—2922no—
728C22—2922no—
729C22—2922no—
730C22—5844no—
731C22—1462no—
732C22—1462no—
733C22—1462no—
734C22#1798923512yes—
735C22#135×D7312yes—
736C22#1798939112yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—2922no—
743C4—2922no—
744C4—2922no—
745C4—734no—
746C4—1462no—
747C4—1462no—
748C4#1798923512yes—
749C4C2×#41×D7311yescharacteristic
750C4C2×#1455663811yescharacteristic
751C2—42no—
752C2—82no—
753C2—2922no—
754C2—5842no—
755C2#2262234814yesdirect product factor
756C2C2×#1798923511yescharacteristic
757C2C2×#135×D7311yescharacteristic
758C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#482×C73C2
socleC23×C73C22×D4
hypercenterC2×#482D73
hypocenterC73C2×#3341
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#17989301C2semidirect
2. C2×#17989300C2semidirect
3. #22622348C2direct (N × H)
4. C2×#17988991C2semidirect
5. C2×#17988914C2semidirect
6. C2×#17988912C2semidirect
7. C2×#17988909C2semidirect
8. C2×#17988876C2semidirect
9. C2×#17988875C2semidirect
10. C2×#17988822C2semidirect
11. C2×#17988821C2semidirect
12. C2×#17988667C2semidirect
13. C2×#17988650C2semidirect
14. C2×#17988623C2semidirect
15. C2×#17988622C2semidirect
16. C2×#482×C73C2semidirect
21. #17989301C22semidirect
23. #17989300C22semidirect
43. #17988991C22semidirect
44. #17988914C22semidirect
45. #17988912C22semidirect
46. #17988909C22semidirect
47. #17988876C22semidirect
48. #17988875C22semidirect
49. #17988822C22semidirect
50. #17988821C22semidirect
51. #17988667C22semidirect
52. #17988650C22semidirect
53. #17988623C22semidirect
54. #17988622C22semidirect
71. #482×C73C22semidirect
374. C2×C73#3341semidirect
387. C2×#482D73semidirect
396. C73C2×#3341semidirect
429. #482C2×D73semidirect
755. C2#22622348direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893012
C2×#179893002
#226223482
C2×#179889912
C2×#179889142
C2×#179889122
C2×#179889092
C2×#179888762
C2×#179888752
C2×#179888222
C2×#179888212
C2×#179886672
C2×#179886502
C2×#179886232
C2×#179886222
C2×#482×C732
C2×#334173