Finite Group Databasebeta

← C2×#22622411 #33964558

Subgroups — C2×#22622411 #33964558

Order 18688.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989295C211yesmaximal, characteristic, complemented
2C2×#17989284C211yesmaximal, characteristic
3#22622411C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988921C211yesmaximal, characteristic, complemented
6C2×#17988904C211yesmaximal, characteristic, complemented
7C2×#17988925C211yesmaximal, characteristic, complemented
8C2×#17988898C211yesmaximal, characteristic, complemented
9C2×#17988892C211yesmaximal, characteristic, complemented
10C2×#17988865C211yesmaximal, characteristic, complemented
11C2×#17988813C211yesmaximal, characteristic, complemented
12C2×#17988688C211yesmaximal, characteristic, complemented
13C2×#17988656C211yesmaximal, characteristic, complemented
14C2×#17988629C211yesmaximal, characteristic, complemented
15C2×#107×D73C211yesmaximal, characteristic, complemented
16C2×#468×C73C211yesmaximal, characteristic, complemented
17C22×C8×D73C2211yescharacteristic
18#17989295—24no—
19#17989295C2218yescomplemented
20#17989284—24no—
21#17989284C2218yes—
22C2×#14556590C2211yescharacteristic
23C2×#14556584—21no—
24C2×#14556582C2211yescharacteristic
25C2×#14556581—21no—
26C2×#14556572—21no—
27C2×#14556571—21no—
28C2×#14556568—21no—
29C2×#14556567C2211yescharacteristic
30C2×#14556562—21no—
31C2×#14556562C2211yescharacteristic
32C2×Q8×Dic73C2211yescharacteristic
33C2×D4×Dic73C2211yescharacteristic
34C2×C4×C22⋊D73C2211yescharacteristic
35C2×#14556551—21no—
36C2×#14556551—21no—
37C2×#14556550C2211yescharacteristic
38C22×C4⋊Dic73C2211yescharacteristic
39C2×C4⋊C4×D73C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41#17988995C2218yescomplemented
42#17988925C2218yescomplemented
43#17988921C2218yescomplemented
44#17988904C2218yescomplemented
45#17988898C2218yescomplemented
46#17988892C2218yescomplemented
47#17988865C2218yescomplemented
48#17988813C2218yescomplemented
49#17988688C2218yescomplemented
50#17988656C2218yescomplemented
51#17988629C2218yescomplemented
52C2×#14556525C2211yescharacteristic
53C2×#14556525C2211yescharacteristic
54C2×#14556524C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57#107×D73C2218yescomplemented
58C2×#14556523C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#468×C73C2218yescomplemented
74C2×#107×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×C22⋊D73—21no—
79C22×C22⋊D73D411yescharacteristic
80C23×Dic73—21no—
81C23×Dic73—21no—
82C22×C4×D73—21no—
83C22×C4×D73—21no—
84C22×C4×D73C2311yescharacteristic
85C22×#10596831C2311yescharacteristic
86C22×#10596831C2311yescharacteristic
87C2×C8×D73—24no—
88C2×C8×D73C2314yes—
89#14556590—22no—
90#14556590C2314yes—
91#14556584—28no—
92#14556582—22no—
93#14556582C2314yes—
94#14556581—28no—
95#14556572—28no—
96#14556571—28no—
97#14556568—28no—
98#14556567—22no—
99#14556567C2314yes—
100#14556562—28no—
101#14556562—22no—
102#14556562C2314yes—
103Q8×Dic73—22no—
104Q8×Dic73C2314yes—
105D4×Dic73—22no—
106D4×Dic73C2314yes—
107C4×C22⋊D73D414yes—
108C4×C22⋊D73C2314yes—
109#14556551—28no—
110#14556551—28no—
111#14556550—22no—
112#14556550C2314yes—
113C2×C4⋊Dic73—21no—
114C2×C4⋊Dic73—21no—
115C2×C4⋊Dic73—22no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73C2311yescharacteristic
118C2×C4⋊Dic73C2311yescharacteristic
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2314yes—
122C2×#11924007—21no—
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007D411yescharacteristic
128C4⋊C4×D73—22no—
129C4⋊C4×D73—22no—
130C4⋊C4×D73C2314yes—
131C4⋊C4×D73C2314yes—
132C2×C22⋊Dic73—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73D411yescharacteristic
136C2×#11924005—21no—
137C2×#11924005D411yescharacteristic
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73C2311yescharacteristic
141#14556525C2314yes—
142#14556525C2314yes—
143#14556524C2314yes—
144#14556524C2314yes—
145#14556524C2314yes—
146#14556523C2314yes—
147#14556523C2314yes—
148#14556522C2314yes—
149#14556520C2314yes—
150#14556515C2314yes—
151#14556515C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154C22⋊#10596831C2314yes—
155#14556503C2314yes—
156#14556501C2314yes—
157C22×Q8×C73C2311yescharacteristic
158C22×D4×C73—21no—
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73C2311yescharacteristic
161C2×SD16×C73—24no—
162C2×SD16×C73C2314yes—
163C2×M16×C73—24no—
164C2×M16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C22⋊Q8×C73—22no—
168C22⋊Q8×C73C2314yes—
169#121×C73—22no—
170#121×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176#107×C73C2314yes—
177#103×C73C2314yes—
178#102×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C2×Dic146—24no—
181C2×Dic146—82no—
182C2×C22⋊D73—24no—
183C2×C22⋊D73—24no—
184C2×C22⋊D73—44no—
185C2×C22⋊D73C2×D414yes—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—24no—
191C22×Dic73—24no—
192C22×Dic73—82no—
193C22×Dic73—82no—
194C22×Dic73C2×D411yescharacteristic
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C2×C4×D73—22no—
198C2×C4×D73—22no—
199C2×C4×D73—24no—
200C2×C4×D73—24no—
201C2×C4×D73—82no—
202C2×C4×D73—82no—
203C2×C4×D73C2×D412yes—
204C2×C4×D73C2412yes—
205C2×#10596831—22no—
206C2×#10596831—22no—
207C2×#10596831C2412yes—
208C2×#10596831C2412yes—
209C8×D73—28no—
210C4⋊Dic73—21no—
211C4⋊Dic73—21no—
212C4⋊Dic73—21no—
213C4⋊Dic73—24no—
214C4⋊Dic73—21no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73C2412yes—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220C4⋊Dic73C2412yes—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
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#11924005C2×D414yes—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73C2×D412yes—
236C4×Dic73C2412yes—
237C24×C73—21no—
238C24×C73C2×D411yescharacteristic
239C2×Q8×C73—21no—
240C2×Q8×C73—22no—
241C2×Q8×C73—22no—
242C2×Q8×C73C2412yes—
243C2×D4×C73—24no—
244C2×D4×C73—21no—
245C2×D4×C73—22no—
246C2×D4×C73—22no—
247C2×D4×C73—82no—
248C2×D4×C73C2412yes—
249C22×C4×C73—22no—
250C22×C4×C73—22no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D412yes—
256C22×C4×C73C2412yes—
257C22×C4×C73C2411yescharacteristic
258SD16×C73—28no—
259M16×C73—28no—
260C2×C8×C73—22no—
261C2×C8×C73#4114yes—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—42no—
276C23×C73—42no—
277C23×C73—42no—
278C23×C73C22×D412yes—
279C23×C73C22×D411yescharacteristic
280C22×D73—22no—
281C22×D73—22no—
282C22×D73#13714yes—
283C22×D73C22×D412yes—
284Q8×C73—22no—
285Q8×C73—22no—
286Q8×C73—42no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—42no—
290D4×C73—84no—
291C2×C4×C73—22no—
292C2×C4×C73—24no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4112yes—
304C2×C4×C732−1+412yes—
305C2×C4×C73C2511yescharacteristic
306C22⋊D73—28no—
307C22⋊D73—48no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—84no—
320C2×Dic73—84no—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C4×D73—24no—
325C4×D73—22no—
326C4×D73—22no—
327C4×D73—84no—
328C4×D73—84no—
329Dic146—84no—
330C8×C73—22no—
331C8×C73C2×#4114yes—
332#10596831—22no—
333#10596831—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—44no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—84no—
342C22×C73#54712yes—
343C22×C73C2×#13712yes—
344C22×C73#57612yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—28no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73C2×#13714yes—
350C4×C73—22no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73#54712yes—
355C4×C73C22×#4111yescharacteristic
356C4×C73C2×2−1+411yescharacteristic
357Dic73—22no—
358Dic73—22no—
359Dic73—22no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#3346—731nomaximal, Sylow
365C2×C73—42no—
366C2×C73—82no—
367C2×C73#334614yescomplemented
368C2×C73C2×#54711yescharacteristic
369C2×C73C22×#13711yescharacteristic
370C2×C73C2×#57611yescharacteristic
371D73—24no—
372C2×#554—731no—
373C2×#553—731no—
374#3346—7316no—
375C2×#501—731no—
376C2×#484—731no—
377C2×#481—731no—
378C2×#485—731no—
379C2×#480—731no—
380C2×#479—731no—
381C2×#474—731no—
382C2×#468D7311yescharacteristic, complemented
383C2×#465—731no—
384C2×#440—731no—
385C2×#435—731no—
386C2×#428—731no—
387C22×#107—731no—
388C73C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16C2×D7311yescharacteristic
390C22×M16C2×D7311yescharacteristic
391C23×C8—731no—
392#554—738no—
393#554—1464no—
394#553—738no—
395#553—1464no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#125—731no—
399C2×#125—1461no—
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—1461no—
403C2×C22⋊Q8—1461no—
404C2×C22⋊Q8C2×D7311yescharacteristic
405C2×#121—731no—
406C2×#121—1461no—
407C2×#121C2×D7311yescharacteristic
408C2×C4×Q8—731no—
409C2×C4×D4—731no—
410C2×C4×D4—731no—
411C2×C4×D4—1461no—
412C2×C4×D4—1461no—
413C2×#117—731no—
414C22×C4⋊C4—731no—
415C22×C4⋊C4—731no—
416C22×C4⋊C4—731no—
417#501—738no—
418#485—738no—
419#484—738no—
420#481—738no—
421#480—738no—
422#479—738no—
423#474—738no—
424#468C2×D7318yescomplemented
425#465—738no—
426#440—738no—
427#435—738no—
428#428—738no—
429C2×#107—731no—
430C2×#107—731no—
431C2×#107—731no—
432C2×#107—731no—
433C2×#107—731no—
434C2×#107—738no—
435C2×#107C2×D7311yescharacteristic
436C2×#106—731no—
437C2×#106—731no—
438C2×#106—731no—
439C2×C4⋊C8—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#102—731no—
445C2×#102C2×D7311yescharacteristic
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×#97—731no—
449C22×Q8—1461no—
450C22×Q8C22×D7311yescharacteristic
451C22×D4—21no—
452C22×D4—731no—
453C22×D4—1461no—
454C22×D4C22×D7311yescharacteristic
455C23×C4—731no—
456C23×C4—1461no—
457C23×C4—1461no—
458C23×C4—1461no—
459C23×C4—1461no—
460C23×C4C22×D7311yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D7314yes—
463C2×M16—24no—
464C2×M16C22×D7314yes—
465C22×C8—731no—
466C22×C8—731no—
467C22×C8—734no—
468C22×C8—1464no—
469C22×C8C22×D7311yescharacteristic
470C22×C8C22×D7311yescharacteristic
471C4⋊Q8—734no—
472C4⋊Q8—1462no—
473#126—1468no—
474#125—734no—
475#125—1462no—
476#125—1468no—
477#123—1468no—
478C22⋊Q8—22no—
479C22⋊Q8—734no—
480C22⋊Q8—1468no—
481C22⋊Q8—1468no—
482C22⋊Q8—1462no—
483C22⋊Q8C22×D7314yes—
484#121—22no—
485#121—734no—
486#121—1462no—
487#121—1468no—
488#121C22×D7314yes—
489C4×Q8—734no—
490C4×Q8—1462no—
491C4×D4—734no—
492C4×D4—734no—
493C4×D4—734no—
494C4×D4—1462no—
495C4×D4—1468no—
496C4×D4—1468no—
497#117—734no—
498#117—1462no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—734no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—734no—
507C2×C4⋊C4—734no—
508C2×C4⋊C4—1462no—
509C2×C4⋊C4—1462no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1462no—
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4—731no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C22⋊C4—1461no—
529C2×C42—731no—
530C2×C42—1461no—
531C2×C42—1461no—
532#107—734no—
533#107—734no—
534#107—734no—
535#107—734no—
536#107—734no—
537#107C22×D7314yes—
538#106—734no—
539#106—734no—
540#106—734no—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103C22×D7314yes—
545#102—734no—
546#102—734no—
547#102C22×D7314yes—
548C22⋊C8—734no—
549C22⋊C8—734no—
550#97—734no—
551C24—21no—
552C24—731no—
553C24D4×D7311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—5842no—
558C2×Q8—1464no—
559C2×Q8C23×D7312yes—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—82no—
565C2×D4—2924no—
566C2×D4—734no—
567C2×D4—1464no—
568C2×D4—1464no—
569C2×D4C23×D7312yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—5842no—
576C22×C4—5842no—
577C22×C4—5842no—
578C22×C4—5842no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—732no—
583C22×C4—732no—
584C22×C4—1464no—
585C22×C4—1464no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1464no—
591C22×C4—1464no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4D4×D7312yes—
595C22×C4D4×D7311yescharacteristic
596C22×C4C23×D7312yes—
597C22×C4C23×D7311yescharacteristic
598SD16—28no—
599M16—28no—
600C2×C8—22no—
601C2×C8—732no—
602C2×C8—732no—
603C2×C8—1462no—
604C2×C8—1462no—
605C2×C8—1468no—
606C2×C8#1192402714yes—
607C2×C8C23×D7312yes—
608C2×C8C23×D7312yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—734no—
613C4⋊C4—732no—
614C4⋊C4—732no—
615C4⋊C4—732no—
616C4⋊C4—732no—
617C4⋊C4—1464no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1464no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—734no—
634C22⋊C4—734no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—732no—
640C42—732no—
641C42—1464no—
642C42—1464no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—734no—
651C23—732no—
652C23—1462no—
653C23—1462no—
654C23C2×D4×D7312yes—
655C23C2×D4×D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—5844no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664D4—2928no—
665D4—1468no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—2922no—
679C2×C4—2922no—
680C2×C4—5844no—
681C2×C4—5844no—
682C2×C4—5844no—
683C2×C4—5844no—
684C2×C4—732no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1464no—
697C2×C4C2×D4×D7312yes—
698C2×C4C2×D4×D7311yescharacteristic
699C2×C4C2×#1192402712yes—
700C2×C4#1455663812yes—
701C2×C4C24×D7311yescharacteristic
702C8—22no—
703C8—1462no—
704C8—1462no—
705C8C2×#1192402714yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—734no—
715C22—1462no—
716C22—1462no—
717C22—1468no—
718C22#1798923712yes—
719C22#137×D7312yes—
720C22#1798939112yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—2922no—
727C4—2922no—
728C4—2922no—
729C4—2922no—
730C4—1462no—
731C4—1462no—
732C4—1462no—
733C4#1798923712yes—
734C4C22×#1192402711yescharacteristic
735C4C2×#1455663811yescharacteristic
736C2—42no—
737C2—82no—
738C2—1464no—
739C2#2262241114yesdirect product factor
740C2C2×#1798923711yescharacteristic
741C2C2×#137×D7311yescharacteristic
742C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#468×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989284C2
hypercenterC2×#468D73
hypocenterC73C2×#3346
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#17989295C2semidirect
3. #22622411C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988921C2semidirect
6. C2×#17988904C2semidirect
7. C2×#17988925C2semidirect
8. C2×#17988898C2semidirect
9. C2×#17988892C2semidirect
10. C2×#17988865C2semidirect
11. C2×#17988813C2semidirect
12. C2×#17988688C2semidirect
13. C2×#17988656C2semidirect
14. C2×#17988629C2semidirect
15. C2×#107×D73C2semidirect
16. C2×#468×C73C2semidirect
19. #17989295C22semidirect
41. #17988995C22semidirect
42. #17988925C22semidirect
43. #17988921C22semidirect
44. #17988904C22semidirect
45. #17988898C22semidirect
46. #17988892C22semidirect
47. #17988865C22semidirect
48. #17988813C22semidirect
49. #17988688C22semidirect
50. #17988656C22semidirect
51. #17988629C22semidirect
57. #107×D73C22semidirect
73. #468×C73C22semidirect
367. C2×C73#3346semidirect
382. C2×#468D73semidirect
388. C73C2×#3346semidirect
424. #468C2×D73semidirect
739. C2#22622411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892952
C2×#179892842
#226224112
C2×#179889952
C2×#179889212
C2×#179889042
C2×#179889252
C2×#179888982
C2×#179888922
C2×#179888652
C2×#179888132
C2×#179886882
C2×#179886562
C2×#179886292
C2×#107×D732
C2×#468×C732
C2×#334673