Finite Group Databasebeta

← C2×#22622532 #33964707

Subgroups — C2×#22622532 #33964707

Order 18688.

1962 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×#17989289C211yesmaximal, characteristic, complemented
2C2×#17989284C211yesmaximal, characteristic, complemented
3#22622532C2116yesmaximal, direct product factor
4C2×#17988987C211yesmaximal, characteristic, complemented
5C2×#17988910C211yesmaximal, characteristic, complemented
6C2×#17988908C211yesmaximal, characteristic, complemented
7C2×#17988899C211yesmaximal, characteristic, complemented
8C2×#17988898C211yesmaximal, characteristic, complemented
9C2×#17988889C211yesmaximal, characteristic, complemented
10C2×#17988885C211yesmaximal, characteristic, complemented
11C2×#17988837C211yesmaximal, characteristic, complemented
12C2×D8×Dic73C211yesmaximal, characteristic, complemented
13C2×#17988663C211yesmaximal, characteristic, complemented
14C2×#17988629C211yesmaximal, characteristic, complemented
15C2×#17988626C211yesmaximal, characteristic, complemented
16C2×#469×C73C211yesmaximal, characteristic, complemented
17C22×#11924011C2211yescharacteristic
18#17989289—24no—
19#17989289C2218yescomplemented
20#17989284—24no—
21#17989284C2218yescomplemented
22C2×#14556584—21no—
23C2×#14556584—21no—
24C2×#14556582C2211yescharacteristic
25C2×#14556582C2211yescharacteristic
26C2×#14556575—21no—
27C2×#14556572—21no—
28C2×#14556563—21no—
29C2×#14556562—21no—
30C2×#14556562C2211yescharacteristic
31C2×#14556562C2211yescharacteristic
32C2×D4×Dic73—21no—
33C2×D4×Dic73C2211yescharacteristic
34C2×D4×Dic73C2211yescharacteristic
35C2×C4×C22⋊D73C2211yescharacteristic
36C2×#14556551—21no—
37C2×#14556550C2211yescharacteristic
38C2×#14556549C2211yescharacteristic
39C22×C4⋊Dic73C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41#17988987C2218yescomplemented
42#17988910C2218yescomplemented
43#17988908C2218yescomplemented
44#17988899C2218yescomplemented
45#17988898C2218yescomplemented
46#17988889C2218yescomplemented
47#17988885C2218yescomplemented
48#17988837C2218yescomplemented
49D8×Dic73C2218yescomplemented
50#17988663C2218yescomplemented
51#17988629C2218yescomplemented
52#17988626C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×D8×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×#121×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#469×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×C22⋊D73—21no—
78C22×C22⋊D73—21no—
79C22×C22⋊D73D411yescharacteristic
80C23×Dic73—21no—
81C23×Dic73—21no—
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C22×C4×D73C2311yescharacteristic
85C2×#11924011—24no—
86C2×#11924011C2314yes—
87C22×#10596831C2311yescharacteristic
88C22×#10596831C2311yescharacteristic
89#14556584—28no—
90#14556584—28no—
91#14556582—22no—
92#14556582—22no—
93#14556582C2314yes—
94#14556582C2314yes—
95#14556575—28no—
96#14556572—28no—
97#14556563—28no—
98#14556562—28no—
99#14556562—22no—
100#14556562—22no—
101#14556562C2314yes—
102#14556562C2314yes—
103D4×Dic73—28no—
104D4×Dic73—22no—
105D4×Dic73—22no—
106D4×Dic73C2314yes—
107D4×Dic73C2314yes—
108C4×C22⋊D73D414yes—
109C4×C22⋊D73C2314yes—
110#14556551—28no—
111#14556550—22no—
112#14556550C2314yes—
113#14556549—22no—
114#14556549C2314yes—
115C2×C4⋊Dic73—21no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—22no—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2314yes—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007D411yescharacteristic
128C4⋊C4×D73—22no—
129C4⋊C4×D73C2314yes—
130C2×C22⋊Dic73—21no—
131C2×C22⋊Dic73—21no—
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#14556512C2314yes—
151#14556512C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154C22⋊#10596831C2314yes—
155#14556503C2314yes—
156C8×Dic73C2314yes—
157C22×D4×C73—21no—
158C22×D4×C73—21no—
159C22×D4×C73C2311yescharacteristic
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73C2311yescharacteristic
162C2×D8×C73—24no—
163C2×D8×C73C2314yes—
164C2×M16×C73—24no—
165C2×M16×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168#121×C73—22no—
169#121×C73—22no—
170#121×C73C2314yes—
171#121×C73C2314yes—
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176#106×C73C2314yes—
177#102×C73C2314yes—
178#102×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C2×C22⋊D73—24no—
181C2×C22⋊D73—24no—
182C2×C22⋊D73—42no—
183C2×C22⋊D73—44no—
184C2×C22⋊D73—82no—
185C2×C22⋊D73C2×D414yes—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—24no—
191C22×Dic73—24no—
192C22×Dic73—24no—
193C22×Dic73—82no—
194C22×Dic73—82no—
195C22×Dic73—82no—
196C22×Dic73C2×D411yescharacteristic
197C22×Dic73C2×D411yescharacteristic
198C22×Dic73C2×D411yescharacteristic
199C2×C4×D73—22no—
200C2×C4×D73—22no—
201C2×C4×D73—24no—
202C2×C4×D73—82no—
203C2×C4×D73C2×D412yes—
204C2×C4×D73C2412yes—
205#11924011—28no—
206C2×#10596831—22no—
207C2×#10596831—22no—
208C2×#10596831C2412yes—
209C2×#10596831C2412yes—
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#11924007C2×D414yes—
225C22⋊Dic73—24no—
226C22⋊Dic73—24no—
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×C73—21no—
239C24×C73C2×D411yescharacteristic
240C2×D4×C73—24no—
241C2×D4×C73—24no—
242C2×D4×C73—21no—
243C2×D4×C73—21no—
244C2×D4×C73—22no—
245C2×D4×C73—22no—
246C2×D4×C73—22no—
247C2×D4×C73—22no—
248C2×D4×C73—44no—
249C2×D4×C73—82no—
250C2×D4×C73C2412yes—
251C2×D4×C73C2412yes—
252C22×C4×C73—22no—
253C22×C4×C73—22no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D412yes—
258C22×C4×C73C2412yes—
259C22×C4×C73C2411yescharacteristic
260D8×C73—28no—
261M16×C73—28no—
262C2×C8×C73—22no—
263C2×C8×C73#4114yes—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C22⋊C4×C73—24no—
271C22⋊C4×C73—24no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73—42no—
282C23×C73—42no—
283C23×C73C22×D412yes—
284C23×C73C22×D411yescharacteristic
285C22×D73—22no—
286C22×D73—22no—
287C22×D73—22no—
288C22×D73C22×D412yes—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—48no—
294D4×C73—42no—
295D4×C73—42no—
296D4×C73—84no—
297C2×C4×C73—22no—
298C2×C4×C73—24no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D411yescharacteristic
307C2×C4×C73C2×#4112yes—
308C2×C4×C732−1+412yes—
309C2×C4×C73C2511yescharacteristic
310C22⋊D73—44no—
311C22⋊D73—48no—
312C22⋊D73—84no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—84no—
325C2×Dic73—84no—
326C2×Dic73—84no—
327C2×Dic73C22×D412yes—
328C2×Dic73C22×D412yes—
329C2×Dic73C22×D412yes—
330C4×D73—24no—
331C4×D73—22no—
332C4×D73—22no—
333C4×D73—84no—
334C8×C73—22no—
335C8×C73C2×#4114yes—
336#10596831—22no—
337#10596831—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—44no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—84no—
349C22×C73—84no—
350C22×C73#54712yes—
351C22×C73#57512yes—
352C22×C73#57612yes—
353C22×C73C23×D411yescharacteristic
354C2×D73—22no—
355C2×D73—22no—
356C2×D73—22no—
357C2×D73—44no—
358C4×C73—22no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73#54712yes—
362C4×C73C22×#4111yescharacteristic
363C4×C73C2×2−1+411yescharacteristic
364Dic73—22no—
365Dic73—22no—
366Dic73—22no—
367Dic73—42no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3355—731nomaximal, Sylow
372C2×C73—42no—
373C2×C73—82no—
374C2×C73—82no—
375C2×C73#335514yescomplemented
376C2×C73C2×#54711yescharacteristic
377C2×C73C2×#57511yescharacteristic
378C2×C73C2×#57611yescharacteristic
379D73—42no—
380C2×#553—731no—
381C2×#553—731no—
382#3355—7316no—
383C2×#499—731no—
384C2×#482—731no—
385C2×#482—731no—
386C2×#480—731no—
387C2×#480—731no—
388C2×#478—731no—
389C2×#478—731no—
390C2×#469—731no—
391C2×#469D7311yescharacteristic, complemented
392C2×C4×D8—731no—
393C2×#436—731no—
394C2×#428—731no—
395C2×#428—731no—
396C73C2×#335511yescharacteristic, complemented, Sylow
397C22×D8C2×D7311yescharacteristic
398C22×M16—731no—
399C22×M16C2×D7311yescharacteristic
400#553—738no—
401#553—738no—
402#553—1464no—
403#553—1464no—
404C2×#126—1461no—
405C2×#126—1461no—
406C2×#125—731no—
407C2×#125—731no—
408C2×#123—1461no—
409C2×#123—1461no—
410C2×#121—731no—
411C2×#121—731no—
412C2×#121—1461no—
413C2×#121—1461no—
414C2×#121C2×D7311yescharacteristic
415C2×#121C2×D7311yescharacteristic
416C2×C4×D4—731no—
417C2×C4×D4—731no—
418C2×C4×D4—731no—
419C2×C4×D4—1461no—
420C2×C4×D4—1461no—
421C2×#117—731no—
422C2×#117—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4—731no—
425#499—738no—
426#482—738no—
427#482—738no—
428#480—738no—
429#480—738no—
430#478—738no—
431#478—738no—
432#469—738no—
433#469C2×D7318yescomplemented
434C4×D8—738no—
435#436—738no—
436#428—738no—
437#428—738no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#107—731no—
442C2×#107—731no—
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⋊C8—731no—
456C2×C4×C8—731no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—731no—
460C22×D4—1461no—
461C22×D4—1461no—
462C22×D4C22×D7311yescharacteristic
463C22×D4C22×D7311yescharacteristic
464C23×C4—731no—
465C23×C4—1461no—
466C23×C4—1461no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4C22×D7311yescharacteristic
470C2×D8—24no—
471C2×D8C22×D7314yes—
472C2×M16—24no—
473C2×M16—734no—
474C2×M16—1464no—
475C2×M16C22×D7314yes—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8C22×D7311yescharacteristic
479C22×C8C22×D7311yescharacteristic
480#126—1468no—
481#126—1468no—
482#125—734no—
483#125—734no—
484#125—1462no—
485#125—1462no—
486#123—1468no—
487#123—1468no—
488#121—22no—
489#121—22no—
490#121—734no—
491#121—734no—
492#121—1462no—
493#121—1462no—
494#121—1468no—
495#121—1468no—
496#121C22×D7314yes—
497#121C22×D7314yes—
498C4×D4—734no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1462no—
503C4×D4—1462no—
504C4×D4—1468no—
505C4×D4—1468no—
506#117—734no—
507#117—734no—
508#117—1462no—
509#117—1462no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—734no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—734no—
517C2×C4⋊C4—1462no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1462no—
525C2×C4⋊C4C22×D7311yescharacteristic
526C2×C4⋊C4C22×D7311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C42—731no—
538C2×C42—1461no—
539C2×C42—1461no—
540#107—734no—
541#107—734no—
542#107—734no—
543#107—734no—
544#107—734no—
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⋊C8—734no—
558C4×C8—734no—
559C24—21no—
560C24—21no—
561C24—731no—
562C24D4×D7311yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—2924no—
574C2×D4—2922no—
575C2×D4—5842no—
576C2×D4—734no—
577C2×D4—1464no—
578C2×D4—1464no—
579C2×D4C23×D7312yes—
580C2×D4C23×D7312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—5842no—
586C22×C4—5842no—
587C22×C4—5842no—
588C22×C4—5842no—
589C22×C4—731no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—732no—
593C22×C4—732no—
594C22×C4—1464no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1464no—
600C22×C4—1464no—
601C22×C4—1464no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4D4×D7312yes—
605C22×C4D4×D7311yescharacteristic
606C22×C4C23×D7312yes—
607C22×C4C23×D7311yescharacteristic
608D8—28no—
609M16—28no—
610M16—1468no—
611C2×C8—22no—
612C2×C8—732no—
613C2×C8—732no—
614C2×C8—1462no—
615C2×C8—1462no—
616C2×C8#1192402714yes—
617C2×C8C23×D7312yes—
618C2×C8C23×D7312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—734no—
622C4⋊C4—732no—
623C4⋊C4—732no—
624C4⋊C4—732no—
625C4⋊C4—732no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1461no—
632C4⋊C4—1461no—
633C4⋊C4—1461no—
634C4⋊C4—1464no—
635C4⋊C4—1461no—
636C4⋊C4C23×D7312yes—
637C4⋊C4C23×D7312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—734no—
641C22⋊C4—734no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C42—732no—
649C42—732no—
650C42—1464no—
651C42—1464no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—732no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23C2×D4×D7312yes—
668C23C2×D4×D7311yescharacteristic
669D4—22no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—84no—
677D4—2928no—
678D4—2924no—
679D4—5844no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—2922no—
689C2×C4—2922no—
690C2×C4—2922no—
691C2×C4—2922no—
692C2×C4—5844no—
693C2×C4—5844no—
694C2×C4—5844no—
695C2×C4—5844no—
696C2×C4—732no—
697C2×C4—732no—
698C2×C4—732no—
699C2×C4—1462no—
700C2×C4—1462no—
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×C4C2×#1192402712yes—
712C2×C4#1455663812yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—1462no—
716C8—1462no—
717C8C2×#1192402714yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—2924no—
731C22—1462no—
732C22—1462no—
733C22—1462no—
734C22#1798923712yes—
735C22#1798938312yes—
736C22#1798939112yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—2922no—
742C4—2922no—
743C4—2922no—
744C4—2922no—
745C4—1462no—
746C4—1462no—
747C4—1462no—
748C4#1798923712yes—
749C4C22×#1192402711yescharacteristic
750C4C2×#1455663811yescharacteristic
751C2—42no—
752C2—82no—
753C2—82no—
754C2—2922no—
755C2#2262253214yesdirect product factor
756C2C2×#1798923711yescharacteristic
757C2C2×#1798938311yescharacteristic
758C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#469×C73C2
socleC23×C73C22×D4
hypercenterC2×#469D73
hypocenterC73C2×#3355
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#17989289C2semidirect
2. C2×#17989284C2semidirect
3. #22622532C2direct (N × H)
4. C2×#17988987C2semidirect
5. C2×#17988910C2semidirect
6. C2×#17988908C2semidirect
7. C2×#17988899C2semidirect
8. C2×#17988898C2semidirect
9. C2×#17988889C2semidirect
10. C2×#17988885C2semidirect
11. C2×#17988837C2semidirect
12. C2×D8×Dic73C2semidirect
13. C2×#17988663C2semidirect
14. C2×#17988629C2semidirect
15. C2×#17988626C2semidirect
16. C2×#469×C73C2semidirect
19. #17989289C22semidirect
21. #17989284C22semidirect
41. #17988987C22semidirect
42. #17988910C22semidirect
43. #17988908C22semidirect
44. #17988899C22semidirect
45. #17988898C22semidirect
46. #17988889C22semidirect
47. #17988885C22semidirect
48. #17988837C22semidirect
49. D8×Dic73C22semidirect
50. #17988663C22semidirect
51. #17988629C22semidirect
52. #17988626C22semidirect
73. #469×C73C22semidirect
375. C2×C73#3355semidirect
391. C2×#469D73semidirect
396. C73C2×#3355semidirect
433. #469C2×D73semidirect
755. C2#22622532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892892
C2×#179892842
#226225322
C2×#179889872
C2×#179889102
C2×#179889082
C2×#179888992
C2×#179888982
C2×#179888892
C2×#179888852
C2×#179888372
C2×D8×Dic732
C2×#179886632
C2×#179886292
C2×#179886262
C2×#469×C732
C2×#335573