Finite Group Databasebeta

← C2×#22620182 #33954287

Subgroups — C2×#22620182 #33954287

Order 18688.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989195C211yesmaximal, characteristic, complemented
2C2×#17989059C211yesmaximal, characteristic
3#22620182C2116yesmaximal, direct product factor
4C2×#17988930C211yesmaximal, characteristic, complemented
5C2×#17988927C211yesmaximal, characteristic, complemented
6C2×#17988890C211yesmaximal, characteristic, complemented
7C2×#17988885C211yesmaximal, characteristic, complemented
8C2×#17988791C211yesmaximal, characteristic, complemented
9C2×#17988790C211yesmaximal, characteristic, complemented
10C2×#17988739C211yesmaximal, characteristic
11C2×#17988736C211yesmaximal, characteristic
12C2×#17988689C211yesmaximal, characteristic, complemented
13C2×C4×#11924015C211yesmaximal, characteristic, complemented
14C2×C4×#11924016C211yesmaximal, characteristic, complemented
15C2×#17988649C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×D4×D73C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21#17989195—24no—
22#17989195C2218yescomplemented
23C2×#14556589C2211yescharacteristic, complemented
24C2×#14556586—21no—
25C2×#14556585—21no—
26C2×#14556583—21no—
27C2×#14556582C2211yescharacteristic, complemented
28C2×#14556581—21no—
29C2×#14556571C2211yescharacteristic
30C2×#14556567C2211yescharacteristic
31#17989059—24no—
32#17989059C2218yes—
33C2×C4×Dic146C2211yescharacteristic, complemented
34C2×C4×D292C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×C4×C22⋊D73—21no—
38C2×#14556551—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548C2211yescharacteristic
41C22×#11924005—21no—
42C2×C22⋊C4×D73—21no—
43#17988930C2218yescomplemented
44#17988927C2218yescomplemented
45#17988890C2218yescomplemented
46#17988885C2218yescomplemented
47#17988791C2218yescomplemented
48#17988790C2218yescomplemented
49#17988739C2218yes—
50#17988736C2218yes—
51#17988689C2218yescomplemented
52C4×#11924015C2218yescomplemented
53C4×#11924016C2218yescomplemented
54#17988649C2218yescomplemented
55C2×#14556525C2211yescharacteristic, complemented
56C2×#14556522C2211yescharacteristic, complemented
57C2×#14556522C2211yescharacteristic, complemented
58C2×#14556520C2211yescharacteristic, complemented
59C2×#14556520C2211yescharacteristic, complemented
60C2×#14556516C2211yescharacteristic, complemented
61C2×#14556515C2211yescharacteristic, complemented
62C2×#14556514C2211yescharacteristic, complemented
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic, complemented
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic, complemented
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic, complemented
74C2×#103×C73C2211yescharacteristic, complemented
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic, complemented
77C24×D73—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C2×D4×D73—24no—
82C2×D4×D73—22no—
83C2×D4×D73—24no—
84C2×D4×D73C2314yes—
85C23×Dic73—21no—
86C22×C4×D73—21no—
87C22×C4×D73—21no—
88C22×C4×D73C2311yescharacteristic
89C2×#11924017—24no—
90C2×#11924017C2314yes—
91C2×#11924016—24no—
92C2×#11924016C2314yes—
93C2×#11924015—24no—
94C2×#11924015C2314yes—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97#14556589—22no—
98#14556589C2314yescomplemented
99#14556586—28no—
100#14556585—28no—
101#14556583—28no—
102#14556582—22no—
103#14556582C2314yescomplemented
104#14556581—28no—
105#14556571—22no—
106#14556571C2314yes—
107#14556567—22no—
108#14556567C2314yes—
109C4×Dic146—22no—
110C4×Dic146C2314yescomplemented
111C4×D292—22no—
112C4×D292C2314yes—
113D4×Dic73—22no—
114D4×Dic73C2314yes—
115#14556553—22no—
116#14556553C2314yes—
117C4×C22⋊D73—28no—
118#14556551—28no—
119#14556549—22no—
120#14556549C2314yes—
121#14556548D414yes—
122#14556548C2314yes—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C2×#11924007D411yescharacteristic
134C2×C22⋊Dic73—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—28no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×#11924005D411yescharacteristic
143C22⋊C4×D73—28no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yescomplemented
148#14556522C2314yescomplemented
149#14556522C2314yescomplemented
150#14556520C2314yescomplemented
151#14556520C2314yescomplemented
152#14556516C2314yescomplemented
153#14556515C2314yescomplemented
154#14556514C2314yescomplemented
155#14556513C2314yes—
156#14556512C2314yes—
157#14556511C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160C4×#10596831C2314yescomplemented
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C23×C4×C73—21no—
164C2×SD16×C73—24no—
165C2×SD16×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yescomplemented
170C4×D4×C73—22no—
171C4×D4×C73C2314yes—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#107×C73C2314yescomplemented
179#103×C73C2314yescomplemented
180#102×C73C2314yes—
181#97×C73C2314yescomplemented
182C23×D73—21no—
183C23×D73—28no—
184C23×D73—24no—
185C23×D73—82no—
186C23×D73—82no—
187C23×D73C2×D411yescharacteristic
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—21no—
191C2×Dic146C2412yes—
192C2×D292—21no—
193C2×D292—22no—
194C2×D292#4114yes—
195C2×D292C2412yes—
196C2×C22⋊D73—28no—
197C2×C22⋊D73—24no—
198D4×D73—216no—
199D4×D73—28no—
200D4×D73—28no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—24no—
205C22×Dic73—82no—
206C22×Dic73C2×D411yescharacteristic
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C2×C4×D73—22no—
210C2×C4×D73—22no—
211C2×C4×D73—24no—
212C2×C4×D73—24no—
213C2×C4×D73—82no—
214C2×C4×D73—82no—
215C2×C4×D73C2×D412yes—
216C2×C4×D73C2412yes—
217#11924017—28no—
218#11924016—28no—
219#11924015—28no—
220C2×#10596831—22no—
221C2×#10596831—22no—
222C2×#10596831C2412yes—
223C2×#10596831C2412yes—
224C4⋊Dic73—21no—
225C4⋊Dic73—21no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2412yes—
229C4⋊Dic73C2412yes—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007C2×D414yes—
236#11924007C2×D414yes—
237C22⋊Dic73—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005C2×D414yes—
244#11924005C2×D414yes—
245C4×Dic73—24no—
246C4×Dic73—24no—
247C4×Dic73C2×D412yes—
248C4×Dic73C2412yes—
249C24×C73—21no—
250C2×Q8×C73—21no—
251C2×Q8×C73—22no—
252C2×Q8×C73—22no—
253C2×Q8×C73C2412yes—
254C2×D4×C73—21no—
255C2×D4×C73—22no—
256C2×D4×C73#4114yes—
257C2×D4×C73C2412yes—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—24no—
262C22×C4×C73—82no—
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266SD16×C73—28no—
267C2×C8×C73—22no—
268C2×C8×C73—22no—
269C2×C8×C73C2412yes—
270C2×C8×C73C2412yes—
271C4⋊C4×C73—24no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73C2412yes—
275C4⋊C4×C73C2412yes—
276C22⋊C4×C73—24no—
277C42×C73—24no—
278C42×C73C2×D412yes—
279C42×C73C2412yes—
280C23×C73—24no—
281C23×C73—22no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73C22×D411yescharacteristic
285C22×D73—22no—
286C22×D73—24no—
287C22×D73—22no—
288C22×D73—22no—
289C22×D73—22no—
290C22×D73—216no—
291C22×D73—42no—
292C22×D73—42no—
293C22×D73—84no—
294C22×D73—84no—
295C22×D73—816no—
296C22×D73C22×D412yes—
297Q8×C73—22no—
298Q8×C73—22no—
299Q8×C73—42no—
300D4×C73—24no—
301D4×C73—22no—
302D4×C73C2×#4114yes—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—42no—
309C2×C4×C73—42no—
310C2×C4×C73—42no—
311C2×C4×C73—84no—
312C2×C4×C73C22×D412yes—
313C2×C4×C73C22×D412yes—
314C2×C4×C73C22×D411yescharacteristic
315C2×C4×C73C2×#4112yes—
316C2×C4×C73C2×#4112yes—
317C2×C4×C73C2511yescharacteristic
318C22⋊D73—216no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—84no—
329C2×Dic73C22×D412yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332D292—24no—
333D292—22no—
334D292C2×#4114yes—
335C4×D73—24no—
336C4×D73—22no—
337C4×D73—22no—
338C4×D73—84no—
339C4×D73—84no—
340Dic146—22no—
341Dic146—22no—
342Dic146—42no—
343C8×C73—22no—
344C8×C73—22no—
345#10596831—22no—
346#10596831—22no—
347C22×C73—24no—
348C22×C73—48no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73#52512yes—
352C22×C73#57712yes—
353C22×C73#57712yes—
354C22×C73C23×D411yescharacteristic
355C2×D73—22no—
356C2×D73—24no—
357C2×D73—22no—
358C2×D73—22no—
359C2×D73—44no—
360C2×D73—48no—
361C2×D73—42no—
362C2×D73—42no—
363C2×D73—816no—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73—42no—
369C4×C73#52512yes—
370C4×C73C22×#4111yescharacteristic
371C4×C73C22×#4111yescharacteristic
372Dic73—22no—
373Dic73—22no—
374Dic73—22no—
375Dic73—42no—
376Dic73—42no—
377Dic73—42no—
378C2×#3123—731nomaximal, Sylow
379C2×C73—44no—
380C2×C73#312314yescomplemented
381C2×C73C2×#52511yescharacteristic
382C2×C73C2×#57711yescharacteristic
383C2×C73C2×#57711yescharacteristic
384D73—42no—
385D73—44no—
386C2×#541—731no—
387C2×#518—731no—
388#3123—7316no—
389C2×#485—731no—
390C2×#485—731no—
391C2×#478—731no—
392C2×#478—731no—
393C2×#461—731no—
394C2×#461—731no—
395C2×#450—731no—
396C2×#450—731no—
397C2×#440—731no—
398C2×#440D7311yescharacteristic, complemented
399C2×C4×SD16—731no—
400C2×C4×SD16—731no—
401C2×#433—731no—
402C73C2×#312311yescharacteristic, complemented, Sylow
403C23×D4—731no—
404C22×SD16—731no—
405C22×SD16—731no—
406C22×SD16—731no—
407C22×SD16C2×D7311yescharacteristic
408#541—738no—
409#541—1464no—
410C2×C4⋊Q8—731no—
411C2×#126—1461no—
412C2×#126—1461no—
413C2×#125—731no—
414C2×#125—1461no—
415C2×#125—1461no—
416C2×C22⋊Q8—731no—
417C2×C22⋊Q8—731no—
418#518—738no—
419#518—1464no—
420C2×C4×Q8—731no—
421C2×C4×Q8C2×D7311yescharacteristic, complemented
422C2×C4×D4—731no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4—1461no—
426C2×C4×D4—1461no—
427C2×C4×D4C2×D7311yescharacteristic
428C2×#117—731no—
429C2×#117—731no—
430C22×C22⋊C4—1461no—
431C22×C22⋊C4—1461no—
432#485—738no—
433#485—738no—
434#478—738no—
435#478—738no—
436#461—738no—
437#461—738no—
438#450—738no—
439#450—738no—
440#440—738no—
441#440C2×D7318yescomplemented
442C4×SD16—738no—
443C4×SD16—738no—
444#433—738no—
445C2×#107—731no—
446C2×#107C2×D7311yescharacteristic, complemented
447C2×#106—731no—
448C2×#106—731no—
449C2×C4⋊C8—731no—
450C2×C4⋊C8—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103C2×D7311yescharacteristic, complemented
455C2×#102—731no—
456C2×#102—731no—
457C2×#102—731no—
458C2×#102C2×D7311yescharacteristic
459C2×C22⋊C8—731no—
460C2×C22⋊C8—731no—
461C2×#97C2×D7311yescharacteristic, complemented
462C2×C4×C8—731no—
463C25—1461no—
464C22×Q8—731no—
465C22×Q8C22×D7311yescharacteristic
466C22×D4—734no—
467C22×D4—731no—
468C22×D4—1462no—
469C22×D4—1461no—
470C22×D4—1464no—
471C22×D4—1464no—
472C22×D4C22×D7311yescharacteristic
473C23×C4—21no—
474C23×C4—731no—
475C23×C4—1461no—
476C23×C4—1461no—
477C23×C4—1461no—
478C2×SD16—24no—
479C2×SD16—734no—
480C2×SD16—734no—
481C2×SD16—734no—
482C2×SD16—1464no—
483C2×SD16—1464no—
484C2×SD16—1464no—
485C2×SD16C22×D7314yes—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C4⋊Q8—734no—
491C4⋊Q8—1462no—
492#126—1468no—
493#126—1468no—
494#125—734no—
495#125—1468no—
496#125—1462no—
497#125—1468no—
498C22⋊Q8—734no—
499C22⋊Q8—734no—
500C22⋊Q8—1462no—
501C22⋊Q8—1462no—
502C4×Q8—22no—
503C4×Q8—734no—
504C4×Q8—1462no—
505C4×Q8C22×D7314yescomplemented
506C4×D4—22no—
507C4×D4—734no—
508C4×D4—734no—
509C4×D4—734no—
510C4×D4—1462no—
511C4×D4—1462no—
512C4×D4—1468no—
513C4×D4—1468no—
514C4×D4—1462no—
515C4×D4C22×D7314yes—
516#117—734no—
517#117—734no—
518#117—734no—
519#117—1462no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1461no—
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—1468no—
538C2×C22⋊C4—1468no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C22⋊C4—1461no—
542C2×C22⋊C4—1461no—
543C2×C22⋊C4—1461no—
544C2×C22⋊C4—1461no—
545C2×C42—21no—
546C2×C42—731no—
547C2×C42—1461no—
548C2×C42—1461no—
549C2×C42C22×D7311yescharacteristic
550#107—734no—
551#107C22×D7314yescomplemented
552#106—734no—
553#106—734no—
554C4⋊C8—734no—
555C4⋊C8—734no—
556#103—734no—
557#103—734no—
558#103—734no—
559#103C22×D7314yescomplemented
560#102—734no—
561#102—734no—
562#102—734no—
563#102C22×D7314yes—
564C22⋊C8—734no—
565C22⋊C8—734no—
566#97C22×D7314yescomplemented
567C4×C8—734no—
568C24—21no—
569C24—5842no—
570C24—5842no—
571C24—731no—
572C24—1464no—
573C24—1468no—
574C24—1461no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—732no—
579C2×Q8—1462no—
580C2×Q8—1462no—
581C2×Q8—1461no—
582C2×Q8C23×D7312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—734no—
586C2×D4—732no—
587C2×D4—1464no—
588C2×D4—1468no—
589C2×D4—14616no—
590C2×D4—1468no—
591C2×D4—1468no—
592C2×D4—1461no—
593C2×D4—1462no—
594C2×D4#1192402814yes—
595C2×D4C23×D7312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—5842no—
602C22×C4—5842no—
603C22×C4—5842no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—732no—
608C22×C4—732no—
609C22×C4—1464no—
610C22×C4—1461no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1464no—
614C22×C4—1464no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4D4×D7311yescharacteristic
618C22×C4D4×D7311yescharacteristic
619C22×C4C23×D7311yescharacteristic
620SD16—28no—
621SD16—1468no—
622SD16—1468no—
623SD16—1468no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—732no—
627C2×C8—732no—
628C2×C8—1462no—
629C2×C8—1462no—
630C2×C8C23×D7312yes—
631C2×C8C23×D7312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—734no—
636C4⋊C4—734no—
637C4⋊C4—732no—
638C4⋊C4—732no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1464no—
642C4⋊C4—1464no—
643C4⋊C4—1464no—
644C4⋊C4—1464no—
645C4⋊C4—1464no—
646C4⋊C4—1461no—
647C4⋊C4—1461no—
648C4⋊C4C23×D7312yes—
649C4⋊C4C23×D7312yes—
650C22⋊C4—24no—
651C22⋊C4—734no—
652C22⋊C4—734no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C22⋊C4—1464no—
657C22⋊C4—1464no—
658C22⋊C4—1464no—
659C42—24no—
660C42—732no—
661C42—732no—
662C42—1464no—
663C42—1464no—
664C42D4×D7312yes—
665C42C23×D7312yes—
666C23—22no—
667C23—24no—
668C23—42no—
669C23—42no—
670C23—2922no—
671C23—2922no—
672C23—58416no—
673C23—5844no—
674C23—5844no—
675C23—732no—
676C23—14616no—
677C23—1462no—
678C23—1462no—
679C23—1462no—
680C23—1462no—
681C23—1464no—
682C23C2×D4×D7311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—2922no—
687Q8—1462no—
688Q8—1462no—
689D4—22no—
690D4—24no—
691D4—734no—
692D4—14616no—
693D4—1462no—
694D4—1464no—
695D4C2×#1192402814yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—2922no—
706C2×C4—2922no—
707C2×C4—2922no—
708C2×C4—5844no—
709C2×C4—5844no—
710C2×C4—5844no—
711C2×C4—732no—
712C2×C4—732no—
713C2×C4—732no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1464no—
723C2×C4C2×D4×D7312yes—
724C2×C4C2×D4×D7312yes—
725C2×C4C2×D4×D7311yescharacteristic
726C2×C4#41×D7312yes—
727C2×C4C2×#1192402812yes—
728C2×C4C24×D7311yescharacteristic
729C8—22no—
730C8—22no—
731C8—1462no—
732C8—1462no—
733C22—24no—
734C22—48no—
735C22—42no—
736C22—42no—
737C22—2928no—
738C22—2924no—
739C22—2922no—
740C22—2922no—
741C22—58416no—
742C22—1462no—
743C22—1462no—
744C22—1462no—
745C22—1464no—
746C22#1798909612yes—
747C22#1798939612yes—
748C22#1798939712yes—
749C22C22×D4×D7311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2922no—
756C4—2922no—
757C4—2922no—
758C4—1462no—
759C4—1462no—
760C4—1462no—
761C4#1798909612yes—
762C4C2×#41×D7311yescharacteristic
763C4C22×#1192402811yescharacteristic
764C2—44no—
765C2—2924no—
766C2—2922no—
767C2#2262018214yesdirect product factor
768C2C2×#1798909611yescharacteristic
769C2C2×#1798939611yescharacteristic
770C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×D73C22
hypercenterC2×#440D73
hypocenterC73C2×#3123
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×#17989195C2semidirect
3. #22620182C2direct (N × H)
4. C2×#17988930C2semidirect
5. C2×#17988927C2semidirect
6. C2×#17988890C2semidirect
7. C2×#17988885C2semidirect
8. C2×#17988791C2semidirect
9. C2×#17988790C2semidirect
12. C2×#17988689C2semidirect
13. C2×C4×#11924015C2semidirect
14. C2×C4×#11924016C2semidirect
15. C2×#17988649C2semidirect
16. C2×#440×C73C2semidirect
22. #17989195C22semidirect
23. C2×#14556589C22semidirect
27. C2×#14556582C22semidirect
33. C2×C4×Dic146C22semidirect
43. #17988930C22semidirect
44. #17988927C22semidirect
45. #17988890C22semidirect
46. #17988885C22semidirect
47. #17988791C22semidirect
48. #17988790C22semidirect
51. #17988689C22semidirect
52. C4×#11924015C22semidirect
53. C4×#11924016C22semidirect
54. #17988649C22semidirect
55. C2×#14556525C22semidirect
56. C2×#14556522C22semidirect
57. C2×#14556522C22semidirect
58. C2×#14556520C22semidirect
59. C2×#14556520C22semidirect
60. C2×#14556516C22semidirect
61. C2×#14556515C22semidirect
62. C2×#14556514C22semidirect
68. C2×C4×#10596831C22semidirect
70. C2×C4×Q8×C73C22semidirect
72. #440×C73C22semidirect
73. C2×#107×C73C22semidirect
74. C2×#103×C73C22semidirect
76. C2×#97×C73C22semidirect
98. #14556589C23semidirect
103. #14556582C23semidirect
110. C4×Dic146C23semidirect
147. #14556525C23semidirect
148. #14556522C23semidirect
149. #14556522C23semidirect
150. #14556520C23semidirect
151. #14556520C23semidirect
152. #14556516C23semidirect
153. #14556515C23semidirect
154. #14556514C23semidirect
160. C4×#10596831C23semidirect
169. C4×Q8×C73C23semidirect
178. #107×C73C23semidirect
179. #103×C73C23semidirect
181. #97×C73C23semidirect
380. C2×C73#3123semidirect
398. C2×#440D73semidirect
402. C73C2×#3123semidirect
421. C2×C4×Q8C2×D73semidirect
441. #440C2×D73semidirect
446. C2×#107C2×D73semidirect
454. C2×#103C2×D73semidirect
461. C2×#97C2×D73semidirect
505. C4×Q8C22×D73semidirect
551. #107C22×D73semidirect
559. #103C22×D73semidirect
566. #97C22×D73semidirect
767. C2#22620182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891952
C2×#179890592
#226201822
C2×#179889302
C2×#179889272
C2×#179888902
C2×#179888852
C2×#179887912
C2×#179887902
C2×#179887392
C2×#179887362
C2×#179886892
C2×C4×#119240152
C2×C4×#119240162
C2×#179886492
C2×#440×C732
C2×#312373