Finite Group Databasebeta

← C2×#22622385 #33964530

Subgroups — C2×#22622385 #33964530

Order 18688.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989298C211yesmaximal, characteristic
2C2×#17989275C211yesmaximal, characteristic
3#22622385C2116yesmaximal, direct product factor
4C2×#17988924C211yesmaximal, characteristic, complemented
5C2×#17988930C211yesmaximal, characteristic, complemented
6C2×#17988919C211yesmaximal, characteristic, complemented
7C2×#17988919C211yesmaximal, characteristic, complemented
8C2×#17988891C211yesmaximal, characteristic, complemented
9C2×#17988869C211yesmaximal, characteristic, complemented
10C2×#17988846C211yesmaximal, characteristic, complemented
11C2×#17988829C211yesmaximal, characteristic, complemented
12C2×#17988695C211yesmaximal, characteristic, complemented
13C2×#17988660C211yesmaximal, characteristic
14C2×#17988628C211yesmaximal, characteristic, complemented
15C2×#106×D73C211yesmaximal, characteristic, complemented
16C2×#501×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#17989298—24no—
21#17989298C2218yes—
22#17989275—24no—
23#17989275C2218yes—
24C2×#14556586—21no—
25C2×#14556582—21no—
26C2×#14556582—21no—
27C2×#14556576—21no—
28C2×#14556571C2211yescharacteristic
29C2×#14556571C2211yescharacteristic
30C2×#14556571C2211yescharacteristic
31C2×#14556571C2211yescharacteristic
32C2×#14556567—21no—
33C2×#14556567—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556553—21no—
38C2×#14556549—21no—
39C2×#14556549C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988930C2218yescomplemented
44#17988924C2218yescomplemented
45#17988919C2218yescomplemented
46#17988919C2218yescomplemented
47#17988891C2218yescomplemented
48#17988869C2218yescomplemented
49#17988846C2218yescomplemented
50#17988829C2218yescomplemented
51#17988695C2218yescomplemented
52#17988660C2218yes—
53#17988628C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59#106×D73C2218yescomplemented
60C2×C4⋊#10596831C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×#14556514C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556503C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#501×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×#106×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×D292D411yescharacteristic
80C22×C4×D73—21no—
81C22×C4×D73—21no—
82C22×C4×D73—21no—
83C22×C4×D73C2311yescharacteristic
84C22×C4×D73C2311yescharacteristic
85C2×Dic292—24no—
86C2×Dic292C2314yes—
87C2×#11924011—24no—
88C2×#11924011C2314yes—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91C2×C8×D73—24no—
92C2×C8×D73C2314yes—
93#14556586—28no—
94#14556582—28no—
95#14556582—28no—
96#14556576—28no—
97#14556571—22no—
98#14556571—22no—
99#14556571—22no—
100#14556571—22no—
101#14556571C2314yes—
102#14556571C2314yes—
103#14556571C2314yes—
104#14556571C2314yes—
105#14556567—28no—
106#14556567—28no—
107C4×Dic146—22no—
108C4×Dic146—22no—
109C4×Dic146C2314yes—
110C4×Dic146C2314yes—
111C4×D292D414yes—
112C4×D292C2314yes—
113#14556553—28no—
114#14556549—22no—
115#14556549—28no—
116#14556549C2314yes—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73D411yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C4⋊C4×D73—22no—
130C4⋊C4×D73—22no—
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C4⋊C4×D73C2314yes—
134C4⋊C4×D73C2314yes—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005D411yescharacteristic
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145#14556524C2314yes—
146#14556523C2314yes—
147#14556522C2314yes—
148#14556522C2314yes—
149#14556522C2314yes—
150C4⋊#10596831C2314yes—
151#14556516C2314yes—
152#14556516C2314yes—
153#14556514C2314yes—
154#14556514C2314yes—
155#14556514C2314yes—
156#14556514C2314yes—
157#14556503C2314yes—
158#14556503C2314yes—
159C22×Q8×C73—21no—
160C22×C8×C73C2311yescharacteristic
161C22×C8×C73C2311yescharacteristic
162C4⋊Q8×C73—22no—
163C4⋊Q8×C73C2314yes—
164#125×C73—22no—
165#125×C73C2314yes—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C42×C73C2311yescharacteristic
174#107×C73C2314yes—
175#107×C73C2314yes—
176#106×C73C2314yes—
177#106×C73C2314yes—
178#97×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C23×D73C2×D411yescharacteristic
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—21no—
187C2×Dic146C2412yes—
188C2×Dic146C2412yes—
189C2×D292—24no—
190C2×D292C2×D414yes—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C2×C4×D73—22no—
198C2×C4×D73—22no—
199C2×C4×D73—22no—
200C2×C4×D73—22no—
201C2×C4×D73—24no—
202C2×C4×D73—24no—
203C2×C4×D73—24no—
204C2×C4×D73—44no—
205C2×C4×D73—82no—
206C2×C4×D73—82no—
207C2×C4×D73C2×D412yes—
208C2×C4×D73C2×D412yes—
209C2×C4×D73C2412yes—
210C2×C4×D73C2412yes—
211Dic292—28no—
212#11924011—28no—
213C2×#10596831—22no—
214C2×#10596831—22no—
215C2×#10596831C2412yes—
216C2×#10596831C2412yes—
217C8×D73—28no—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—24no—
221C4⋊Dic73—24no—
222C4⋊Dic73—24no—
223C4⋊Dic73—24no—
224C4⋊Dic73C2×D414yes—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005C2×D414yes—
238#11924005C2×D414yes—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C2×Q8×C73—24no—
243C2×Q8×C73—82no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2411yescharacteristic
251C2×C8×C73—22no—
252C2×C8×C73#4114yes—
253C2×C8×C73C2412yes—
254C2×C8×C73C2412yes—
255C4⋊C4×C73—24no—
256C4⋊C4×C73—24no—
257C4⋊C4×C73—24no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73C2412yes—
263C4⋊C4×C73C2412yes—
264C4⋊C4×C73C2412yes—
265C4⋊C4×C73C2412yes—
266C42×C73C2×D412yes—
267C42×C73C2412yes—
268C23×C73C22×D411yescharacteristic
269C22×D73—22no—
270C22×D73—22no—
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—22no—
274C22×D73#13714yes—
275C22×D73C22×D412yes—
276C22×D73C22×D412yes—
277Q8×C73—84no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73C22×D412yes—
289C2×C4×C73C22×D412yes—
290C2×C4×C73C22×D411yescharacteristic
291C2×C4×C73C2×#4112yes—
292C2×C4×C732−1+412yes—
293C2×C4×C73C2511yescharacteristic
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—42no—
301C2×Dic73—42no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73C22×D412yes—
305C2×Dic73C22×D412yes—
306D292—28no—
307C4×D73—24no—
308C4×D73—24no—
309C4×D73—22no—
310C4×D73—22no—
311C4×D73—22no—
312C4×D73—22no—
313C4×D73—48no—
314C4×D73—84no—
315C4×D73—84no—
316Dic146—22no—
317Dic146—22no—
318Dic146—22no—
319Dic146—22no—
320Dic146—42no—
321Dic146—42no—
322C8×C73—22no—
323C8×C73C2×#4114yes—
324#10596831—22no—
325#10596831—22no—
326C22×C73#54712yes—
327C22×C73C2×#13712yes—
328C22×C73#57712yes—
329C22×C73C23×D411yescharacteristic
330C2×D73—28no—
331C2×D73—22no—
332C2×D73—22no—
333C2×D73—22no—
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—44no—
337C2×D73C2×#13714yes—
338C4×C73—22no—
339C4×C73—22no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73#54712yes—
345C4×C73C22×#4111yescharacteristic
346C4×C73C2×2−1+411yescharacteristic
347Dic73—22no—
348Dic73—22no—
349Dic73—42no—
350Dic73—42no—
351Dic73—42no—
352Dic73—42no—
353C2×#3344—731nomaximal, Sylow
354C2×C73#334414yescomplemented
355C2×C73C2×#54711yescharacteristic
356C2×C73C22×#13711yescharacteristic
357C2×C73C2×#57711yescharacteristic
358D73—24no—
359D73—42no—
360C2×#554—731no—
361C2×#552—731no—
362#3344—7316no—
363C2×#501D7311yescharacteristic, complemented
364C2×#484—731no—
365C2×#485—731no—
366C2×#483—731no—
367C2×#483—731no—
368C2×#479—731no—
369C2×#475—731no—
370C2×#470—731no—
371C2×#467—731no—
372C2×#441—731no—
373C2×#435—731no—
374C2×#428—731no—
375C22×#106—731no—
376C73C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—731no—
378C22×M16—731no—
379C23×C8—731no—
380#554—738no—
381#554—1464no—
382#552—738no—
383#552—1464no—
384C2×C4⋊Q8C2×D7311yescharacteristic
385C2×#126—1461no—
386C2×#125—1461no—
387C2×#125—1461no—
388C2×#125C2×D7311yescharacteristic
389C2×#123—1461no—
390C2×C22⋊Q8—731no—
391C2×C22⋊Q8—731no—
392C2×C22⋊Q8—731no—
393C2×C22⋊Q8—731no—
394C2×C22⋊Q8—1461no—
395C2×C22⋊Q8—1461no—
396C2×C4×Q8—731no—
397C2×C4×Q8—731no—
398C2×C4×D4—731no—
399C2×C4×D4—1461no—
400C2×#117—731no—
401C2×#117—1461no—
402C22×C4⋊C4—731no—
403C22×C4⋊C4—731no—
404C22×C4⋊C4—731no—
405#501C2×D7318yescomplemented
406#485—738no—
407#484—738no—
408#483—738no—
409#483—738no—
410#479—738no—
411#475—738no—
412#470—738no—
413#467—738no—
414#441—738no—
415#435—738no—
416#428—738no—
417C2×#107—731no—
418C2×#107C2×D7311yescharacteristic
419C2×#107C2×D7311yescharacteristic
420C2×#106—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×#106—731no—
424C2×#106—738no—
425C2×#106C2×D7311yescharacteristic
426C2×#106C2×D7311yescharacteristic
427C2×C4⋊C8—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#103—731no—
433C2×#103—731no—
434C2×C22⋊C8—731no—
435C2×C22⋊C8—731no—
436C2×#97C2×D7311yescharacteristic
437C22×Q8—21no—
438C22×Q8—731no—
439C22×Q8—731no—
440C22×D4—731no—
441C23×C4—731no—
442C23×C4—731no—
443C23×C4—1461no—
444C23×C4—1461no—
445C23×C4—1461no—
446C2×Q16—734no—
447C2×Q16—1464no—
448C2×M16—734no—
449C2×M16—1464no—
450C22×C8—731no—
451C22×C8—731no—
452C22×C8—734no—
453C22×C8—1464no—
454C22×C8C22×D7311yescharacteristic
455C22×C8C22×D7311yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8C22×D7314yes—
458#126—1468no—
459#125—22no—
460#125—1468no—
461#125—1468no—
462#125C22×D7314yes—
463#123—1468no—
464C22⋊Q8—734no—
465C22⋊Q8—734no—
466C22⋊Q8—734no—
467C22⋊Q8—734no—
468C22⋊Q8—1468no—
469C22⋊Q8—1468no—
470C22⋊Q8—1462no—
471C22⋊Q8—1462no—
472C22⋊Q8—1462no—
473C22⋊Q8—1462no—
474C4×Q8—734no—
475C4×Q8—734no—
476C4×Q8—1462no—
477C4×Q8—1462no—
478C4×D4—734no—
479C4×D4—734no—
480C4×D4—1468no—
481#117—734no—
482#117—1468no—
483#117—1462no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—731no—
488C2×C4⋊C4—731no—
489C2×C4⋊C4—731no—
490C2×C4⋊C4—734no—
491C2×C4⋊C4—734no—
492C2×C4⋊C4—734no—
493C2×C4⋊C4—1462no—
494C2×C4⋊C4—1462no—
495C2×C4⋊C4—1462no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4—1461no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4C22×D7311yescharacteristic
506C2×C4⋊C4C22×D7311yescharacteristic
507C2×C4⋊C4C22×D7311yescharacteristic
508C2×C4⋊C4C22×D7311yescharacteristic
509C2×C22⋊C4—731no—
510C2×C22⋊C4—731no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C42—1461no—
517C2×C42—1461no—
518C2×C42—1461no—
519C2×C42C22×D7311yescharacteristic
520#107—734no—
521#107C22×D7314yes—
522#107C22×D7314yes—
523#106—734no—
524#106—734no—
525#106—734no—
526#106—734no—
527#106C22×D7314yes—
528#106C22×D7314yes—
529C4⋊C8—734no—
530#103—734no—
531#103—734no—
532#103—734no—
533#103—734no—
534#103—734no—
535#103—734no—
536C22⋊C8—734no—
537C22⋊C8—734no—
538#97C22×D7314yes—
539C24—731no—
540C24—731no—
541C2×Q8—24no—
542C2×Q8—82no—
543C2×Q8—732no—
544C2×Q8—732no—
545C2×Q8—1462no—
546C2×Q8—1462no—
547C2×Q8—1462no—
548C2×Q8—1462no—
549C2×Q8—1461no—
550C2×Q8—1461no—
551C2×D4—734no—
552C2×D4—1464no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—2924no—
558C22×C4—5842no—
559C22×C4—5842no—
560C22×C4—731no—
561C22×C4—731no—
562C22×C4—732no—
563C22×C4—732no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—1464no—
567C22×C4—1464no—
568C22×C4—1464no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4D4×D7311yescharacteristic
578C22×C4D4×D7311yescharacteristic
579C22×C4C23×D7311yescharacteristic
580Q16—1468no—
581M16—1468no—
582C2×C8—22no—
583C2×C8—732no—
584C2×C8—732no—
585C2×C8—1462no—
586C2×C8—1462no—
587C2×C8—1468no—
588C2×C8#1192402914yes—
589C2×C8C23×D7312yes—
590C2×C8C23×D7312yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—734no—
599C4⋊C4—732no—
600C4⋊C4—732no—
601C4⋊C4—1464no—
602C4⋊C4—1464no—
603C4⋊C4—1464no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1464no—
608C4⋊C4—1464no—
609C4⋊C4—1464no—
610C4⋊C4—1461no—
611C4⋊C4—1461no—
612C4⋊C4C23×D7312yes—
613C4⋊C4C23×D7312yes—
614C4⋊C4C23×D7312yes—
615C4⋊C4C23×D7312yes—
616C22⋊C4—734no—
617C22⋊C4—734no—
618C22⋊C4—1464no—
619C22⋊C4—1464no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C22⋊C4—1464no—
623C42—1464no—
624C42—1464no—
625C42—1464no—
626C42D4×D7312yes—
627C42C23×D7312yes—
628C23—734no—
629C23—732no—
630C23—732no—
631C23—1462no—
632C23—1462no—
633C23—1462no—
634C23—1462no—
635C23—1462no—
636C23C2×D4×D7311yescharacteristic
637Q8—84no—
638Q8—2922no—
639Q8—2922no—
640Q8—1462no—
641Q8—1462no—
642Q8—1462no—
643Q8—1462no—
644D4—1468no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—2928no—
656C2×C4—2922no—
657C2×C4—2922no—
658C2×C4—2922no—
659C2×C4—2922no—
660C2×C4—5844no—
661C2×C4—5844no—
662C2×C4—732no—
663C2×C4—732no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1462no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1464no—
675C2×C4—1464no—
676C2×C4C2×D4×D7312yes—
677C2×C4C2×D4×D7312yes—
678C2×C4C2×D4×D7311yescharacteristic
679C2×C4C2×#1192402912yes—
680C2×C4#1455663912yes—
681C2×C4C24×D7311yescharacteristic
682C8—22no—
683C8—1462no—
684C8—1462no—
685C8C2×#1192402914yes—
686C22—2924no—
687C22—734no—
688C22—1462no—
689C22—1462no—
690C22—1462no—
691C22—1462no—
692C22—1468no—
693C22—1462no—
694C22#1798924012yes—
695C22#137×D7312yes—
696C22#1798939712yes—
697C22C22×D4×D7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—2922no—
705C4—2922no—
706C4—2922no—
707C4—2922no—
708C4—1462no—
709C4—1462no—
710C4#1798924012yes—
711C4C22×#1192402911yescharacteristic
712C4C2×#1455663911yescharacteristic
713C2—2922no—
714C2—1464no—
715C2#2262238514yesdirect product factor
716C2C2×#1798924011yescharacteristic
717C2C2×#137×D7311yescharacteristic
718C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#501×C73C2
socleC23×C73C22×D4
prime radicalC22×D292D4
hypercenterC2×#501D73
hypocenterC73C2×#3344
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #22622385C2direct (N × H)
4. C2×#17988924C2semidirect
5. C2×#17988930C2semidirect
6. C2×#17988919C2semidirect
7. C2×#17988919C2semidirect
8. C2×#17988891C2semidirect
9. C2×#17988869C2semidirect
10. C2×#17988846C2semidirect
11. C2×#17988829C2semidirect
12. C2×#17988695C2semidirect
14. C2×#17988628C2semidirect
15. C2×#106×D73C2semidirect
16. C2×#501×C73C2semidirect
43. #17988930C22semidirect
44. #17988924C22semidirect
45. #17988919C22semidirect
46. #17988919C22semidirect
47. #17988891C22semidirect
48. #17988869C22semidirect
49. #17988846C22semidirect
50. #17988829C22semidirect
51. #17988695C22semidirect
53. #17988628C22semidirect
59. #106×D73C22semidirect
71. #501×C73C22semidirect
354. C2×C73#3344semidirect
363. C2×#501D73semidirect
376. C73C2×#3344semidirect
405. #501C2×D73semidirect
715. C2#22622385direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892982
C2×#179892752
#226223852
C2×#179889242
C2×#179889302
C2×#179889192
C2×#179888912
C2×#179888692
C2×#179888462
C2×#179888292
C2×#179886952
C2×#179886602
C2×#179886282
C2×#106×D732
C2×#501×C732
C2×#334473