Finite Group Databasebeta

← C2×#22622746 #33965720

Subgroups — C2×#22622746 #33965720

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989320C211yesmaximal, characteristic
2C2×Q8×Dic146C211yesmaximal, characteristic, complemented
3#22622746C2116yesmaximal, direct product factor
4C2×#17988947C211yesmaximal, characteristic, complemented
5C2×#17988945C211yesmaximal, characteristic, complemented
6C2×#17988932C211yesmaximal, characteristic
7C2×#17988881C211yesmaximal, characteristic, complemented
8C2×#17988867C211yesmaximal, characteristic, complemented
9C2×#17988866C211yesmaximal, characteristic, complemented
10C2×#17988809C211yesmaximal, characteristic, complemented
11C2×#17988807C211yesmaximal, characteristic, complemented
12C2×#17988785C211yesmaximal, characteristic
13C2×#17988715C211yesmaximal, characteristic, complemented
14C2×#17988690C211yesmaximal, characteristic, complemented
15C2×#17988679C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19#17989320—24no—
20#17989320C2218yes—
21Q8×Dic146—24no—
22Q8×Dic146C2218yescomplemented
23C2×#14556591—21no—
24C2×#14556591C2211yescharacteristic
25C2×#14556590—21no—
26C2×#14556590—21no—
27C2×#14556590C2211yescharacteristic
28C2×#14556590C2211yescharacteristic
29C2×#14556587C2211yescharacteristic
30C2×#14556579C2211yescharacteristic
31C2×#14556578C2211yescharacteristic
32C2×#14556577—21no—
33C2×#14556574—21no—
34C2×#14556573—21no—
35C2×Q8×Dic73C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×C4×Dic146—21no—
38C2×C4×Dic146C2211yescharacteristic
39C2×#14556556C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×C4×C22⋊D73—21no—
42#17988947C2218yescomplemented
43#17988945C2218yescomplemented
44#17988932C2218yes—
45#17988881C2218yescomplemented
46#17988867C2218yescomplemented
47#17988866C2218yescomplemented
48#17988809C2218yescomplemented
49#17988807C2218yescomplemented
50#17988785C2218yes—
51#17988715C2218yescomplemented
52#17988690C2218yescomplemented
53#17988679C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C22×Dic146C2311yescharacteristic
82C22×D292C2311yescharacteristic
83C22×C22⋊D73—21no—
84C22×C22⋊D73—21no—
85C22×C4×D73—21no—
86C2×#11924018—24no—
87C2×#11924018C2314yes—
88C2×#11924015—24no—
89C2×#11924015C2314yes—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92#14556591—28no—
93#14556591—22no—
94#14556591C2314yes—
95#14556590—28no—
96#14556590—28no—
97#14556590—22no—
98#14556590—22no—
99#14556590C2314yes—
100#14556590C2314yes—
101#14556587—22no—
102#14556587C2314yes—
103#14556579—22no—
104#14556579C2314yes—
105#14556578—22no—
106#14556578C2314yes—
107#14556577—28no—
108#14556574—28no—
109#14556573—28no—
110Q8×Dic73—22no—
111Q8×Dic73—22no—
112Q8×Dic73C2314yes—
113Q8×Dic73C2314yes—
114C4×Dic146—28no—
115C4×Dic146D414yes—
116C4×Dic146C2314yes—
117#14556556—22no—
118#14556556C2314yes—
119#14556553—22no—
120#14556553C2314yes—
121C4×C22⋊D73—28no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73D411yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007D411yescharacteristic
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×C4×Dic73—21no—
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73C2311yescharacteristic
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556524C2314yes—
145C4⋊#10596831C2314yes—
146#14556520C2314yes—
147#14556520C2314yes—
148#14556516C2314yes—
149#14556516C2314yes—
150#14556514C2314yes—
151#14556513C2314yes—
152#14556513C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155#14556511C2314yes—
156#14556501C2314yes—
157C8×Dic73C2314yes—
158C22×Q8×C73C2311yescharacteristic
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73—21no—
161C2×SD16×C73—24no—
162C2×SD16×C73C2314yes—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C4×Q8×C73—22no—
166C4×Q8×C73C2314yes—
167C4×D4×C73—22no—
168C4×D4×C73C2314yes—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C42×C73—21no—
174C2×C42×C73C2311yescharacteristic
175#107×C73C2314yes—
176#103×C73C2314yes—
177#102×C73C2314yes—
178#97×C73C2314yes—
179C23×D73—21no—
180C2×Dic146—24no—
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—21no—
184C2×Dic146—24no—
185C2×Dic146—24no—
186C2×Dic146—24no—
187C2×Dic146—82no—
188C2×Dic146—82no—
189C2×Dic146—82no—
190C2×Dic146C2×D414yes—
191C2×Dic146C2412yes—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—21no—
195C2×D292C2412yes—
196C2×C22⋊D73—24no—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—44no—
199C2×C22⋊D73—82no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—24no—
208C2×C4×D73—82no—
209#11924018—28no—
210#11924015—28no—
211C2×#10596831—22no—
212C2×#10596831—22no—
213C2×#10596831C2412yes—
214C2×#10596831C2412yes—
215C4⋊Dic73—24no—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—24no—
219C4⋊Dic73—24no—
220C4⋊Dic73C2×D414yes—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223#11924007—24no—
224#11924007—24no—
225#11924007—24no—
226#11924007C2×D414yes—
227#11924007C2×D414yes—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73C2×D412yes—
237C4×Dic73C2×D412yes—
238C4×Dic73C2412yes—
239C4×Dic73C2412yes—
240C24×C73—21no—
241C2×Q8×C73—21no—
242C2×Q8×C73—22no—
243C2×Q8×C73#4114yes—
244C2×Q8×C73C2412yes—
245C2×D4×C73—21no—
246C2×D4×C73—22no—
247C2×D4×C73—22no—
248C2×D4×C73C2412yes—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—24no—
253C22×C4×C73—82no—
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2411yescharacteristic
257SD16×C73—28no—
258C2×C8×C73—22no—
259C2×C8×C73—22no—
260C2×C8×C73C2412yes—
261C2×C8×C73C2412yes—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73C2412yes—
266C4⋊C4×C73C2412yes—
267C22⋊C4×C73—24no—
268C42×C73—24no—
269C42×C73C2×D412yes—
270C42×C73C2412yes—
271C23×C73—22no—
272C23×C73—42no—
273C23×C73—42no—
274C23×C73—42no—
275C23×C73C22×D411yescharacteristic
276C22×D73—22no—
277C22×D73—42no—
278C22×D73—42no—
279C22×D73—42no—
280Q8×C73—24no—
281Q8×C73—22no—
282Q8×C73C2×#4114yes—
283D4×C73—22no—
284D4×C73—22no—
285D4×C73—42no—
286C2×C4×C73—24no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—84no—
295C2×C4×C73C22×D412yes—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4112yes—
299C2×C4×C732−1+412yes—
300C2×C4×C73C2511yescharacteristic
301C22⋊D73—48no—
302C22⋊D73—84no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312C2×Dic73#13714yes—
313C2×Dic73C22×D412yes—
314C2×Dic73C22×D412yes—
315C2×Dic73C22×D412yes—
316C2×Dic73C22×D412yes—
317D292—22no—
318D292—22no—
319D292—42no—
320C4×D73—84no—
321Dic146—28no—
322Dic146—22no—
323Dic146—22no—
324Dic146—42no—
325Dic146—84no—
326Dic146—84no—
327Dic146—84no—
328C8×C73—22no—
329C8×C73—22no—
330#10596831—22no—
331#10596831—22no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—84no—
336C22×C73#54812yes—
337C22×C73C2×#13712yes—
338C22×C73#57612yes—
339C22×C73C23×D411yescharacteristic
340C2×D73—42no—
341C2×D73—42no—
342C2×D73—42no—
343C2×D73—84no—
344C4×C73—24no—
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73#54812yes—
350C4×C73C22×#4111yescharacteristic
351C4×C73C2×2−1+411yescharacteristic
352Dic73—22no—
353Dic73—22no—
354Dic73—22no—
355Dic73—42no—
356Dic73—42no—
357Dic73—42no—
358Dic73C2×#13714yes—
359C2×#3375—731nomaximal, Sylow
360C2×C73—82no—
361C2×C73#337514yescomplemented
362C2×C73C2×#54811yescharacteristic
363C2×C73C22×#13711yescharacteristic
364C2×C73C2×#57611yescharacteristic
365D73—82no—
366C2×#559—731no—
367C2×Q82—731no—
368#3375—7316no—
369C2×#489—731no—
370C2×#489—731no—
371C2×#486—731no—
372C2×#477—731no—
373C2×#474—731no—
374C2×#474—731no—
375C2×#464—731no—
376C2×#464—731no—
377C2×#460—731no—
378C2×#446—731no—
379C2×#440—731no—
380C2×#440D7311yescharacteristic, complemented
381C2×C4×Q16—731no—
382C73C2×#337511yescharacteristic, complemented, Sylow
383C22×Q16—731no—
384C22×SD16—731no—
385C22×SD16C2×D7311yescharacteristic
386#559—738no—
387#559—1464no—
388Q82—738no—
389Q82—1464no—
390C2×C4⋊Q8—731no—
391C2×C4⋊Q8—731no—
392C2×C4⋊Q8—731no—
393C2×C4⋊Q8—1461no—
394C2×C4⋊Q8—1461no—
395C2×C4⋊Q8—1461no—
396C2×#127—731no—
397C2×#124—731no—
398C2×#124—731no—
399C2×#124—1461no—
400C2×#123—1461no—
401C2×#123—1461no—
402C2×C4×Q8—731no—
403C2×C4×Q8—731no—
404C2×C4×Q8—731no—
405C2×C4×Q8—731no—
406C2×C4×Q8—1461no—
407C2×C4×Q8C2×D7311yescharacteristic
408C2×C4×D4—731no—
409C2×C4×D4—1461no—
410C2×C4×D4C2×D7311yescharacteristic
411#489—738no—
412#489—738no—
413#486—738no—
414#477—738no—
415#474—738no—
416#474—738no—
417#464—738no—
418#464—738no—
419#460—738no—
420#446—738no—
421#440—738no—
422#440C2×D7318yescomplemented
423C4×Q16—738no—
424C2×#107—731no—
425C2×#107—731no—
426C2×#107C2×D7311yescharacteristic
427C2×C4⋊C8—731no—
428C2×C4⋊C8—731no—
429C2×C4⋊C8—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#103—731no—
433C2×#103C2×D7311yescharacteristic
434C2×#102—731no—
435C2×#102—731no—
436C2×#102—731no—
437C2×#102—731no—
438C2×#102—731no—
439C2×#102C2×D7311yescharacteristic
440C2×#97—731no—
441C2×#97C2×D7311yescharacteristic
442C2×C4×C8—731no—
443C22×Q8—731no—
444C22×Q8—731no—
445C22×Q8—1461no—
446C22×Q8—1461no—
447C22×Q8—1461no—
448C22×Q8C22×D7311yescharacteristic
449C22×D4—731no—
450C22×D4—1461no—
451C22×D4—1461no—
452C22×D4C22×D7311yescharacteristic
453C23×C4—21no—
454C23×C4—1461no—
455C2×Q16—734no—
456C2×Q16—1464no—
457C2×SD16—24no—
458C2×SD16—734no—
459C2×SD16—1464no—
460C2×SD16C22×D7314yes—
461C22×C8—731no—
462C22×C8—731no—
463C22×C8C22×D7311yescharacteristic
464C22×C8C22×D7311yescharacteristic
465C4⋊Q8—734no—
466C4⋊Q8—734no—
467C4⋊Q8—734no—
468C4⋊Q8—1468no—
469C4⋊Q8—1462no—
470C4⋊Q8—1462no—
471C4⋊Q8—1468no—
472C4⋊Q8—1468no—
473C4⋊Q8—1462no—
474#127—734no—
475#127—1462no—
476#124—734no—
477#124—734no—
478#124—1462no—
479#124—1468no—
480#124—1462no—
481#123—1468no—
482#123—1468no—
483C4×Q8—22no—
484C4×Q8—734no—
485C4×Q8—734no—
486C4×Q8—734no—
487C4×Q8—734no—
488C4×Q8—734no—
489C4×Q8—1468no—
490C4×Q8—1462no—
491C4×Q8—1462no—
492C4×Q8—1462no—
493C4×Q8C22×D7314yes—
494C4×D4—22no—
495C4×D4—734no—
496C4×D4—1462no—
497C4×D4—1468no—
498C4×D4C22×D7314yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4C22×D7311yescharacteristic
512C2×C4⋊C4C22×D7311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C42—21no—
520C2×C42—731no—
521C2×C42—731no—
522C2×C42—1461no—
523C2×C42—1461no—
524C2×C42—1461no—
525C2×C42C22×D7311yescharacteristic
526#107—734no—
527#107—734no—
528#107C22×D7314yes—
529C4⋊C8—734no—
530C4⋊C8—734no—
531C4⋊C8—734no—
532#103—734no—
533#103—734no—
534#103—734no—
535#103C22×D7314yes—
536#102—734no—
537#102—734no—
538#102—734no—
539#102—734no—
540#102—734no—
541#102C22×D7314yes—
542#97—734no—
543#97C22×D7314yes—
544C4×C8—734no—
545C24—21no—
546C24—1461no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—5842no—
550C2×Q8—5842no—
551C2×Q8—5842no—
552C2×Q8—734no—
553C2×Q8—732no—
554C2×Q8—1464no—
555C2×Q8—1464no—
556C2×Q8—1464no—
557C2×Q8—1462no—
558C2×Q8—1462no—
559C2×Q8—1461no—
560C2×Q8—1464no—
561C2×Q8#1192402814yes—
562C2×Q8C23×D7312yes—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—2924no—
567C2×D4—5842no—
568C2×D4—732no—
569C2×D4—1464no—
570C2×D4—1464no—
571C2×D4—1461no—
572C2×D4—1462no—
573C2×D4—1462no—
574C2×D4C23×D7312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—5842no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—1464no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4D4×D7311yescharacteristic
590C22×C4D4×D7311yescharacteristic
591C22×C4C23×D7311yescharacteristic
592Q16—1468no—
593SD16—28no—
594SD16—1468no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—732no—
598C2×C8—732no—
599C2×C8—1462no—
600C2×C8—1462no—
601C2×C8C23×D7312yes—
602C2×C8C23×D7312yes—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—734no—
607C4⋊C4—734no—
608C4⋊C4—734no—
609C4⋊C4—732no—
610C4⋊C4—732no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1461no—
617C4⋊C4—1461no—
618C4⋊C4—1464no—
619C4⋊C4C23×D7312yes—
620C4⋊C4C23×D7312yes—
621C22⋊C4—24no—
622C22⋊C4—1464no—
623C22⋊C4—1464no—
624C22⋊C4—1464no—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C42—24no—
628C42—732no—
629C42—732no—
630C42—732no—
631C42—732no—
632C42—1464no—
633C42—1464no—
634C42—1464no—
635C42D4×D7312yes—
636C42C23×D7312yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—2922no—
642C23—2922no—
643C23—2922no—
644C23—1462no—
645C23C2×D4×D7311yescharacteristic
646Q8—22no—
647Q8—24no—
648Q8—2922no—
649Q8—5844no—
650Q8—5844no—
651Q8—5844no—
652Q8—1468no—
653Q8—1462no—
654Q8—1462no—
655Q8C2×#1192402814yes—
656D4—22no—
657D4—22no—
658D4—42no—
659D4—2928no—
660D4—2922no—
661D4—5844no—
662D4—1462no—
663D4—1462no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—5844no—
677C2×C4—734no—
678C2×C4—732no—
679C2×C4—732no—
680C2×C4—732no—
681C2×C4—732no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4C2×D4×D7312yes—
689C2×C4C2×D4×D7312yes—
690C2×C4C2×D4×D7311yescharacteristic
691C2×C4C2×#1192402812yes—
692C2×C4#1455663812yes—
693C2×C4C24×D7311yescharacteristic
694C8—22no—
695C8—22no—
696C8—1462no—
697C8—1462no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—2922no—
703C22—2922no—
704C22—2922no—
705C22—5844no—
706C22#1798924612yes—
707C22#137×D7312yes—
708C22#1798939112yes—
709C22C22×D4×D7311yescharacteristic
710C4—22no—
711C4—24no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—2922no—
716C4—2922no—
717C4—2922no—
718C4—734no—
719C4—1462no—
720C4—1462no—
721C4—1462no—
722C4#1798924612yes—
723C4C22×#1192402811yescharacteristic
724C4C2×#1455663811yescharacteristic
725C2—82no—
726C2—5842no—
727C2#2262274614yesdirect product factor
728C2C2×#1798924611yescharacteristic
729C2C2×#137×D7311yescharacteristic
730C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556587C22
hypercenterC2×#440D73
hypocenterC73C2×#3375
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
2. C2×Q8×Dic146C2semidirect
3. #22622746C2direct (N × H)
4. C2×#17988947C2semidirect
5. C2×#17988945C2semidirect
7. C2×#17988881C2semidirect
8. C2×#17988867C2semidirect
9. C2×#17988866C2semidirect
10. C2×#17988809C2semidirect
11. C2×#17988807C2semidirect
13. C2×#17988715C2semidirect
14. C2×#17988690C2semidirect
15. C2×#17988679C2semidirect
16. C2×#440×C73C2semidirect
22. Q8×Dic146C22semidirect
42. #17988947C22semidirect
43. #17988945C22semidirect
45. #17988881C22semidirect
46. #17988867C22semidirect
47. #17988866C22semidirect
48. #17988809C22semidirect
49. #17988807C22semidirect
51. #17988715C22semidirect
52. #17988690C22semidirect
53. #17988679C22semidirect
72. #440×C73C22semidirect
361. C2×C73#3375semidirect
380. C2×#440D73semidirect
382. C73C2×#3375semidirect
422. #440C2×D73semidirect
727. C2#22622746direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893202
C2×Q8×Dic1462
#226227462
C2×#179889472
C2×#179889452
C2×#179889322
C2×#179888812
C2×#179888672
C2×#179888662
C2×#179888092
C2×#179888072
C2×#179887852
C2×#179887152
C2×#179886902
C2×#179886792
C2×#440×C732
C2×#337573