Finite Group Databasebeta

← C2×#22621034 #33957373

Subgroups — C2×#22621034 #33957373

Order 18688.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989163C211yesmaximal, characteristic, complemented
2#22621034C2116yesmaximal, direct product factor
3C2×#17988982C211yesmaximal, characteristic, complemented
4C2×#17988969C211yesmaximal, characteristic, complemented
5C2×#17988949C211yesmaximal, characteristic, complemented
6C2×#17988939C211yesmaximal, characteristic, complemented
7C2×#17988809C211yesmaximal, characteristic, complemented
8C2×#17988797C211yesmaximal, characteristic, complemented
9C2×#17988802C211yesmaximal, characteristic, complemented
10C2×#17988792C211yesmaximal, characteristic, complemented
11C2×#17988747C211yesmaximal, characteristic, complemented
12C2×#17988730C211yesmaximal, characteristic
13C2×#17988742C211yesmaximal, characteristic, complemented
14C2×#17988725C211yesmaximal, characteristic, complemented
15C2×#17988648C211yesmaximal, characteristic, complemented
16C2×#542×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924018C2211yescharacteristic
22C22×#11924016C2211yescharacteristic
23C22×#11924016C2211yescharacteristic
24C22×#11924016C2211yescharacteristic
25C22×#11924015C2211yescharacteristic
26C22×#11924013C2211yescharacteristic
27#17989163—24no—
28#17989163C2218yescomplemented
29C2×#14556591C2211yescharacteristic
30C2×#14556591C2211yescharacteristic
31C2×#14556579C2211yescharacteristic
32C2×#14556579C2211yescharacteristic
33C2×#14556575—21no—
34C2×#14556575—21no—
35C2×#14556571—21no—
36C2×#14556571—21no—
37#17988982C2218yescomplemented
38#17988969C2218yescomplemented
39#17988949C2218yescomplemented
40#17988939C2218yescomplemented
41#17988809C2218yescomplemented
42#17988802C2218yescomplemented
43#17988797C2218yescomplemented
44#17988792C2218yescomplemented
45#17988747C2218yescomplemented
46#17988742C2218yescomplemented
47#17988730C2218yes—
48#17988725C2218yescomplemented
49#17988648C2218yescomplemented
50C2×C4⋊#10596831C2211yescharacteristic
51C2×C4⋊#10596831C2211yescharacteristic
52C2×#14556514C2211yescharacteristic
53C2×#14556514C2211yescharacteristic
54C2×#14556514C2211yescharacteristic
55C2×#14556514C2211yescharacteristic
56C2×#14556514C2211yescharacteristic
57C2×#14556514C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×C22⋊#10596831C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#542×C73—24no—
65#542×C73C2218yescomplemented
66C2×C4⋊Q8×C73C2211yescharacteristic
67C2×#126×C73—21no—
68C2×#124×C73—21no—
69C2×#124×C73C2211yescharacteristic
70C2×#123×C73—21no—
71C2×C22⋊Q8×C73—21no—
72C2×C22⋊Q8×C73C2211yescharacteristic
73C2×#121×C73C2211yescharacteristic
74C2×C4×Q8×C73C2211yescharacteristic
75C2×C4×D4×C73C2211yescharacteristic
76C2×#117×C73C2211yescharacteristic
77C2×#11924028—22no—
78C2×#11924028—42no—
79C2×#11924028—42no—
80C2×#11924028C2314yes—
81C22×Dic146—22no—
82C22×Dic146—21no—
83C22×Dic146—42no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2311yescharacteristic
88C22×Dic146C2314yes—
89C22×D292C2311yescharacteristic
90C22×C22⋊D73—21no—
91C23×Dic73—21no—
92C22×C4×D73—21no—
93C2×#11924018—42no—
94C2×#11924018—42no—
95C2×#11924018—42no—
96C2×#11924018C2314yes—
97C2×#11924018C2314yes—
98C2×#11924018C2314yes—
99C2×#11924016—42no—
100C2×#11924016—42no—
101C2×#11924016—42no—
102C2×#11924016C2314yes—
103C2×#11924016C2314yes—
104C2×#11924016C2314yes—
105C2×#11924015—42no—
106C2×#11924015C2314yes—
107C2×#11924013—42no—
108C2×#11924013C2314yes—
109C22×#10596831C2311yescharacteristic
110C22×#10596831C2311yescharacteristic
111C22×#10596831C2311yescharacteristic
112C22×#10596831C2311yescharacteristic
113#14556591—22no—
114#14556591—22no—
115#14556591C2314yes—
116#14556591C2314yes—
117#14556579—22no—
118#14556579—22no—
119#14556579C2314yes—
120#14556579C2314yes—
121#14556575—28no—
122#14556575—28no—
123#14556571—28no—
124#14556571—28no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—21no—
129C2×#11924005—21no—
130C2×#11924005—21no—
131C2×#11924005—21no—
132C2×#11924005—21no—
133C4⋊#10596831C2314yes—
134C4⋊#10596831C2314yes—
135#14556514C2314yes—
136#14556514C2314yes—
137#14556514C2314yes—
138#14556514C2314yes—
139#14556514C2314yes—
140#14556514C2314yes—
141#14556511C2314yes—
142#14556511C2314yes—
143C22⋊#10596831C2314yes—
144C22⋊#10596831C2314yes—
145#14556502C2314yes—
146C4×#10596831C2314yes—
147C22×Q8×C73—21no—
148C22×Q8×C73C2311yescharacteristic
149C22×D4×C73—21no—
150C22×D4×C73C2311yescharacteristic
151C23×C4×C73—21no—
152C23×C4×C73C2311yescharacteristic
153C4⋊Q8×C73—22no—
154C4⋊Q8×C73C2314yes—
155#126×C73—28no—
156#124×C73—28no—
157#124×C73—22no—
158#124×C73C2314yes—
159#123×C73—28no—
160C22⋊Q8×C73—22no—
161C22⋊Q8×C73—28no—
162C22⋊Q8×C73C2314yes—
163#121×C73—22no—
164#121×C73C2314yes—
165C4×Q8×C73—22no—
166C4×Q8×C73C2314yes—
167C4×D4×C73—22no—
168C4×D4×C73C2314yes—
169#117×C73D414yes—
170#117×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73D411yescharacteristic
175C2×C4⋊C4×C73D411yescharacteristic
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182C2×C22⋊C4×C73—21no—
183C2×C22⋊C4×C73D411yescharacteristic
184C2×C22⋊C4×C73D411yescharacteristic
185C2×C42×C73—21no—
186C2×C42×C73C2311yescharacteristic
187C2×C42×C73C2311yescharacteristic
188C23×D73—21no—
189#11924028—44no—
190#11924028—44no—
191#11924028—48no—
192C2×Dic146—22no—
193C2×Dic146—22no—
194C2×Dic146—22no—
195C2×Dic146—22no—
196C2×Dic146—22no—
197C2×Dic146—22no—
198C2×Dic146—24no—
199C2×Dic146—21no—
200C2×Dic146—21no—
201C2×Dic146—21no—
202C2×Dic146—44no—
203C2×Dic146—44no—
204C2×Dic146—44no—
205C2×Dic146—48no—
206C2×Dic146C2412yes—
207C2×Dic146C2412yes—
208C2×Dic146C2412yes—
209C2×D292—22no—
210C2×D292—22no—
211C2×D292—21no—
212C2×D292C2412yes—
213C2×C22⋊D73—24no—
214C2×C22⋊D73—44no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—24no—
219C22×Dic73—44no—
220C2×C4×D73—24no—
221C2×C4×D73—44no—
222#11924018—44no—
223#11924018—44no—
224#11924018—44no—
225#11924016—44no—
226#11924016—44no—
227#11924016—44no—
228#11924015—44no—
229#11924013—44no—
230C2×#10596831—22no—
231C2×#10596831—22no—
232C2×#10596831—22no—
233C2×#10596831—22no—
234C2×#10596831C2412yes—
235C2×#10596831C2412yes—
236C2×#10596831C2412yes—
237C2×#10596831C2412yes—
238C4⋊Dic73—24no—
239C4⋊Dic73—24no—
240C4⋊Dic73—24no—
241C4⋊Dic73—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005—24no—
246C24×C73—21no—
247C24×C73C2×D411yescharacteristic
248C2×Q8×C73—21no—
249C2×Q8×C73—24no—
250C2×Q8×C73—22no—
251C2×Q8×C73—22no—
252C2×Q8×C73—82no—
253C2×Q8×C73C2412yes—
254C2×D4×C73—24no—
255C2×D4×C73—21no—
256C2×D4×C73—22no—
257C2×D4×C73—22no—
258C2×D4×C73—82no—
259C2×D4×C73C2412yes—
260C22×C4×C73—22no—
261C22×C4×C73—22no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—24no—
266C22×C4×C73—82no—
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2×D411yescharacteristic
271C22×C4×C73C2×D411yescharacteristic
272C22×C4×C73C2×D412yes—
273C22×C4×C73C2412yes—
274C22×C4×C73C2411yescharacteristic
275C4⋊C4×C73—24no—
276C4⋊C4×C73—24no—
277C4⋊C4×C73—24no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73C2×D414yes—
281C4⋊C4×C73C2×D414yes—
282C4⋊C4×C73C2412yes—
283C4⋊C4×C73C2412yes—
284C22⋊C4×C73—24no—
285C22⋊C4×C73—24no—
286C22⋊C4×C73—24no—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—24no—
289C22⋊C4×C73C2×D414yes—
290C22⋊C4×C73C2×D414yes—
291C42×C73—24no—
292C42×C73C2×D412yes—
293C42×C73C2×D412yes—
294C42×C73C2412yes—
295C42×C73C2412yes—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—42no—
301C23×C73—42no—
302C23×C73—42no—
303C23×C73C22×D412yes—
304C23×C73C22×D411yescharacteristic
305C22×D73—22no—
306C22×D73—42no—
307C22×D73—42no—
308C22×D73—42no—
309Q8×C73—22no—
310Q8×C73—22no—
311Q8×C73—42no—
312Q8×C73—84no—
313D4×C73—22no—
314D4×C73—22no—
315D4×C73—42no—
316D4×C73—84no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—24no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—42no—
329C2×C4×C73—42no—
330C2×C4×C73—42no—
331C2×C4×C73—84no—
332C2×C4×C73C22×D412yes—
333C2×C4×C73C22×D412yes—
334C2×C4×C73C22×D412yes—
335C2×C4×C73C22×D412yes—
336C2×C4×C73C22×D412yes—
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73H(5,𝔽2)12yes—
339C2×C4×C73H(5,𝔽2)12yes—
340C2×C4×C73C2511yescharacteristic
341C22⋊D73—48no—
342C2×Dic73—22no—
343C2×Dic73—22no—
344C2×Dic73—22no—
345C2×Dic73—48no—
346C2×Dic73—42no—
347C2×Dic73—42no—
348C2×Dic73—42no—
349D292—22no—
350D292—22no—
351D292—42no—
352C4×D73—48no—
353Dic146—22no—
354Dic146—22no—
355Dic146—22no—
356Dic146—22no—
357Dic146—22no—
358Dic146—22no—
359Dic146—48no—
360Dic146—42no—
361Dic146—42no—
362Dic146—42no—
363#10596831—22no—
364#10596831—22no—
365#10596831—22no—
366#10596831—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—44no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—84no—
375C22×C73#53512yes—
376C22×C73#57712yes—
377C22×C73#57812yes—
378C22×C73C23×D411yescharacteristic
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C2×D73—84no—
383C4×C73—22no—
384C4×C73—22no—
385C4×C73—22no—
386C4×C73—22no—
387C4×C73—22no—
388C4×C73—42no—
389C4×C73—42no—
390C4×C73—42no—
391C4×C73#53512yes—
392C4×C73C2×H(5,𝔽2)11yescharacteristic
393C4×C73C2×H(5,𝔽2)11yescharacteristic
394Dic73—42no—
395Dic73—42no—
396Dic73—42no—
397C2×#3225—731nomaximal, Sylow
398C2×C73—42no—
399C2×C73—82no—
400C2×C73#322514yescomplemented
401C2×C73C2×#53511yescharacteristic
402C2×C73C2×#57711yescharacteristic
403C2×C73C2×#57811yescharacteristic
404D73—82no—
405C2×#542D7311yescharacteristic, complemented
406C2×#536—731no—
407#3225—7316no—
408C2×#497—731no—
409C2×#495—731no—
410C2×#489—731no—
411C2×#487—731no—
412C2×#464—731no—
413C2×#462—731no—
414C2×#463—731no—
415C2×#461—731no—
416C2×#452—731no—
417C2×#449—731no—
418C2×#451—731no—
419C2×#448—731no—
420C2×#433—731no—
421C73C2×#322511yescharacteristic, complemented, Sylow
422C22×#41—731no—
423C23×Q8—731no—
424C22×Q16—731no—
425C22×Q16—731no—
426C22×Q16—731no—
427C22×SD16—731no—
428C22×SD16—731no—
429C22×SD16—731no—
430C22×SD16—731no—
431C22×D8—731no—
432#542—24no—
433#542C2×D7318yescomplemented
434#536—738no—
435#536—1464no—
436C2×C4⋊Q8—731no—
437C2×C4⋊Q8—731no—
438C2×C4⋊Q8C2×D7311yescharacteristic
439C2×#126—21no—
440C2×#124—21no—
441C2×#124—731no—
442C2×#124—731no—
443C2×#124C2×D7311yescharacteristic
444C2×#123—21no—
445C2×#123—1461no—
446C2×#123—1461no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—1461no—
449C2×C22⋊Q8—1461no—
450C2×C22⋊Q8C2×D7311yescharacteristic
451C2×#121C2×D7311yescharacteristic
452C2×C4×Q8C2×D7311yescharacteristic
453C2×C4×D4C2×D7311yescharacteristic
454C2×#117C2×D7311yescharacteristic
455#497—738no—
456#495—738no—
457#489—738no—
458#487—738no—
459#464—738no—
460#463—738no—
461#462—738no—
462#461—738no—
463#452—738no—
464#451—738no—
465#449—738no—
466#448—738no—
467#433—738no—
468C2×C4⋊C8—731no—
469C2×C4⋊C8—731no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#103—731no—
473C2×#103—731no—
474C2×#103—731no—
475C2×#103—731no—
476C2×#102—731no—
477C2×#102—731no—
478C2×C22⋊C8—731no—
479C2×C22⋊C8—731no—
480C2×#97—731no—
481C2×C4×C8—731no—
482C2×#41—2922no—
483C2×#41—2922no—
484C2×#41—734no—
485C2×#41—1462no—
486C22×Q8—21no—
487C22×Q8—2922no—
488C22×Q8—2922no—
489C22×Q8—734no—
490C22×Q8—731no—
491C22×Q8—731no—
492C22×Q8—731no—
493C22×Q8—1461no—
494C22×Q8—1462no—
495C22×Q8C22×D7311yescharacteristic
496C22×D4—21no—
497C22×D4—731no—
498C22×D4—1461no—
499C22×D4C22×D7311yescharacteristic
500C23×C4—21no—
501C23×C4—1461no—
502C23×C4—1461no—
503C23×C4C22×D7311yescharacteristic
504C2×Q16—2922no—
505C2×Q16—2922no—
506C2×Q16—2922no—
507C2×Q16—734no—
508C2×Q16—734no—
509C2×Q16—734no—
510C2×SD16—2922no—
511C2×SD16—2922no—
512C2×SD16—2922no—
513C2×SD16—2922no—
514C2×SD16—734no—
515C2×SD16—734no—
516C2×SD16—734no—
517C2×SD16—734no—
518C2×D8—2922no—
519C2×D8—734no—
520C22×C8—731no—
521C22×C8—731no—
522C22×C8—731no—
523C22×C8—731no—
524C4⋊Q8—22no—
525C4⋊Q8—734no—
526C4⋊Q8—734no—
527C4⋊Q8—1462no—
528C4⋊Q8—1462no—
529C4⋊Q8C22×D7314yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—734no—
534#124—734no—
535#124—1462no—
536#124—1462no—
537#124C22×D7314yes—
538#123—28no—
539#123—1468no—
540#123—1468no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—1468no—
544C22⋊Q8—1468no—
545C22⋊Q8C22×D7314yes—
546#121—22no—
547#121C22×D7314yes—
548C4×Q8—22no—
549C4×Q8C22×D7314yes—
550C4×D4—22no—
551C4×D4C22×D7314yes—
552#117C22⋊D7314yes—
553#117C22×D7314yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4—1461no—
559C2×C4⋊C4—1461no—
560C2×C4⋊C4—1461no—
561C2×C4⋊C4C22⋊D7311yescharacteristic
562C2×C4⋊C4C22⋊D7311yescharacteristic
563C2×C4⋊C4C22×D7311yescharacteristic
564C2×C4⋊C4C22×D7311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1461no—
571C2×C22⋊C4—1461no—
572C2×C22⋊C4—1461no—
573C2×C22⋊C4—1461no—
574C2×C22⋊C4C22⋊D7311yescharacteristic
575C2×C22⋊C4C22⋊D7311yescharacteristic
576C2×C42—21no—
577C2×C42C22×D7311yescharacteristic
578C2×C42C22×D7311yescharacteristic
579C4⋊C8—734no—
580C4⋊C8—734no—
581#103—734no—
582#103—734no—
583#103—734no—
584#103—734no—
585#103—734no—
586#103—734no—
587#102—734no—
588#102—734no—
589C22⋊C8—734no—
590C22⋊C8—734no—
591#97—734no—
592C4×C8—734no—
593C24—21no—
594C24—1461no—
595C24C2×C22⋊D7311yescharacteristic
596#41—2928no—
597#41—2924no—
598#41—2924no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—2924no—
605C2×Q8—2928no—
606C2×Q8—2924no—
607C2×Q8—2924no—
608C2×Q8—732no—
609C2×Q8—732no—
610C2×Q8—732no—
611C2×Q8—1462no—
612C2×Q8—1462no—
613C2×Q8—1462no—
614C2×Q8—1462no—
615C2×Q8—1462no—
616C2×Q8—1462no—
617C2×Q8—1464no—
618C2×Q8—1461no—
619C2×Q8—1461no—
620C2×Q8—1461no—
621C2×Q8C23×D7312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—2924no—
628C2×D4—732no—
629C2×D4—1464no—
630C2×D4—1461no—
631C2×D4—1462no—
632C2×D4—1462no—
633C2×D4C23×D7312yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—2924no—
642C22×C4—2924no—
643C22×C4—1464no—
644C22×C4—1461no—
645C22×C4—1461no—
646C22×C4—1461no—
647C22×C4—1464no—
648C22×C4C2×C22⋊D7312yes—
649C22×C4C2×C22⋊D7311yescharacteristic
650C22×C4C2×C22⋊D7311yescharacteristic
651C22×C4C2×C22⋊D7311yescharacteristic
652C22×C4C2×C22⋊D7311yescharacteristic
653C22×C4C2×C22⋊D7311yescharacteristic
654C22×C4C23×D7312yes—
655C22×C4C23×D7311yescharacteristic
656Q16—2924no—
657Q16—2924no—
658Q16—2924no—
659SD16—2924no—
660SD16—2924no—
661SD16—2924no—
662SD16—2924no—
663D8—2924no—
664C2×C8—732no—
665C2×C8—732no—
666C2×C8—732no—
667C2×C8—732no—
668C2×C8—1462no—
669C2×C8—1462no—
670C2×C8—1462no—
671C2×C8—1462no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—1464no—
678C4⋊C4—1464no—
679C4⋊C4—1464no—
680C4⋊C4—1464no—
681C4⋊C4C2×C22⋊D7314yes—
682C4⋊C4C2×C22⋊D7314yes—
683C4⋊C4C23×D7312yes—
684C4⋊C4C23×D7312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—1464no—
691C22⋊C4—1464no—
692C22⋊C4—1464no—
693C22⋊C4—1464no—
694C22⋊C4C2×C22⋊D7314yes—
695C22⋊C4C2×C22⋊D7314yes—
696C42—24no—
697C42C2×C22⋊D7312yes—
698C42C2×C22⋊D7312yes—
699C42C23×D7312yes—
700C42C23×D7312yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—2922no—
709C23—2922no—
710C23—2922no—
711C23—1462no—
712C23C22×C22⋊D7312yes—
713C23C22×C22⋊D7311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—2928no—
719Q8—2922no—
720Q8—2922no—
721Q8—2922no—
722Q8—1462no—
723Q8—1462no—
724Q8—1462no—
725Q8—1462no—
726Q8—1462no—
727Q8—1462no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—2928no—
733D4—2922no—
734D4—1462no—
735D4—1462no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—2928no—
752C2×C4—2928no—
753C2×C4—2922no—
754C2×C4—2922no—
755C2×C4—2922no—
756C2×C4—1462no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4C22×C22⋊D7312yes—
760C2×C4C22×C22⋊D7312yes—
761C2×C4C22×C22⋊D7312yes—
762C2×C4C22×C22⋊D7312yes—
763C2×C4C22×C22⋊D7312yes—
764C2×C4C22×C22⋊D7311yescharacteristic
765C2×C4#1455663712yes—
766C2×C4#1455663712yes—
767C2×C4C24×D7311yescharacteristic
768C8—1462no—
769C8—1462no—
770C8—1462no—
771C8—1462no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—2922no—
781C22—2922no—
782C22—2922no—
783C22—5844no—
784C22#1798915112yes—
785C22#1798939812yes—
786C22#1798940212yes—
787C22C23×C22⋊D7311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2922no—
797C4—2922no—
798C4—2922no—
799C4#1798915112yes—
800C4C2×#1455663711yescharacteristic
801C4C2×#1455663711yescharacteristic
802C2—42no—
803C2—82no—
804C2—5842no—
805C2#2262103414yesdirect product factor
806C2C2×#1798915111yescharacteristic
807C2C2×#1798939811yescharacteristic
808C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#542×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988730C2
hypercenterC2×#542D73
hypocenterC73C2×#3225
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17989163C2semidirect
2. #22621034C2direct (N × H)
3. C2×#17988982C2semidirect
4. C2×#17988969C2semidirect
5. C2×#17988949C2semidirect
6. C2×#17988939C2semidirect
7. C2×#17988809C2semidirect
8. C2×#17988797C2semidirect
9. C2×#17988802C2semidirect
10. C2×#17988792C2semidirect
11. C2×#17988747C2semidirect
13. C2×#17988742C2semidirect
14. C2×#17988725C2semidirect
15. C2×#17988648C2semidirect
16. C2×#542×C73C2semidirect
28. #17989163C22semidirect
37. #17988982C22semidirect
38. #17988969C22semidirect
39. #17988949C22semidirect
40. #17988939C22semidirect
41. #17988809C22semidirect
42. #17988802C22semidirect
43. #17988797C22semidirect
44. #17988792C22semidirect
45. #17988747C22semidirect
46. #17988742C22semidirect
48. #17988725C22semidirect
49. #17988648C22semidirect
65. #542×C73C22semidirect
400. C2×C73#3225semidirect
405. C2×#542D73semidirect
421. C73C2×#3225semidirect
433. #542C2×D73semidirect
805. C2#22621034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891632
#226210342
C2×#179889822
C2×#179889692
C2×#179889492
C2×#179889392
C2×#179888092
C2×#179887972
C2×#179888022
C2×#179887922
C2×#179887472
C2×#179887302
C2×#179887422
C2×#179887252
C2×#179886482
C2×#542×C732
C2×#322573