Finite Group Databasebeta

← C2×#22621040 #33957379

Subgroups — C2×#22621040 #33957379

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×#17989208C211yesmaximal, characteristic, complemented
2#22621040C2116yesmaximal, direct product factor
3C2×#17988979C211yesmaximal, characteristic, complemented
4C2×#17988969C211yesmaximal, characteristic, complemented
5C2×#17988946C211yesmaximal, characteristic, complemented
6C2×#17988937C211yesmaximal, characteristic, complemented
7C2×#17988806C211yesmaximal, characteristic, complemented
8C2×#17988794C211yesmaximal, characteristic, complemented
9C2×#17988799C211yesmaximal, characteristic, complemented
10C2×#17988789C211yesmaximal, characteristic, complemented
11C2×#17988749C211yesmaximal, characteristic, complemented
12C2×#17988732C211yesmaximal, characteristic
13C2×#17988743C211yesmaximal, characteristic, complemented
14C2×#17988726C211yesmaximal, characteristic, complemented
15C2×#17988648C211yesmaximal, characteristic, complemented
16C2×#536×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×#11924015C2211yescharacteristic
23C22×#11924015C2211yescharacteristic
24C22×#11924013C2211yescharacteristic
25#17989208—24no—
26#17989208C2218yescomplemented
27C2×#14556591C2211yescharacteristic
28C2×#14556586—21no—
29C2×#14556579C2211yescharacteristic
30C2×#14556577—21no—
31C2×#14556573—21no—
32C2×#14556570C2211yescharacteristic
33C2×#14556569—21no—
34C2×#14556565C2211yescharacteristic
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37#17988979C2218yescomplemented
38#17988969C2218yescomplemented
39#17988946C2218yescomplemented
40#17988937C2218yescomplemented
41#17988806C2218yescomplemented
42#17988799C2218yescomplemented
43#17988794C2218yescomplemented
44#17988789C2218yescomplemented
45#17988749C2218yescomplemented
46#17988743C2218yescomplemented
47#17988732C2218yes—
48#17988726C2218yescomplemented
49#17988648C2218yescomplemented
50C2×C4⋊#10596831C2211yescharacteristic
51C2×C4⋊#10596831C2211yescharacteristic
52C2×#14556515C2211yescharacteristic
53C2×#14556515C2211yescharacteristic
54C2×#14556515C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556515C2211yescharacteristic
58C2×#14556512C2211yescharacteristic
59C2×#14556512C2211yescharacteristic
60C2×C22⋊#10596831C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64C22×#41×C73C2211yescharacteristic
65C23×Q8×C73C2211yescharacteristic
66#536×C73—24no—
67#536×C73C2218yescomplemented
68C2×C4⋊Q8×C73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#124×C73C2211yescharacteristic
71C2×#124×C73C2211yescharacteristic
72C2×#123×C73—21no—
73C2×#123×C73—21no—
74C2×C22⋊Q8×C73—21no—
75C2×C22⋊Q8×C73—21no—
76C2×#117×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C4×D73—21no—
82C2×#11924018—42no—
83C2×#11924018—42no—
84C2×#11924018—42no—
85C2×#11924018C2314yes—
86C2×#11924018C2314yes—
87C2×#11924018C2314yes—
88C2×#11924016—42no—
89C2×#11924016C2314yes—
90C2×#11924015—42no—
91C2×#11924015—42no—
92C2×#11924015—42no—
93C2×#11924015C2314yes—
94C2×#11924015C2314yes—
95C2×#11924015C2314yes—
96C2×#11924013—42no—
97C2×#11924013C2314yes—
98C22×#10596831C2311yescharacteristic
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2311yescharacteristic
102#14556591—22no—
103#14556591C2314yes—
104#14556586—28no—
105#14556579—22no—
106#14556579C2314yes—
107#14556577—28no—
108#14556573—28no—
109#14556570—22no—
110#14556570C2314yes—
111#14556569—28no—
112#14556565—22no—
113#14556565C2314yes—
114C4×Dic146—22no—
115C4×Dic146C2314yes—
116C4×D292—22no—
117C4×D292C2314yes—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73C2311yescharacteristic
120C2×C4⋊Dic73C2311yescharacteristic
121C2×#11924007—21no—
122C2×#11924007—21no—
123C2×C22⋊Dic73—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×#11924005—21no—
127C2×#11924005—21no—
128C2×C4×Dic73—21no—
129C4⋊#10596831C2314yes—
130C4⋊#10596831C2314yes—
131#14556515C2314yes—
132#14556515C2314yes—
133#14556515C2314yes—
134#14556515C2314yes—
135#14556515C2314yes—
136#14556515C2314yes—
137#14556512C2314yes—
138#14556512C2314yes—
139C22⋊#10596831C2314yes—
140C22⋊#10596831C2314yes—
141#14556502C2314yes—
142C4×#10596831C2314yes—
143C2×#41×C73—22no—
144C2×#41×C73—42no—
145C2×#41×C73—42no—
146C2×#41×C73C2314yes—
147C22×Q8×C73—21no—
148C22×Q8×C73—22no—
149C22×Q8×C73—42no—
150C22×Q8×C73—42no—
151C22×Q8×C73C2311yescharacteristic
152C22×Q8×C73C2311yescharacteristic
153C22×Q8×C73C2311yescharacteristic
154C22×Q8×C73C2314yes—
155C22×D4×C73—21no—
156C22×D4×C73C2311yescharacteristic
157C23×C4×C73—21no—
158C23×C4×C73—21no—
159C23×C4×C73C2311yescharacteristic
160C4⋊Q8×C73—22no—
161C4⋊Q8×C73—22no—
162C4⋊Q8×C73C2314yes—
163C4⋊Q8×C73C2314yes—
164#124×C73—22no—
165#124×C73—22no—
166#124×C73C2314yes—
167#124×C73C2314yes—
168#123×C73—28no—
169#123×C73—28no—
170C22⋊Q8×C73—28no—
171C22⋊Q8×C73—28no—
172#117×C73D414yes—
173#117×C73C2314yes—
174C2×C4⋊C4×C73—21no—
175C2×C4⋊C4×C73—21no—
176C2×C4⋊C4×C73—21no—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73D411yescharacteristic
179C2×C4⋊C4×C73D411yescharacteristic
180C2×C22⋊C4×C73—21no—
181C2×C22⋊C4×C73—21no—
182C2×C22⋊C4×C73—21no—
183C2×C22⋊C4×C73—21no—
184C2×C22⋊C4×C73D411yescharacteristic
185C2×C22⋊C4×C73D411yescharacteristic
186C2×C42×C73C2311yescharacteristic
187C2×C42×C73C2311yescharacteristic
188C23×D73—21no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—21no—
192C2×Dic146—24no—
193C2×Dic146—82no—
194C2×Dic146C2412yes—
195C2×D292—22no—
196C2×D292—22no—
197C2×D292—21no—
198C2×D292C2412yes—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—82no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C2×C4×D73—24no—
205C2×C4×D73—82no—
206#11924018—44no—
207#11924018—44no—
208#11924018—44no—
209#11924016—44no—
210#11924015—44no—
211#11924015—44no—
212#11924015—44no—
213#11924013—44no—
214C2×#10596831—22no—
215C2×#10596831—22no—
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C2×#10596831C2412yes—
221C2×#10596831C2412yes—
222C4⋊Dic73—24no—
223C4⋊Dic73—21no—
224C4⋊Dic73—21no—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229C22⋊Dic73—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234C4×Dic73—24no—
235C24×C73—21no—
236C24×C73C2×D411yescharacteristic
237#41×C73—44no—
238#41×C73—44no—
239#41×C73—48no—
240C2×Q8×C73—24no—
241C2×Q8×C73—21no—
242C2×Q8×C73—21no—
243C2×Q8×C73—21no—
244C2×Q8×C73—22no—
245C2×Q8×C73—22no—
246C2×Q8×C73—22no—
247C2×Q8×C73—22no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73—44no—
251C2×Q8×C73—44no—
252C2×Q8×C73—44no—
253C2×Q8×C73—48no—
254C2×Q8×C73C2412yes—
255C2×Q8×C73C2412yes—
256C2×Q8×C73C2412yes—
257C2×D4×C73—24no—
258C2×D4×C73—21no—
259C2×D4×C73—22no—
260C2×D4×C73—22no—
261C2×D4×C73—44no—
262C2×D4×C73C2412yes—
263C22×C4×C73—22no—
264C22×C4×C73—22no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—24no—
269C22×C4×C73—24no—
270C22×C4×C73—44no—
271C22×C4×C73—44no—
272C22×C4×C73C2×D411yescharacteristic
273C22×C4×C73C2×D411yescharacteristic
274C22×C4×C73C2×D411yescharacteristic
275C22×C4×C73C2×D411yescharacteristic
276C22×C4×C73C2×D411yescharacteristic
277C22×C4×C73C2×D412yes—
278C22×C4×C73C2412yes—
279C22×C4×C73C2411yescharacteristic
280C4⋊C4×C73—24no—
281C4⋊C4×C73—24no—
282C4⋊C4×C73—24no—
283C4⋊C4×C73—24no—
284C4⋊C4×C73C2×D414yes—
285C4⋊C4×C73C2×D414yes—
286C22⋊C4×C73—24no—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—24no—
289C22⋊C4×C73—24no—
290C22⋊C4×C73C2×D414yes—
291C22⋊C4×C73C2×D414yes—
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—22no—
312Q8×C73—22no—
313Q8×C73—22no—
314Q8×C73—22no—
315Q8×C73—48no—
316Q8×C73—42no—
317Q8×C73—42no—
318Q8×C73—42no—
319D4×C73—22no—
320D4×C73—22no—
321D4×C73—48no—
322D4×C73—42no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—24no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—48no—
335C2×C4×C73—48no—
336C2×C4×C73—42no—
337C2×C4×C73—42no—
338C2×C4×C73—42no—
339C2×C4×C73C22×D412yes—
340C2×C4×C73C22×D412yes—
341C2×C4×C73C22×D412yes—
342C2×C4×C73C22×D412yes—
343C2×C4×C73C22×D412yes—
344C2×C4×C73C22×D411yescharacteristic
345C2×C4×C73H(5,𝔽2)12yes—
346C2×C4×C73H(5,𝔽2)12yes—
347C2×C4×C73C2511yescharacteristic
348C22⋊D73—84no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—22no—
352C2×Dic73—42no—
353C2×Dic73—42no—
354C2×Dic73—42no—
355D292—22no—
356D292—22no—
357D292—42no—
358C4×D73—84no—
359Dic146—22no—
360Dic146—22no—
361Dic146—42no—
362Dic146—84no—
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×#542—731no—
406C2×#536D7311yescharacteristic, complemented
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×#41C2×D7311yescharacteristic
423C23×Q8C2×D7311yescharacteristic
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—738no—
433#542—1464no—
434#536—24no—
435#536C2×D7318yescomplemented
436C2×C4⋊Q8—731no—
437C2×C4⋊Q8C2×D7311yescharacteristic
438C2×C4⋊Q8C2×D7311yescharacteristic
439C2×#126—1461no—
440C2×#124—731no—
441C2×#124—1461no—
442C2×#124C2×D7311yescharacteristic
443C2×#124C2×D7311yescharacteristic
444C2×#123—21no—
445C2×#123—21no—
446C2×#123—1461no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—731no—
450C2×C22⋊Q8—1461no—
451C2×#121—731no—
452C2×C4×Q8—731no—
453C2×C4×D4—731no—
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—22no—
483C2×#41—42no—
484C2×#41—42no—
485C2×#41C22×D7314yes—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—42no—
489C22×Q8—42no—
490C22×Q8—731no—
491C22×Q8—1461no—
492C22×Q8C22×D7311yescharacteristic
493C22×Q8C22×D7311yescharacteristic
494C22×Q8C22×D7311yescharacteristic
495C22×Q8C22×D7314yes—
496C22×D4—21no—
497C22×D4—731no—
498C22×D4—1461no—
499C22×D4C22×D7311yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
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—22no—
526C4⋊Q8—734no—
527C4⋊Q8—1462no—
528C4⋊Q8C22×D7314yes—
529C4⋊Q8C22×D7314yes—
530#126—1468no—
531#124—22no—
532#124—22no—
533#124—734no—
534#124—1468no—
535#124—1462no—
536#124C22×D7314yes—
537#124C22×D7314yes—
538#123—28no—
539#123—28no—
540#123—1468no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—734no—
544C22⋊Q8—1462no—
545C22⋊Q8—1468no—
546#121—734no—
547#121—1462no—
548C4×Q8—734no—
549C4×Q8—1462no—
550C4×D4—734no—
551C4×D4—1462no—
552#117C22⋊D7314yes—
553#117C22×D7314yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—731no—
559C2×C4⋊C4—731no—
560C2×C4⋊C4—1461no—
561C2×C4⋊C4—1461no—
562C2×C4⋊C4—1461no—
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—1461no—
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—1461no—
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—44no—
597#41—44no—
598#41—48no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8—5842no—
614C2×Q8—732no—
615C2×Q8—1462no—
616C2×Q8—1462no—
617C2×Q8—1461no—
618C2×Q8—1464no—
619C2×Q8C23×D7312yes—
620C2×Q8C23×D7312yes—
621C2×Q8C23×D7312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—5842no—
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—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—5842no—
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—24no—
676C4⋊C4—732no—
677C4⋊C4—732no—
678C4⋊C4—1464no—
679C4⋊C4—1464no—
680C4⋊C4—1461no—
681C4⋊C4—1461no—
682C4⋊C4—1464no—
683C4⋊C4C2×C22⋊D7314yes—
684C4⋊C4C2×C22⋊D7314yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—1464no—
690C22⋊C4—1464no—
691C22⋊C4—1464no—
692C22⋊C4—1464no—
693C22⋊C4—1464no—
694C22⋊C4C2×C22⋊D7314yes—
695C22⋊C4C2×C22⋊D7314yes—
696C42—1464no—
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—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—2922no—
725Q8—5844no—
726Q8—1462no—
727Q8—1462no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—2922no—
733D4—5844no—
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—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—2922no—
753C2×C4—2922no—
754C2×C4—2922no—
755C2×C4—5844no—
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#1455663612yes—
766C2×C4#1455663612yes—
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#1798915412yes—
785C22#1798939512yes—
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#1798915412yes—
800C4C2×#1455663611yescharacteristic
801C4C2×#1455663611yescharacteristic
802C2—42no—
803C2—82no—
804C2—5842no—
805C2#2262104014yesdirect product factor
806C2C2×#1798915411yescharacteristic
807C2C2×#1798939511yescharacteristic
808C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#536×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988732C2
hypercenterC2×#536D73
hypocenterC73C2×#3225
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#17989208C2semidirect
2. #22621040C2direct (N × H)
3. C2×#17988979C2semidirect
4. C2×#17988969C2semidirect
5. C2×#17988946C2semidirect
6. C2×#17988937C2semidirect
7. C2×#17988806C2semidirect
8. C2×#17988794C2semidirect
9. C2×#17988799C2semidirect
10. C2×#17988789C2semidirect
11. C2×#17988749C2semidirect
13. C2×#17988743C2semidirect
14. C2×#17988726C2semidirect
15. C2×#17988648C2semidirect
16. C2×#536×C73C2semidirect
26. #17989208C22semidirect
37. #17988979C22semidirect
38. #17988969C22semidirect
39. #17988946C22semidirect
40. #17988937C22semidirect
41. #17988806C22semidirect
42. #17988799C22semidirect
43. #17988794C22semidirect
44. #17988789C22semidirect
45. #17988749C22semidirect
46. #17988743C22semidirect
48. #17988726C22semidirect
49. #17988648C22semidirect
67. #536×C73C22semidirect
400. C2×C73#3225semidirect
406. C2×#536D73semidirect
421. C73C2×#3225semidirect
435. #536C2×D73semidirect
805. C2#22621040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892082
#226210402
C2×#179889792
C2×#179889692
C2×#179889462
C2×#179889372
C2×#179888062
C2×#179887942
C2×#179887992
C2×#179887892
C2×#179887492
C2×#179887322
C2×#179887432
C2×#179887262
C2×#179886482
C2×#536×C732
C2×#322573