Finite Group Databasebeta

← C2×#22623006 #33967000

Subgroups — C2×#22623006 #33967000

Order 18688.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989310C211yesmaximal, characteristic, complemented
2#22623006C2116yesmaximal, direct product factor
3C2×#17988982C211yesmaximal, characteristic, complemented
4C2×#17988979C211yesmaximal, characteristic, complemented
5C2×#17988969C211yesmaximal, characteristic
6C2×#17988809C211yesmaximal, characteristic, complemented
7C2×#17988806C211yesmaximal, characteristic, complemented
8C2×#17988797C211yesmaximal, characteristic, complemented
9C2×#17988794C211yesmaximal, characteristic, complemented
10C2×#17988802C211yesmaximal, characteristic
11C2×#17988799C211yesmaximal, characteristic
12C2×#17988718C211yesmaximal, characteristic, complemented
13C2×#17988687C211yesmaximal, characteristic, complemented
14C2×#17988685C211yesmaximal, characteristic, complemented
15C2×C4×#11924018C211yesmaximal, characteristic, complemented
16C2×#556×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924016C2211yescharacteristic
22C22×#11924016C2211yescharacteristic
23C22×#11924015C2211yescharacteristic
24C22×#11924015C2211yescharacteristic
25C22×#11924013C2211yescharacteristic
26#17989310—24no—
27#17989310C2218yescomplemented
28C2×#14556591C2211yescharacteristic
29C2×#14556586—21no—
30C2×#14556586—21no—
31C2×#14556579C2211yescharacteristic
32C2×#14556579C2211yescharacteristic
33C2×#14556567—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556549—21no—
38#17988982C2218yescomplemented
39#17988979C2218yescomplemented
40#17988969C2218yes—
41#17988809C2218yescomplemented
42#17988806C2218yescomplemented
43#17988802C2218yes—
44#17988799C2218yes—
45#17988797C2218yescomplemented
46#17988794C2218yescomplemented
47#17988718C2218yescomplemented
48#17988687C2218yescomplemented
49#17988685C2218yescomplemented
50C4×#11924018C2218yescomplemented
51C2×#14556524C2211yescharacteristic
52C2×C4⋊#10596831C2211yescharacteristic
53C2×C4⋊#10596831C2211yescharacteristic
54C2×C4⋊#10596831C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556514C2211yescharacteristic
58C2×#14556514C2211yescharacteristic
59C2×#14556512C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×#14556502C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#556×C73—24no—
65#556×C73C2218yescomplemented
66C2×C4⋊Q8×C73C2211yescharacteristic
67C2×#126×C73—21no—
68C2×#126×C73—21no—
69C2×#124×C73C2211yescharacteristic
70C2×#124×C73C2211yescharacteristic
71C2×C22⋊Q8×C73—21no—
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×Q8×C73C2211yescharacteristic
74C2×C4×Q8×C73C2211yescharacteristic
75C2×C4×D4×C73C2211yescharacteristic
76C2×#117×C73—21no—
77C22×Dic146C2311yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C4×D73—21no—
81C2×#11924018—24no—
82C2×#11924018—42no—
83C2×#11924018—42no—
84C2×#11924018—42no—
85C2×#11924018C2314yes—
86C2×#11924018C2314yes—
87C2×#11924018C2314yes—
88C2×#11924018C2314yes—
89C2×#11924016—24no—
90C2×#11924016—42no—
91C2×#11924016C2314yes—
92C2×#11924016C2314yes—
93C2×#11924015—24no—
94C2×#11924015—42no—
95C2×#11924015C2314yes—
96C2×#11924015C2314yes—
97C2×#11924013—42no—
98C2×#11924013C2314yes—
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2311yescharacteristic
102C22×#10596831C2311yescharacteristic
103#14556591—22no—
104#14556591C2314yes—
105#14556586—28no—
106#14556586—28no—
107#14556579—22no—
108#14556579—22no—
109#14556579C2314yes—
110#14556579C2314yes—
111#14556567—28no—
112C4×Dic146—22no—
113C4×Dic146—22no—
114C4×Dic146C2314yes—
115C4×Dic146C2314yes—
116C4×D292—22no—
117C4×D292C2314yes—
118#14556549—28no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73C2311yescharacteristic
122C2×#11924007—21no—
123C2×#11924007—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×#11924005—21no—
127C2×#11924005—21no—
128C2×#11924005—21no—
129C2×C4×Dic73—21no—
130C2×C4×Dic73—21no—
131#14556524C2314yes—
132C4⋊#10596831C2314yes—
133C4⋊#10596831C2314yes—
134C4⋊#10596831C2314yes—
135#14556515C2314yes—
136#14556515C2314yes—
137#14556514C2314yes—
138#14556514C2314yes—
139#14556512C2314yes—
140#14556511C2314yes—
141#14556502C2314yes—
142#14556502C2314yes—
143C4×#10596831C2314yes—
144C22×Q8×C73D411yescharacteristic
145C22×Q8×C73C2311yescharacteristic
146C22×Q8×C73C2311yescharacteristic
147C22×D4×C73C2311yescharacteristic
148C23×C4×C73—21no—
149C4⋊Q8×C73—22no—
150C4⋊Q8×C73C2314yes—
151#126×C73—28no—
152#126×C73—28no—
153#124×C73—22no—
154#124×C73—22no—
155#124×C73C2314yes—
156#124×C73C2314yes—
157C22⋊Q8×C73—28no—
158C4×Q8×C73—22no—
159C4×Q8×C73—22no—
160C4×Q8×C73D414yes—
161C4×Q8×C73C2314yes—
162C4×Q8×C73C2314yes—
163C4×Q8×C73C2314yes—
164C4×D4×C73—22no—
165C4×D4×C73C2314yes—
166#117×C73—28no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73D411yescharacteristic
172C2×C4⋊C4×C73D411yescharacteristic
173C2×C4⋊C4×C73D411yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C42×C73—21no—
181C2×C42×C73—21no—
182C2×C42×C73C2311yescharacteristic
183C2×C42×C73C2311yescharacteristic
184C2×C42×C73C2311yescharacteristic
185C23×D73—21no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—21no—
191C2×Dic146—21no—
192C2×Dic146C2412yes—
193C2×Dic146C2412yes—
194C2×D292—22no—
195C2×D292—22no—
196C2×D292—21no—
197C2×D292C2412yes—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C2×C4×D73—24no—
202C2×C4×D73—44no—
203#11924018—28no—
204#11924018—44no—
205#11924018—44no—
206#11924018—44no—
207#11924016—28no—
208#11924016—44no—
209#11924015—28no—
210#11924015—44no—
211#11924013—44no—
212C2×#10596831—22no—
213C2×#10596831—22no—
214C2×#10596831—22no—
215C2×#10596831#4114yes—
216C2×#10596831C2412yes—
217C2×#10596831C2412yes—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C4⋊Dic73—24no—
221C4⋊Dic73—24no—
222C4⋊Dic73—21no—
223C4⋊Dic73C2412yes—
224#11924007—24no—
225#11924007—24no—
226#11924005—24no—
227#11924005—24no—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231C4×Dic73—24no—
232C4×Dic73—24no—
233C24×C73—21no—
234C2×Q8×C73—21no—
235C2×Q8×C73—21no—
236C2×Q8×C73—22no—
237C2×Q8×C73—22no—
238C2×Q8×C73—22no—
239C2×Q8×C73—22no—
240C2×Q8×C73—42no—
241C2×Q8×C73C2×D414yes—
242C2×Q8×C73C2412yes—
243C2×Q8×C73C2412yes—
244C2×D4×C73—21no—
245C2×D4×C73—22no—
246C2×D4×C73—22no—
247C2×D4×C73C2412yes—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—24no—
252C22×C4×C73—44no—
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2411yescharacteristic
260C4⋊C4×C73—24no—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73C2×D414yes—
266C4⋊C4×C73C2×D414yes—
267C4⋊C4×C73C2×D414yes—
268C4⋊C4×C73C2412yes—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—24no—
271C22⋊C4×C73—24no—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C42×C73—24no—
275C42×C73—24no—
276C42×C73C2×D412yes—
277C42×C73C2×D412yes—
278C42×C73C2×D412yes—
279C42×C73C2412yes—
280C42×C73C2412yes—
281C42×C73C2412yes—
282C23×C73—22no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73C22×D411yescharacteristic
287C22×D73—22no—
288C22×D73—42no—
289C22×D73—42no—
290C22×D73—42no—
291Q8×C73—22no—
292Q8×C73—22no—
293Q8×C73—22no—
294Q8×C73—22no—
295Q8×C73—44no—
296Q8×C73—42no—
297Q8×C73—42no—
298D4×C73—22no—
299D4×C73—22no—
300D4×C73—42no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—48no—
311C2×C4×C73—42no—
312C2×C4×C73—42no—
313C2×C4×C73—42no—
314C2×C4×C73C22×D412yes—
315C2×C4×C73C22×D412yes—
316C2×C4×C73C22×D412yes—
317C2×C4×C73C22×D412yes—
318C2×C4×C73C22×D412yes—
319C2×C4×C73C22×D412yes—
320C2×C4×C73C22×D411yescharacteristic
321C2×C4×C73C2×#4112yes—
322C2×C4×C73H(5,𝔽2)12yes—
323C2×C4×C73C2511yescharacteristic
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330D292—22no—
331D292—22no—
332D292—42no—
333C4×D73—48no—
334Dic146—22no—
335Dic146—22no—
336Dic146—22no—
337Dic146—22no—
338Dic146—42no—
339Dic146—42no—
340#10596831—22no—
341#10596831—22no—
342#10596831—22no—
343#10596831C2×#4114yes—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—84no—
348C22×C73#55012yes—
349C22×C73#57512yes—
350C22×C73#57812yes—
351C22×C73C23×D411yescharacteristic
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—84no—
356C4×C73—22no—
357C4×C73—22no—
358C4×C73—22no—
359C4×C73—22no—
360C4×C73—22no—
361C4×C73—22no—
362C4×C73—42no—
363C4×C73—42no—
364C4×C73—42no—
365C4×C73#55012yes—
366C4×C73C22×#4111yescharacteristic
367C4×C73C2×H(5,𝔽2)11yescharacteristic
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3402—731nomaximal, Sylow
372C2×C73—82no—
373C2×C73#340214yescomplemented
374C2×C73C2×#55011yescharacteristic
375C2×C73C2×#57511yescharacteristic
376C2×C73C2×#57811yescharacteristic
377D73—82no—
378C2×#556—731no—
379C2×#556D7311yescharacteristic, complemented
380#3402—7316no—
381C2×#497—731no—
382C2×#497—731no—
383C2×#495—731no—
384C2×#464—731no—
385C2×#464—731no—
386C2×#462—731no—
387C2×#462—731no—
388C2×#463—731no—
389C2×#463—731no—
390C2×#446—731no—
391C2×#440—731no—
392C2×#440—731no—
393C2×C4×Q16—731no—
394C73C2×#340211yescharacteristic, complemented, Sylow
395C22×Q16—731no—
396C22×Q16—731no—
397C22×Q16—731no—
398C22×Q16—731no—
399C22×SD16—731no—
400C22×SD16—731no—
401C22×SD16—731no—
402C22×SD16—731no—
403C22×D8—731no—
404#556—24no—
405#556—738no—
406#556—1464no—
407#556C2×D7318yescomplemented
408C2×C4⋊Q8—731no—
409C2×C4⋊Q8C2×D7311yescharacteristic
410C2×#126—21no—
411C2×#126—21no—
412C2×#126—1461no—
413C2×#126—1461no—
414C2×#124—731no—
415C2×#124—731no—
416C2×#124C2×D7311yescharacteristic
417C2×#124C2×D7311yescharacteristic
418C2×C22⋊Q8—21no—
419C2×C22⋊Q8—1461no—
420C2×C4×Q8—731no—
421C2×C4×Q8—731no—
422C2×C4×Q8C2×D7311yescharacteristic
423C2×C4×Q8C2×D7311yescharacteristic
424C2×C4×Q8C2×D7311yescharacteristic
425C2×C4×D4—731no—
426C2×C4×D4C2×D7311yescharacteristic
427C2×#117—21no—
428C2×#117—1461no—
429#497—738no—
430#497—738no—
431#495—738no—
432#464—738no—
433#464—738no—
434#463—738no—
435#463—738no—
436#462—738no—
437#462—738no—
438#446—738no—
439#440—738no—
440#440—738no—
441C4×Q16—738no—
442C2×#107—731no—
443C2×C4⋊C8—731no—
444C2×C4⋊C8—731no—
445C2×C4⋊C8—731no—
446C2×#103—731no—
447C2×#103—731no—
448C2×#103—731no—
449C2×#103—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#97—731no—
453C2×#97—731no—
454C2×C4×C8—731no—
455C22×Q8—731no—
456C22×Q8—731no—
457C22×Q8C22⋊D7311yescharacteristic
458C22×Q8C22×D7311yescharacteristic
459C22×Q8C22×D7311yescharacteristic
460C22×D4—731no—
461C22×D4C22×D7311yescharacteristic
462C23×C4—21no—
463C23×C4—1461no—
464C2×Q16—2922no—
465C2×Q16—2922no—
466C2×Q16—2922no—
467C2×Q16—734no—
468C2×Q16—734no—
469C2×Q16—734no—
470C2×Q16—734no—
471C2×Q16—1464no—
472C2×SD16—2922no—
473C2×SD16—2922no—
474C2×SD16—734no—
475C2×SD16—734no—
476C2×SD16—734no—
477C2×SD16—734no—
478C2×SD16—1464no—
479C2×SD16—1464no—
480C2×D8—2922no—
481C2×D8—734no—
482C22×C8—731no—
483C22×C8—731no—
484C22×C8—731no—
485C22×C8—731no—
486C4⋊Q8—22no—
487C4⋊Q8—734no—
488C4⋊Q8—1462no—
489C4⋊Q8C22×D7314yes—
490#126—28no—
491#126—28no—
492#126—1468no—
493#126—1468no—
494#124—22no—
495#124—22no—
496#124—734no—
497#124—734no—
498#124—1462no—
499#124—1462no—
500#124C22×D7314yes—
501#124C22×D7314yes—
502C22⋊Q8—28no—
503C22⋊Q8—1468no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—734no—
507C4×Q8—734no—
508C4×Q8—1462no—
509C4×Q8—1462no—
510C4×Q8C22⋊D7314yes—
511C4×Q8C22×D7314yes—
512C4×Q8C22×D7314yes—
513C4×Q8C22×D7314yes—
514C4×D4—22no—
515C4×D4—734no—
516C4×D4—1462no—
517C4×D4C22×D7314yes—
518#117—28no—
519#117—1468no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4C22⋊D7311yescharacteristic
530C2×C4⋊C4C22⋊D7311yescharacteristic
531C2×C4⋊C4C22⋊D7311yescharacteristic
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C22⋊C4—1461no—
542C2×C22⋊C4—1461no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1461no—
546C2×C42—1461no—
547C2×C42C22×D7311yescharacteristic
548C2×C42C22×D7311yescharacteristic
549C2×C42C22×D7311yescharacteristic
550#107—734no—
551C4⋊C8—734no—
552C4⋊C8—734no—
553C4⋊C8—734no—
554#103—734no—
555#103—734no—
556#103—734no—
557#103—734no—
558#102—734no—
559#102—734no—
560#97—734no—
561#97—734no—
562C4×C8—734no—
563C24—21no—
564C24—1461no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—732no—
573C2×Q8—732no—
574C2×Q8—1462no—
575C2×Q8—1462no—
576C2×Q8—1462no—
577C2×Q8—1462no—
578C2×Q8—1461no—
579C2×Q8—1461no—
580C2×Q8C2×C22⋊D7314yes—
581C2×Q8C23×D7312yes—
582C2×Q8C23×D7312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—732no—
587C2×D4—1461no—
588C2×D4—1462no—
589C2×D4—1462no—
590C2×D4C23×D7312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—2924no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1464no—
601C22×C4C2×C22⋊D7311yescharacteristic
602C22×C4C2×C22⋊D7311yescharacteristic
603C22×C4C2×C22⋊D7311yescharacteristic
604C22×C4C2×C22⋊D7311yescharacteristic
605C22×C4C2×C22⋊D7311yescharacteristic
606C22×C4C2×C22⋊D7311yescharacteristic
607C22×C4C23×D7311yescharacteristic
608Q16—2924no—
609Q16—2924no—
610Q16—2924no—
611Q16—1468no—
612SD16—2924no—
613SD16—2924no—
614SD16—1468no—
615SD16—1468no—
616D8—2924no—
617C2×C8—734no—
618C2×C8—732no—
619C2×C8—732no—
620C2×C8—732no—
621C2×C8—732no—
622C2×C8—1462no—
623C2×C8—1462no—
624C2×C8—1462no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—732no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1461no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4C2×C22⋊D7314yes—
637C4⋊C4C2×C22⋊D7314yes—
638C4⋊C4C2×C22⋊D7314yes—
639C4⋊C4C23×D7312yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C22⋊C4—1464no—
649C22⋊C4—1464no—
650C42—24no—
651C42—24no—
652C42—1464no—
653C42—1464no—
654C42C2×C22⋊D7312yes—
655C42C2×C22⋊D7312yes—
656C42C2×C22⋊D7312yes—
657C42C23×D7312yes—
658C42C23×D7312yes—
659C42C23×D7312yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—2922no—
665C23—2922no—
666C23—2922no—
667C23—1462no—
668C23C22×C22⋊D7311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—2922no—
677Q8—2922no—
678Q8—1462no—
679Q8—1462no—
680Q8—1462no—
681Q8—1462no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—2922no—
686D4—1462no—
687D4—1462no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—2928no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4C22×C22⋊D7312yes—
709C2×C4C22×C22⋊D7312yes—
710C2×C4C22×C22⋊D7312yes—
711C2×C4C22×C22⋊D7312yes—
712C2×C4C22×C22⋊D7312yes—
713C2×C4C22×C22⋊D7312yes—
714C2×C4C22×C22⋊D7311yescharacteristic
715C2×C4#41×D7312yes—
716C2×C4#1455663712yes—
717C2×C4C24×D7311yescharacteristic
718C8—734no—
719C8—1462no—
720C8—1462no—
721C8—1462no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2922no—
727C22—2922no—
728C22—2922no—
729C22—5844no—
730C22#1798925612yes—
731C22#1798938512yes—
732C22#1798940212yes—
733C22C23×C22⋊D7311yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2922no—
744C4—2922no—
745C4—2922no—
746C4#1798925612yes—
747C4C2×#41×D7311yescharacteristic
748C4C2×#1455663711yescharacteristic
749C2—82no—
750C2—5842no—
751C2#2262300614yesdirect product factor
752C2C2×#1798925611yescharacteristic
753C2C2×#1798938511yescharacteristic
754C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#556×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
hypercenterC2×#556D73
hypocenterC73C2×#3402
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#17989310C2semidirect
2. #22623006C2direct (N × H)
3. C2×#17988982C2semidirect
4. C2×#17988979C2semidirect
6. C2×#17988809C2semidirect
7. C2×#17988806C2semidirect
8. C2×#17988797C2semidirect
9. C2×#17988794C2semidirect
12. C2×#17988718C2semidirect
13. C2×#17988687C2semidirect
14. C2×#17988685C2semidirect
15. C2×C4×#11924018C2semidirect
16. C2×#556×C73C2semidirect
27. #17989310C22semidirect
38. #17988982C22semidirect
39. #17988979C22semidirect
41. #17988809C22semidirect
42. #17988806C22semidirect
45. #17988797C22semidirect
46. #17988794C22semidirect
47. #17988718C22semidirect
48. #17988687C22semidirect
49. #17988685C22semidirect
50. C4×#11924018C22semidirect
65. #556×C73C22semidirect
373. C2×C73#3402semidirect
379. C2×#556D73semidirect
394. C73C2×#3402semidirect
407. #556C2×D73semidirect
751. C2#22623006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893102
#226230062
C2×#179889822
C2×#179889792
C2×#179889692
C2×#179888092
C2×#179888062
C2×#179887972
C2×#179887942
C2×#179888022
C2×#179887992
C2×#179887182
C2×#179886872
C2×#179886852
C2×C4×#119240182
C2×#556×C732
C2×#340273