Finite Group Databasebeta

← C2×#22617951 #33292143

Subgroups — C2×#22617951 #33292143

Order 18688.

2674 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556576C211yesmaximal, characteristic
2C22×#14556569C211yesmaximal, characteristic, complemented
3#22617951C2116yesmaximal, direct product factor
4C2×#17988521C211yesmaximal, characteristic, complemented
5C2×#17988520C211yesmaximal, characteristic, complemented
6C2×#17988516C211yesmaximal, characteristic, complemented
7C2×#17988516C211yesmaximal, characteristic, complemented
8C2×#17988514C211yesmaximal, characteristic, complemented
9C2×#17988509C211yesmaximal, characteristic, complemented
10C2×#17988509C211yesmaximal, characteristic, complemented
11C2×#17988507C211yesmaximal, characteristic, complemented
12C2×#17988505C211yesmaximal, characteristic
13C2×#17988504C211yesmaximal, characteristic
14C2×#17988500C211yesmaximal, characteristic, complemented
15C2×#17988444C211yesmaximal, characteristic, complemented
16C2×#398×C73C211yesmaximal, characteristic, complemented
17C23×Dic146C2211yescharacteristic
18C23×D292C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C2×#14556576—28no—
21C2×#14556576C2218yes—
22C2×#14556569—28no—
23C2×#14556569C2218yescomplemented
24C22×C4⋊Dic73C2211yescharacteristic
25C22×C4⋊Dic73C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×#11924005C2211yescharacteristic
33C22×#11924005C2211yescharacteristic
34C22×#11924005C2211yescharacteristic
35C22×#11924005C2211yescharacteristic
36C22×#11924005C2211yescharacteristic
37C22×#11924005C2211yescharacteristic
38C22×#11924005C2211yescharacteristic
39C22×#11924005C2211yescharacteristic
40C22×#11924005C2211yescharacteristic
41C22×#11924005C2211yescharacteristic
42#17988521C2218yescomplemented
43#17988520C2218yescomplemented
44#17988516C2218yescomplemented
45#17988516C2218yescomplemented
46#17988514C2218yescomplemented
47#17988509C2218yescomplemented
48#17988509C2218yescomplemented
49#17988507C2218yescomplemented
50#17988505C2218yes—
51#17988504C2218yes—
52#17988500C2218yescomplemented
53#17988444C2218yescomplemented
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C4⋊C4×C73C2211yescharacteristic
65#398×C73C2218yescomplemented
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C2×#95×C73C2211yescharacteristic
69C24×D73C2311yescharacteristic
70C24×D73C2311yescharacteristic
71C22×Dic146—24no—
72C22×Dic146—42no—
73C22×Dic146—42no—
74C22×Dic146C2314yes—
75C22×D292—24no—
76C22×D292—42no—
77C22×D292—42no—
78C22×D292C2314yes—
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2311yescharacteristic
84C23×Dic73C2311yescharacteristic
85C22×C4×D73—42no—
86C22×C4×D73—42no—
87C22×C4×D73D418yes—
88C22×C4×D73C2314yes—
89#14556576—232no—
90#14556569—232no—
91C2×C4⋊Dic73—42no—
92C2×C4⋊Dic73—42no—
93C2×C4⋊Dic73C2314yes—
94C2×C4⋊Dic73C2314yes—
95C2×#11924007—24no—
96C2×#11924007—24no—
97C2×#11924007—24no—
98C2×#11924007—42no—
99C2×#11924007—42no—
100C2×#11924007C2314yes—
101C2×#11924007C2314yes—
102C2×#11924007C2314yes—
103C2×#11924007C2314yes—
104C2×#11924007C2314yes—
105C2×#11924005—24no—
106C2×#11924005—24no—
107C2×#11924005—24no—
108C2×#11924005—24no—
109C2×#11924005—24no—
110C2×#11924005—42no—
111C2×#11924005—42no—
112C2×#11924005—42no—
113C2×#11924005—42no—
114C2×#11924005—42no—
115C2×#11924005—42no—
116C2×#11924005C2314yes—
117C2×#11924005C2314yes—
118C2×#11924005C2314yes—
119C2×#11924005C2314yes—
120C2×#11924005C2314yes—
121C2×#11924005C2314yes—
122C2×#11924005C2314yes—
123C2×#11924005C2314yes—
124C2×#11924005C2314yes—
125C2×#11924005C2314yes—
126C2×#11924005C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129#14556498C2314yes—
130#14556498C2314yes—
131#14556498C2314yes—
132#14556498C2314yes—
133#14556498C2314yes—
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2311yescharacteristic
139C23×C4×C73C2311yescharacteristic
140C23×C4×C73C2311yescharacteristic
141C2×C4⋊C4×C73—24no—
142C2×C4⋊C4×C73—24no—
143C2×C4⋊C4×C73—42no—
144C2×C4⋊C4×C73—42no—
145C2×C4⋊C4×C73C2314yes—
146C2×C4⋊C4×C73C2314yes—
147C2×C4⋊C4×C73C2314yes—
148C2×C4⋊C4×C73C2314yes—
149#95×C73C2314yes—
150#95×C73C2314yes—
151#95×C73C2314yes—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73—22no—
155C23×D73—22no—
156C23×D73—22no—
157C23×D73—22no—
158C23×D73—22no—
159C23×D73—22no—
160C23×D73—22no—
161C23×D73—22no—
162C23×D73—22no—
163C23×D73—22no—
164C23×D73—22no—
165C23×D73C2×D414yes—
166C23×D73C2412yes—
167C23×D73C2412yes—
168C2×Dic146—28no—
169C2×Dic146—44no—
170C2×Dic146—44no—
171C2×Dic146—416no—
172C2×D292—28no—
173C2×D292—44no—
174C2×D292—44no—
175C2×D292—416no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—22no—
179C22×Dic73—22no—
180C22×Dic73—22no—
181C22×Dic73—22no—
182C22×Dic73—22no—
183C22×Dic73—22no—
184C22×Dic73—22no—
185C22×Dic73—22no—
186C22×Dic73—22no—
187C22×Dic73—22no—
188C22×Dic73—22no—
189C22×Dic73—22no—
190C22×Dic73—22no—
191C22×Dic73—22no—
192C22×Dic73—22no—
193C22×Dic73C2×D414yes—
194C22×Dic73C2412yes—
195C22×Dic73C2412yes—
196C22×Dic73C2412yes—
197C22×Dic73C2412yes—
198C22×Dic73C2412yes—
199C22×Dic73C2412yes—
200C2×C4×D73—416no—
201C2×C4×D73—44no—
202C2×C4×D73—44no—
203C2×C4×D73C2×D4116yes—
204C4⋊Dic73—44no—
205C4⋊Dic73—44no—
206#11924007—28no—
207#11924007—28no—
208#11924007—28no—
209#11924007—44no—
210#11924007—44no—
211#11924005—28no—
212#11924005—28no—
213#11924005—28no—
214#11924005—28no—
215#11924005—28no—
216#11924005—44no—
217#11924005—44no—
218#11924005—44no—
219#11924005—44no—
220#11924005—44no—
221#11924005—44no—
222C24×C73C2411yescharacteristic
223C22×C4×C73—22no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—22no—
234C22×C4×C73—22no—
235C22×C4×C73—22no—
236C22×C4×C73—22no—
237C22×C4×C73—22no—
238C22×C4×C73—22no—
239C22×C4×C73—22no—
240C22×C4×C73—22no—
241C22×C4×C73—22no—
242C22×C4×C73—22no—
243C22×C4×C73C2×D414yes—
244C22×C4×C73C2412yes—
245C22×C4×C73C2412yes—
246C22×C4×C73C2412yes—
247C22×C4×C73C2412yes—
248C22×C4×C73C2412yes—
249C22×C4×C73C2412yes—
250C22×C4×C73C2412yes—
251C4⋊C4×C73—28no—
252C4⋊C4×C73—28no—
253C4⋊C4×C73—44no—
254C4⋊C4×C73—44no—
255C23×C73C22×D412yes—
256C23×C73H(5,𝔽2)12yes—
257C23×C73H(5,𝔽2)12yes—
258C23×C73H(5,𝔽2)12yes—
259C23×C732−1+412yes—
260C23×C732−1+412yes—
261C23×C732−1+412yes—
262C23×C73C2511yescharacteristic
263C22×D73—28no—
264C22×D73—28no—
265C22×D73—28no—
266C22×D73—22no—
267C22×D73—22no—
268C22×D73—22no—
269C22×D73—22no—
270C22×D73—22no—
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—22no—
274C22×D73—22no—
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—44no—
280C22×D73—44no—
281C22×D73—44no—
282C22×D73—44no—
283C22×D73—44no—
284C22×D73—44no—
285C22×D73—44no—
286C22×D73—44no—
287C22×D73—44no—
288C22×D73—44no—
289C22×D73—44no—
290C22×D73C22×D414yes—
291C2×C4×C73—28no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
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—22no—
311C2×C4×C73—22no—
312C2×C4×C73—44no—
313C2×C4×C73—44no—
314C2×C4×C73—44no—
315C2×C4×C73—44no—
316C2×C4×C73—44no—
317C2×C4×C73—44no—
318C2×C4×C73C22×D414yes—
319C2×Dic73—28no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—44no—
338C2×Dic73—44no—
339C2×Dic73—44no—
340C2×Dic73—44no—
341C2×Dic73—44no—
342C2×Dic73C22×D414yes—
343D292—416no—
344C4×D73—416no—
345Dic146—416no—
346C22×C73#53414yes—
347C22×C73#53614yes—
348C22×C73#53714yes—
349C22×C73#56214yes—
350C22×C73#56214yes—
351C22×C73#56314yes—
352C22×C73#56314yes—
353C22×C73C23×D411yescharacteristic
354C22×C73C2×H(5,𝔽2)11yescharacteristic
355C22×C73C2×H(5,𝔽2)11yescharacteristic
356C22×C73C2×H(5,𝔽2)11yescharacteristic
357C22×C73C2×2−1+411yescharacteristic
358C22×C73C2×2−1+411yescharacteristic
359C22×C73C2×2−1+411yescharacteristic
360C2×D73—24no—
361C2×D73—24no—
362C2×D73—24no—
363C2×D73—42no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—42no—
367C2×D73—416no—
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—88no—
376C4×C73—24no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73—42no—
381C4×C73—42no—
382C4×C73—42no—
383Dic73—24no—
384Dic73—42no—
385Dic73—42no—
386Dic73—42no—
387Dic73—42no—
388Dic73—42no—
389C2×#2814—731nomaximal, Sylow
390C2×C73#281418yescomplemented
391C2×C73C2×#53411yescharacteristic
392C2×C73C2×#53611yescharacteristic
393C2×C73C2×#53711yescharacteristic
394C2×C73C2×#56211yescharacteristic
395C2×C73C2×#56211yescharacteristic
396C2×C73C2×#56311yescharacteristic
397C2×C73C2×#56311yescharacteristic
398D73—44no—
399D73—82no—
400C22×#123—731no—
401C22×C22⋊Q8—731no—
402#2814—7316no—
403C2×#398—731no—
404C2×#398—731no—
405C2×#398D7311yescharacteristic, complemented
406C2×#397—731no—
407C2×#397—731no—
408C2×#397—731no—
409C2×#396—731no—
410C2×#396—731no—
411C2×#395—731no—
412C2×#394—731no—
413C2×#394—731no—
414C2×#393—731no—
415C2×#380—731no—
416C73C2×#281411yescharacteristic, complemented, Sylow
417C23×Q8—731no—
418C23×D4—731no—
419C24×C4—731no—
420C2×#123—738no—
421C2×#123—1468no—
422C2×C22⋊Q8—738no—
423C2×C22⋊Q8—1468no—
424C22×C4⋊C4—731no—
425C22×C4⋊C4—731no—
426C22×C4⋊C4—731no—
427C22×C4⋊C4—731no—
428C22×C4⋊C4—731no—
429C22×C4⋊C4—731no—
430C22×C4⋊C4—731no—
431C22×C4⋊C4C2×D7311yescharacteristic
432C22×C4⋊C4C2×D7311yescharacteristic
433C22×C4⋊C4C2×D7311yescharacteristic
434C22×C4⋊C4C2×D7311yescharacteristic
435C22×C22⋊C4—731no—
436C22×C22⋊C4—731no—
437C22×C22⋊C4—731no—
438C22×C22⋊C4—731no—
439C22×C22⋊C4—731no—
440C22×C22⋊C4—731no—
441C22×C22⋊C4—731no—
442C22×C22⋊C4—731no—
443C22×C22⋊C4—731no—
444C22×C22⋊C4—731no—
445C22×C22⋊C4—731no—
446#398—738no—
447#398—738no—
448#398C2×D7318yescomplemented
449#397—738no—
450#397—738no—
451#397—738no—
452#396—738no—
453#396—738no—
454#395—738no—
455#394—738no—
456#394—738no—
457#393—738no—
458#380—738no—
459C2×#95—731no—
460C2×#95—731no—
461C2×#95—731no—
462C2×#95—731no—
463C2×#95—731no—
464C2×#95—731no—
465C2×#95—731no—
466C2×#95C2×D7311yescharacteristic
467C2×#95C2×D7311yescharacteristic
468C2×#95C2×D7311yescharacteristic
469C25—731no—
470C25—731no—
471C22×Q8—2922no—
472C22×Q8—2922no—
473C22×Q8—734no—
474C22×Q8—1464no—
475C22×D4—2922no—
476C22×D4—2922no—
477C22×D4—734no—
478C22×D4—1464no—
479C23×C4—2922no—
480C23×C4—2922no—
481C23×C4—738no—
482C23×C4—734no—
483C23×C4—731no—
484C23×C4—731no—
485C23×C4—731no—
486C23×C4—731no—
487C23×C4—731no—
488C23×C4—731no—
489C23×C4C22×D7311yescharacteristic
490C23×C4C22×D7311yescharacteristic
491C23×C4C22×D7311yescharacteristic
492C23×C4C22×D7311yescharacteristic
493C23×C4C22×D7311yescharacteristic
494C23×C4C22×D7311yescharacteristic
495C23×C4C22×D7311yescharacteristic
496#123—14632no—
497C22⋊Q8—14632no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—2922no—
503C2×C4⋊C4—2922no—
504C2×C4⋊C4—2922no—
505C2×C4⋊C4—2922no—
506C2×C4⋊C4—734no—
507C2×C4⋊C4—734no—
508C2×C4⋊C4—734no—
509C2×C4⋊C4—734no—
510C2×C4⋊C4—734no—
511C2×C4⋊C4—734no—
512C2×C4⋊C4—734no—
513C2×C4⋊C4—1464no—
514C2×C4⋊C4—1464no—
515C2×C4⋊C4—1464no—
516C2×C4⋊C4C22×D7314yes—
517C2×C4⋊C4C22×D7314yes—
518C2×C4⋊C4C22×D7314yes—
519C2×C4⋊C4C22×D7314yes—
520C2×C22⋊C4—2922no—
521C2×C22⋊C4—2922no—
522C2×C22⋊C4—2922no—
523C2×C22⋊C4—2922no—
524C2×C22⋊C4—2922no—
525C2×C22⋊C4—2922no—
526C2×C22⋊C4—734no—
527C2×C22⋊C4—734no—
528C2×C22⋊C4—734no—
529C2×C22⋊C4—734no—
530C2×C22⋊C4—734no—
531C2×C22⋊C4—734no—
532C2×C22⋊C4—734no—
533C2×C22⋊C4—734no—
534C2×C22⋊C4—734no—
535C2×C22⋊C4—734no—
536C2×C22⋊C4—734no—
537C2×C22⋊C4—1464no—
538C2×C22⋊C4—1464no—
539C2×C22⋊C4—1464no—
540C2×C22⋊C4—1464no—
541C2×C22⋊C4—1464no—
542#95—734no—
543#95—734no—
544#95—734no—
545#95—734no—
546#95—734no—
547#95—734no—
548#95—734no—
549#95C22×D7314yes—
550#95C22×D7314yes—
551#95C22×D7314yes—
552C24—734no—
553C24—732no—
554C24—732no—
555C24—1462no—
556C24—1462no—
557C24—1462no—
558C24—1462no—
559C24—1462no—
560C24—1462no—
561C24—1462no—
562C24—1462no—
563C24—1462no—
564C24—1462no—
565C24—1462no—
566C24—1462no—
567C24—1462no—
568C24C23×D7311yescharacteristic
569C2×Q8—2924no—
570C2×Q8—2924no—
571C2×Q8—29216no—
572C2×Q8—1468no—
573C2×D4—2924no—
574C2×D4—2924no—
575C2×D4—29216no—
576C2×D4—1468no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—29216no—
598C22×C4—2924no—
599C22×C4—2924no—
600C22×C4—7316no—
601C22×C4—734no—
602C22×C4—732no—
603C22×C4—732no—
604C22×C4—732no—
605C22×C4—732no—
606C22×C4—732no—
607C22×C4—732no—
608C22×C4—1462no—
609C22×C4—1462no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1462no—
613C22×C4—1462no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4—1462no—
620C22×C4—1462no—
621C22×C4—1462no—
622C22×C4—1462no—
623C22×C4—1462no—
624C22×C4—1462no—
625C22×C4D4×D7314yes—
626C22×C4C23×D7312yes—
627C22×C4C23×D7312yes—
628C22×C4C23×D7312yes—
629C22×C4C23×D7312yes—
630C22×C4C23×D7312yes—
631C22×C4C23×D7312yes—
632C22×C4C23×D7312yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—2924no—
638C4⋊C4—2924no—
639C4⋊C4—2924no—
640C4⋊C4—2924no—
641C4⋊C4—1468no—
642C4⋊C4—1468no—
643C4⋊C4—1468no—
644C22⋊C4—2924no—
645C22⋊C4—2924no—
646C22⋊C4—2924no—
647C22⋊C4—2924no—
648C22⋊C4—2924no—
649C22⋊C4—2924no—
650C22⋊C4—1468no—
651C22⋊C4—1468no—
652C22⋊C4—1468no—
653C22⋊C4—1468no—
654C22⋊C4—1468no—
655C23—2924no—
656C23—2924no—
657C23—2924no—
658C23—2924no—
659C23—2924no—
660C23—2924no—
661C23—2924no—
662C23—2924no—
663C23—2924no—
664C23—2924no—
665C23—2924no—
666C23—734no—
667C23—1462no—
668C23—1462no—
669C23—1462no—
670C23—1462no—
671C23—1462no—
672C23—1462no—
673C23—1462no—
674C23—1468no—
675C23—1468no—
676C23—1462no—
677C23—1462no—
678C23—1462no—
679C23—1462no—
680C23—1462no—
681C23—1462no—
682C23—1468no—
683C23C2×D4×D7312yes—
684C23#1455663612yes—
685C23#1455663712yes—
686C23#1455663712yes—
687C23#1455663812yes—
688C23#1455663912yes—
689C23#1455663912yes—
690C23C24×D7311yescharacteristic
691Q8—29216no—
692D4—29216no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—29216no—
721C2×C4—2924no—
722C2×C4—2924no—
723C2×C4—2924no—
724C2×C4—2924no—
725C2×C4—2924no—
726C2×C4—734no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1462no—
738C2×C4—1462no—
739C2×C4—1462no—
740C2×C4—1462no—
741C2×C4—1462no—
742C2×C4—1468no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4C2×D4×D7314yes—
746C22—2922no—
747C22—2922no—
748C22—2922no—
749C22—2922no—
750C22—29216no—
751C22—2922no—
752C22—2922no—
753C22—2922no—
754C22—2922no—
755C22—2922no—
756C22—2922no—
757C22—2922no—
758C22—5848no—
759C22—1464no—
760C22—1464no—
761C22—1464no—
762C22#1798914514yes—
763C22#1798916014yes—
764C22#1798916714yes—
765C22#1798933414yes—
766C22#1798933514yes—
767C22#1798933614yes—
768C22#1798934114yes—
769C22C22×D4×D7311yescharacteristic
770C22C2×#1455663611yescharacteristic
771C22C2×#1455663711yescharacteristic
772C22C2×#1455663711yescharacteristic
773C22C2×#1455663811yescharacteristic
774C22C2×#1455663911yescharacteristic
775C22C2×#1455663911yescharacteristic
776C4—24no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—2922no—
784C4—2922no—
785C4—2922no—
786C4—2922no—
787C4—2922no—
788C4—1464no—
789C2—2924no—
790C2—5842no—
791C2#2261795118yesdirect product factor
792C2C2×#1798914511yescharacteristic
793C2C2×#1798916011yescharacteristic
794C2C2×#1798916711yescharacteristic
795C2C2×#1798933411yescharacteristic
796C2C2×#1798933511yescharacteristic
797C2C2×#1798933611yescharacteristic
798C2C2×#1798934111yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#398×C73C2
socleC24×C73C24
prime radicalC23×D292C22
hypercenterC2×#398D73
hypocenterC73C2×#2814
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#14556569C2semidirect
3. #22617951C2direct (N × H)
4. C2×#17988521C2semidirect
5. C2×#17988520C2semidirect
6. C2×#17988516C2semidirect
7. C2×#17988516C2semidirect
8. C2×#17988514C2semidirect
9. C2×#17988509C2semidirect
10. C2×#17988509C2semidirect
11. C2×#17988507C2semidirect
14. C2×#17988500C2semidirect
15. C2×#17988444C2semidirect
16. C2×#398×C73C2semidirect
23. C2×#14556569C22semidirect
42. #17988521C22semidirect
43. #17988520C22semidirect
44. #17988516C22semidirect
45. #17988516C22semidirect
46. #17988514C22semidirect
47. #17988509C22semidirect
48. #17988509C22semidirect
49. #17988507C22semidirect
52. #17988500C22semidirect
53. #17988444C22semidirect
65. #398×C73C22semidirect
390. C2×C73#2814semidirect
405. C2×#398D73semidirect
416. C73C2×#2814semidirect
448. #398C2×D73semidirect
791. C2#22617951direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565762
C22×#145565692
#226179512
C2×#179885212
C2×#179885202
C2×#179885162
C2×#179885142
C2×#179885092
C2×#179885072
C2×#179885052
C2×#179885042
C2×#179885002
C2×#179884442
C2×#398×C732
C2×#281473