Finite Group Databasebeta

← C2×#23773437 #35156305

Subgroups — C2×#23773437 #35156305

Order 20224.

2138 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099117C211yesmaximal, characteristic
2C2×C4×Q8×D79C211yesmaximal, characteristic
3#23773437C2116yesmaximal, direct product factor
4C2×#19098900C211yesmaximal, characteristic
5C2×#19098897C211yesmaximal, characteristic
6C2×#19098857C211yesmaximal, characteristic, complemented
7C2×#19098856C211yesmaximal, characteristic, complemented
8C2×#19098772C211yesmaximal, characteristic, complemented
9C2×#19098771C211yesmaximal, characteristic, complemented
10C2×#19098720C211yesmaximal, characteristic
11C2×#19098717C211yesmaximal, characteristic
12C2×C4×Dic316C211yesmaximal, characteristic, complemented
13C2×C4×#11929614C211yesmaximal, characteristic, complemented
14C2×C4×#11929614C211yesmaximal, characteristic, complemented
15C2×#19098614C211yesmaximal, characteristic
16C2×C4×Q16×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929614C2211yescharacteristic
21#19099117—24no—
22#19099117C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579159C2211yescharacteristic
25C2×#14579151—21no—
26C2×#14579141C2211yescharacteristic
27C2×#14579139—21no—
28C2×#14579137C2211yescharacteristic
29C2×Q8×Dic79C2211yescharacteristic
30C2×C4×Dic158—21no—
31C2×C4×Dic158—21no—
32C2×C4×Dic158C2211yescharacteristic
33C2×C4×Dic158C2211yescharacteristic
34C2×#14579126—21no—
35C2×#14579126C2211yescharacteristic
36C4×Q8×D79—24no—
37C4×Q8×D79C2218yes—
38C2×#14579118—21no—
39C2×C4⋊C4×D79—21no—
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C42×D79—21no—
42C2×C42×D79C2211yescharacteristic
43#19098900C2218yes—
44#19098897C2218yes—
45#19098857C2218yescomplemented
46#19098856C2218yescomplemented
47#19098772C2218yescomplemented
48#19098771C2218yescomplemented
49#19098720C2218yes—
50#19098717C2218yes—
51C4×Dic316C2218yescomplemented
52C4×#11929614C2218yescomplemented
53C4×#11929614C2218yescomplemented
54#19098614C2218yes—
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579084C2211yescharacteristic
65C2×#14579084C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C4×C79⋊C8C2211yescharacteristic
69C22×Q16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×Q8×C79C2211yescharacteristic
72C4×Q16×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C4×C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158C2311yescharacteristic
80C22×Dic158C2311yescharacteristic
81C2×Q8×D79—24no—
82C2×Q8×D79—24no—
83C2×Q8×D79—22no—
84C2×Q8×D79C2314yes—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79D411yescharacteristic
88C22×C4×D79D411yescharacteristic
89C22×C4×D79C2311yescharacteristic
90C2×Dic316—24no—
91C2×Dic316C2314yes—
92C2×#11929614—24no—
93C2×#11929614—24no—
94C2×#11929614C2314yes—
95C2×#11929614C2314yes—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98#14579160—22no—
99#14579160C2314yes—
100#14579159—22no—
101#14579159C2314yes—
102#14579151—28no—
103#14579141—22no—
104#14579141C2314yes—
105#14579139—28no—
106#14579137—22no—
107#14579137C2314yes—
108Q8×Dic79—22no—
109Q8×Dic79C2314yes—
110C4×Dic158—22no—
111C4×Dic158—22no—
112C4×Dic158—28no—
113C4×Dic158—28no—
114C4×Dic158C2314yes—
115C4×Dic158C2314yes—
116#14579126—22no—
117#14579126—28no—
118#14579126C2314yes—
119#14579118—28no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C4⋊C4×D79—28no—
133C4⋊C4×D79—22no—
134C4⋊C4×D79C2314yes—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×C4×Dic79—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79D411yescharacteristic
142C2×C4×Dic79D411yescharacteristic
143C2×C4×Dic79C2311yescharacteristic
144C42×D79—28no—
145C42×D79D414yes—
146C42×D79C2314yes—
147#14579095C2314yes—
148#14579094C2314yes—
149#14579094C2314yes—
150Dic79⋊C8C2314yes—
151Dic79⋊C8C2314yes—
152#14579086C2314yes—
153#14579086C2314yes—
154#14579085C2314yes—
155#14579085C2314yes—
156#14579084C2314yes—
157#14579084C2314yes—
158(C2×D79)⋊C8C2314yes—
159(C2×D79)⋊C8C2314yes—
160C4×C79⋊C8C2314yes—
161C22×Q8×C79C2311yescharacteristic
162C22×Q8×C79C2311yescharacteristic
163C2×Q16×C79—24no—
164C2×Q16×C79C2314yes—
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C4×Q8×C79—22no—
168C4×Q8×C79—22no—
169C4×Q8×C79C2314yes—
170C4×Q8×C79C2314yes—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C42×C79—21no—
176C2×C42×C79—21no—
177C2×C42×C79C2311yescharacteristic
178#107×C79C2314yes—
179#103×C79C2314yes—
180#103×C79C2314yes—
181C4×C8×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C2×Dic158—28no—
184C2×Dic158—24no—
185C2×Dic158—24no—
186C2×Dic158—21no—
187C2×Dic158—21no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—44no—
192C2×Dic158#4114yes—
193C2×Dic158C2412yes—
194C2×Dic158C2412yes—
195Q8×D79—216no—
196Q8×D79—28no—
197Q8×D79—28no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—28no—
206C2×C4×D79—24no—
207C2×C4×D79—24no—
208C2×C4×D79—22no—
209C2×C4×D79—22no—
210C2×C4×D79—42no—
211C2×C4×D79—44no—
212C2×C4×D79Q1618yescomplemented
213C2×C4×D79C2×D412yes—
214C2×C4×D79C2×D414yes—
215C2×C4×D79C2×D414yes—
216C2×C4×D79C2412yes—
217Dic316—28no—
218#11929614—28no—
219#11929614—28no—
220C2×C79⋊C8—22no—
221C2×C79⋊C8—22no—
222C2×C79⋊C8C2412yes—
223C2×C79⋊C8C2412yes—
224C4⋊Dic79—24no—
225C4⋊Dic79—24no—
226C4⋊Dic79—21no—
227C4⋊Dic79—21no—
228C4⋊Dic79C2412yes—
229C4⋊Dic79C2412yes—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240C4×Dic79—24no—
241C4×Dic79—24no—
242C4×Dic79—24no—
243C4×Dic79—24no—
244C4×Dic79C2×D412yes—
245C4×Dic79C2×D414yes—
246C4×Dic79C2×D414yes—
247C4×Dic79C2412yes—
248C2×Q8×C79—21no—
249C2×Q8×C79—21no—
250C2×Q8×C79—22no—
251C2×Q8×C79—22no—
252C2×Q8×C79—22no—
253C2×Q8×C79#4114yes—
254C2×Q8×C79C2412yes—
255C2×Q8×C79C2412yes—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2411yescharacteristic
263Q16×C79—28no—
264C2×C8×C79—22no—
265C2×C8×C79—22no—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79—24no—
269C4⋊C4×C79—24no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79C2412yes—
273C4⋊C4×C79C2412yes—
274C42×C79—24no—
275C42×C79—24no—
276C42×C79C2×D412yes—
277C42×C79C2412yes—
278C23×C79C22×D411yescharacteristic
279C22×D79—22no—
280C22×D79—22no—
281C22×D79C2×Q1614yes—
282C22×D79C22×D412yes—
283Q8×C79—24no—
284Q8×C79—22no—
285Q8×C79—22no—
286Q8×C79—22no—
287Q8×C79—42no—
288Q8×C79C2×#4114yes—
289C2×C4×C79—24no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—42no—
296C2×C4×C79—42no—
297C2×C4×C79—42no—
298C2×C4×C79C2×Q1614yes—
299C2×C4×C79C22×D412yes—
300C2×C4×C79C22×D411yescharacteristic
301C2×C4×C79C22×D412yes—
302C2×C4×C79C2×#4112yes—
303C2×C4×C79C2×#4112yes—
304C2×C4×C79C2511yescharacteristic
305C2×Dic79—24no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—42no—
313C2×Dic79—42no—
314C2×Dic79—42no—
315C2×Dic79C2×Q1614yes—
316C2×Dic79C22×D412yes—
317C2×Dic79C22×D412yes—
318C2×Dic79C22×D412yes—
319C4×D79—216no—
320C4×D79—24no—
321C4×D79—22no—
322C4×D79—22no—
323C4×D79—44no—
324C4×D79—48no—
325C4×D79C2×Q16116yescomplemented
326Dic158—216no—
327Dic158—24no—
328Dic158—22no—
329Dic158—22no—
330Dic158—22no—
331Dic158—48no—
332Dic158—42no—
333Dic158C2×#4114yes—
334C8×C79—22no—
335C8×C79—22no—
336C79⋊C8—22no—
337C79⋊C8—22no—
338C22×C79#52512yes—
339C22×C79C22×Q1612yes—
340C22×C79#57512yes—
341C22×C79C23×D411yescharacteristic
342C2×D79—28no—
343C2×D79—22no—
344C2×D79—22no—
345C2×D79C22×Q1614yes—
346C4×C79—24no—
347C4×C79—22no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79#52512yes—
352C4×C79C22×Q1614yes—
353C4×C79C22×#4111yescharacteristic
354C4×C79C22×#4111yescharacteristic
355Dic79—22no—
356Dic79—24no—
357Dic79—22no—
358Dic79—42no—
359Dic79—42no—
360Dic79—42no—
361Dic79C22×Q1614yes—
362C2×#3104—791nomaximal, Sylow
363C2×C79#310414yescomplemented
364C2×C79C2×#52511yescharacteristic
365C2×C79C23×Q1611yescharacteristic
366C2×C79C2×#57511yescharacteristic
367D79—24no—
368C2×#533—791no—
369C22×C4×Q8—791no—
370#3104—7916no—
371C2×#484—791no—
372C2×#484—791no—
373C2×#477—791no—
374C2×#477—791no—
375C2×#462—791no—
376C2×#462—791no—
377C2×#451—791no—
378C2×#451—791no—
379C2×C4×Q16—791no—
380C2×C4×Q16—791no—
381C2×C4×Q16—791no—
382C2×C4×Q16D7911yescharacteristic, complemented
383C2×#431—791no—
384C79C2×#310411yescharacteristic, complemented, Sylow
385C23×Q8—791no—
386C22×Q16—791no—
387C22×Q16—791no—
388C22×Q16—791no—
389C22×Q16C2×D7911yescharacteristic
390#533—798no—
391#533—1584no—
392C2×C4⋊Q8—791no—
393C2×C4⋊Q8—791no—
394C2×#125—1581no—
395C2×C22⋊Q8—791no—
396C2×C22⋊Q8—791no—
397C2×C22⋊Q8—1581no—
398C2×C4×Q8—791no—
399C2×C4×Q8—798no—
400C2×C4×Q8—791no—
401C2×C4×Q8—791no—
402C2×C4×Q8—791no—
403C2×C4×Q8—1581no—
404C2×C4×Q8—1581no—
405C2×C4×Q8—1581no—
406C2×C4×Q8—1584no—
407C2×C4×Q8C2×D7911yescharacteristic
408C2×C4×Q8C2×D7911yescharacteristic
409C2×#117—1581no—
410C22×C4⋊C4—791no—
411C22×C4⋊C4—1581no—
412C22×C42—791no—
413C22×C42—1581no—
414#484—798no—
415#484—798no—
416#477—798no—
417#477—798no—
418#462—798no—
419#462—798no—
420#451—798no—
421#451—798no—
422C4×Q16—798no—
423C4×Q16—798no—
424C4×Q16—798no—
425C4×Q16C2×D7918yescomplemented
426#431—798no—
427C2×#107—791no—
428C2×#107—791no—
429C2×#107—791no—
430C2×#107C2×D7911yescharacteristic
431C2×C4⋊C8—791no—
432C2×C4⋊C8—791no—
433C2×#103—791no—
434C2×#103—791no—
435C2×#103—791no—
436C2×#103—791no—
437C2×#103—791no—
438C2×#103—791no—
439C2×#103C2×D7911yescharacteristic
440C2×#103C2×D7911yescharacteristic
441C2×C22⋊C8—791no—
442C2×C22⋊C8—791no—
443C2×C4×C8—791no—
444C2×C4×C8C2×D7911yescharacteristic
445C22×Q8—794no—
446C22×Q8—791no—
447C22×Q8—791no—
448C22×Q8—1581no—
449C22×Q8—1581no—
450C22×Q8—1582no—
451C22×Q8—1584no—
452C22×Q8—1584no—
453C22×Q8C22×D7911yescharacteristic
454C22×Q8C22×D7911yescharacteristic
455C23×C4—791no—
456C23×C4—791no—
457C23×C4—791no—
458C23×C4—1581no—
459C23×C4—1581no—
460C2×Q16—24no—
461C2×Q16—794no—
462C2×Q16—794no—
463C2×Q16—794no—
464C2×Q16—1584no—
465C2×Q16—1584no—
466C2×Q16—1584no—
467C2×Q16C22×D7914yes—
468C22×C8—791no—
469C22×C8—791no—
470C22×C8C22×D7911yescharacteristic
471C22×C8C22×D7911yescharacteristic
472C4⋊Q8—794no—
473C4⋊Q8—794no—
474C4⋊Q8—1582no—
475C4⋊Q8—1582no—
476#125—1588no—
477C22⋊Q8—794no—
478C22⋊Q8—794no—
479C22⋊Q8—1582no—
480C22⋊Q8—1588no—
481C22⋊Q8—1582no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—794no—
485C4×Q8—794no—
486C4×Q8—794no—
487C4×Q8—794no—
488C4×Q8—1588no—
489C4×Q8—1588no—
490C4×Q8—1588no—
491C4×Q8—1582no—
492C4×Q8—1582no—
493C4×Q8—1582no—
494C4×Q8—1582no—
495C4×Q8C22×D7914yes—
496C4×Q8C22×D7914yes—
497#117—1588no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—794no—
503C2×C4⋊C4—1582no—
504C2×C4⋊C4—1588no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4C22×D7911yescharacteristic
516C2×C4⋊C4C22×D7911yescharacteristic
517C2×C22⋊C4—1581no—
518C2×C22⋊C4—1581no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—791no—
522C2×C42—791no—
523C2×C42—791no—
524C2×C42—794no—
525C2×C42—794no—
526C2×C42—1588no—
527C2×C42—1581no—
528C2×C42—1581no—
529C2×C42—1581no—
530C2×C42—1581no—
531C2×C42C22×D7911yescharacteristic
532#107—794no—
533#107—794no—
534#107—794no—
535#107C22×D7914yes—
536C4⋊C8—794no—
537C4⋊C8—794no—
538#103—794no—
539#103—794no—
540#103—794no—
541#103—794no—
542#103—794no—
543#103—794no—
544#103C22×D7914yes—
545#103C22×D7914yes—
546C22⋊C8—794no—
547C22⋊C8—794no—
548C4×C8—794no—
549C4×C8C22×D7914yes—
550C24—791no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—3164no—
557C2×Q8—794no—
558C2×Q8—792no—
559C2×Q8—792no—
560C2×Q8—1584no—
561C2×Q8—1584no—
562C2×Q8—1588no—
563C2×Q8—1582no—
564C2×Q8—1582no—
565C2×Q8—1588no—
566C2×Q8—15816no—
567C2×Q8—1588no—
568C2×Q8—1582no—
569C2×Q8—1581no—
570C2×Q8—1581no—
571C2×Q8#1192962414yes—
572C2×Q8C23×D7912yes—
573C2×Q8C23×D7912yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—3162no—
579C22×C4—3164no—
580C22×C4—794no—
581C22×C4—791no—
582C22×C4—798no—
583C22×C4—794no—
584C22×C4—791no—
585C22×C4—791no—
586C22×C4—792no—
587C22×C4—792no—
588C22×C4—1584no—
589C22×C4—1584no—
590C22×C4—1588no—
591C22×C4—1581no—
592C22×C4—1581no—
593C22×C4—1581no—
594C22×C4—1581no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4D4×D7911yescharacteristic
598C22×C4D4×D7911yescharacteristic
599C22×C4C23×D7911yescharacteristic
600Q16—28no—
601Q16—1588no—
602Q16—1588no—
603Q16—1588no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—1582no—
609C2×C8—1582no—
610C2×C8C23×D7912yes—
611C2×C8C23×D7912yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—792no—
617C4⋊C4—792no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1584no—
628C4⋊C4—1581no—
629C4⋊C4—1581no—
630C4⋊C4C23×D7912yes—
631C4⋊C4C23×D7912yes—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C42—24no—
635C42—24no—
636C42—792no—
637C42—794no—
638C42—794no—
639C42—792no—
640C42—1584no—
641C42—1584no—
642C42—1584no—
643C42—1584no—
644C42D4×D7912yes—
645C42C23×D7912yes—
646C23—794no—
647C23—792no—
648C23—1582no—
649C23—1582no—
650C23C2×D4×D7911yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—3168no—
657Q8—3162no—
658Q8—794no—
659Q8—15816no—
660Q8—1582no—
661Q8—1582no—
662Q8—1584no—
663Q8—1582no—
664Q8C2×#1192962414yes—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—3164no—
675C2×C4—3168no—
676C2×C4—3162no—
677C2×C4—3162no—
678C2×C4—3162no—
679C2×C4—794no—
680C2×C4—792no—
681C2×C4—7916no—
682C2×C4—792no—
683C2×C4—792no—
684C2×C4—15816no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4—1582no—
689C2×C4—1584no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1584no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4Q16×D7914yes—
696C2×C4C2×D4×D7912yes—
697C2×C4C2×D4×D7911yescharacteristic
698C2×C4C2×D4×D7912yes—
699C2×C4#41×D7912yes—
700C2×C4C2×#1192962412yes—
701C2×C4C24×D7911yescharacteristic
702C8—22no—
703C8—22no—
704C8—1582no—
705C8—1582no—
706C22—794no—
707C22—1582no—
708C22—1582no—
709C22—1588no—
710C22#1909907212yes—
711C22C2×Q16×D7912yes—
712C22#1909936012yes—
713C22C22×D4×D7911yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—3162no—
720C4—3162no—
721C4—3162no—
722C4—794no—
723C4—1582no—
724C4—1582no—
725C4—1584no—
726C4#1909907212yes—
727C4C2×Q16×D7914yes—
728C4C2×#41×D7911yescharacteristic
729C4C22×#1192962411yescharacteristic
730C2—1584no—
731C2#2377343714yesdirect product factor
732C2C2×#1909907211yescharacteristic
733C2C22×Q16×D7911yescharacteristic
734C2C2×#1909936011yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×C4×Q16×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×C4×Q16D79
hypocenterC79C2×#3104
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #23773437C2direct (N × H)
6. C2×#19098857C2semidirect
7. C2×#19098856C2semidirect
8. C2×#19098772C2semidirect
9. C2×#19098771C2semidirect
12. C2×C4×Dic316C2semidirect
13. C2×C4×#11929614C2semidirect
14. C2×C4×#11929614C2semidirect
16. C2×C4×Q16×C79C2semidirect
45. #19098857C22semidirect
46. #19098856C22semidirect
47. #19098772C22semidirect
48. #19098771C22semidirect
51. C4×Dic316C22semidirect
52. C4×#11929614C22semidirect
53. C4×#11929614C22semidirect
72. C4×Q16×C79C22semidirect
212. C2×C4×D79Q16semidirect
325. C4×D79C2×Q16semidirect
363. C2×C79#3104semidirect
382. C2×C4×Q16D79semidirect
384. C79C2×#3104semidirect
425. C4×Q16C2×D79semidirect
731. C2#23773437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991172
C2×C4×Q8×D792
#237734372
C2×#190989002
C2×#190988972
C2×#190988572
C2×#190988562
C2×#190987722
C2×#190987712
C2×#190987202
C2×#190987172
C2×C4×Dic3162
C2×C4×#119296142
C2×#190986142
C2×C4×Q16×C792
C2×#310479