Finite Group Databasebeta

← C2×#23773235 #35155833

Subgroups — C2×#23773235 #35155833

Order 20224.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099190C211yesmaximal, characteristic
2C2×#19099039C211yesmaximal, characteristic
3#23773235C2116yesmaximal, direct product factor
4C2×#19098873C211yesmaximal, characteristic, complemented
5C2×#19098871C211yesmaximal, characteristic, complemented
6C2×#19098870C211yesmaximal, characteristic, complemented
7C2×#19098868C211yesmaximal, characteristic, complemented
8C2×#19098856C211yesmaximal, characteristic, complemented
9C2×#19098855C211yesmaximal, characteristic, complemented
10C2×#19098847C211yesmaximal, characteristic, complemented
11C2×#19098602C211yesmaximal, characteristic
12C2×#19098598C211yesmaximal, characteristic
13C2×#19098588C211yesmaximal, characteristic
14C2×#19098570C211yesmaximal, characteristic
15C2×#103×D79C211yesmaximal, characteristic
16C2×#475×C79C211yesmaximal, characteristic, complemented
17C22×Q8×D79C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099190—24no—
21#19099190C2218yes—
22C2×#14579160C2211yescharacteristic
23C2×#14579159—21no—
24C2×#14579153C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579151—21no—
27C2×#14579139—21no—
28C2×#14579137—21no—
29#19099039—24no—
30#19099039C2218yes—
31C2×Q8×Dic79C2211yescharacteristic
32C2×C4×Dic158—21no—
33C2×C4×Dic158C2211yescharacteristic
34C2×#14579126—21no—
35C2×#14579126C2211yescharacteristic
36C2×#14579119—21no—
37C2×#14579119C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C2×#14579118—21no—
40C2×#14579118C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098873C2218yescomplemented
43#19098871C2218yescomplemented
44#19098870C2218yescomplemented
45#19098868C2218yescomplemented
46#19098856C2218yescomplemented
47#19098855C2218yescomplemented
48#19098847C2218yescomplemented
49#19098602C2218yes—
50#19098598C2218yes—
51C2×#14579095C2211yescharacteristic
52C2×#14579094C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54C2×#14579094C2211yescharacteristic
55C2×#14579093C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57#19098588C2218yes—
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×Dic79⋊C8C2211yescharacteristic
61#19098570C2218yes—
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579085C2211yescharacteristic
65C2×#14579085C2211yescharacteristic
66C2×#14579084C2211yescharacteristic
67C2×#14579084C2211yescharacteristic
68#103×D79C2218yes—
69C2×C4⋊Q8×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71#475×C79C2218yescomplemented
72C2×#106×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158C2311yescharacteristic
80C2×Q8×D79—22no—
81C2×Q8×D79—24no—
82C2×Q8×D79Q818yescomplemented
83C2×Q8×D79C2314yes—
84C22×C4×D79—21no—
85C22×C4×D79—21no—
86C22×C4×D79C2311yescharacteristic
87C2×#11929607—24no—
88C2×#11929607C2314yes—
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91C2×C8×D79—24no—
92C2×C8×D79C2314yes—
93#14579160—22no—
94#14579160C2314yes—
95#14579159—28no—
96#14579153—22no—
97#14579153C2314yes—
98#14579152—22no—
99#14579152C2314yes—
100#14579151—28no—
101#14579139—28no—
102#14579137—28no—
103Q8×Dic79—22no—
104Q8×Dic79C2314yes—
105C4×Dic158—22no—
106C4×Dic158—28no—
107C4×Dic158C2314yes—
108#14579126—28no—
109#14579126—22no—
110#14579126C2314yes—
111#14579119—22no—
112#14579119—22no—
113#14579119—28no—
114#14579119C2314yes—
115#14579119C2314yes—
116#14579118—28no—
117#14579118D414yes—
118#14579118C2314yes—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79C2311yescharacteristic
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⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C4⋊C4×D79—22no—
134C4⋊C4×D79C2314yes—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4D411yescharacteristic
138C2×(C2×D79)⋊C4D411yescharacteristic
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579095C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579094C2314yes—
149#14579093C2314yes—
150#14579092C2314yes—
151C4⋊(C79⋊C8)C2314yes—
152Dic79⋊C8C2314yes—
153Dic79⋊C8C2314yes—
154#14579086C2314yes—
155#14579086C2314yes—
156#14579085C2314yes—
157#14579085C2314yes—
158#14579084C2314yes—
159#14579084C2314yes—
160C22×Q8×C79—21no—
161C22×Q8×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C4⋊Q8×C79—22no—
165C4⋊Q8×C79C2314yes—
166C4×Q8×C79—22no—
167C4×Q8×C79C2314yes—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#106×C79C2314yes—
176#106×C79C2314yes—
177C4⋊C8×C79C2314yes—
178#103×C79C2314yes—
179#103×C79C2314yes—
180C23×D79C2×D411yescharacteristic
181C2×Dic158—28no—
182C2×Dic158—24no—
183C2×Dic158—24no—
184C2×Dic158—21no—
185C2×Dic158—22no—
186C2×Dic158—82no—
187C2×Dic158C2×Q814yes—
188C2×Dic158C2412yes—
189Q8×D79—216no—
190Q8×D79—28no—
191Q8×D79C2×Q8116yescomplemented
192C22×Dic79—21no—
193C22×Dic79—21no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—28no—
200C2×C4×D79—24no—
201C2×C4×D79—24no—
202C2×C4×D79—82no—
203C2×C4×D79C2×D412yes—
204C2×C4×D79C2×Q814yes—
205C2×C4×D79#4114yes—
206C2×C4×D79C2412yes—
207#11929607—28no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8—22no—
210C2×C79⋊C8C2412yes—
211C2×C79⋊C8C2412yes—
212C8×D79—28no—
213C4⋊Dic79—24no—
214C4⋊Dic79—24no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4C2×D414yes—
229Dic79⋊C4C2×D414yes—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4C2×D414yes—
233(C2×D79)⋊C4C2×D414yes—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79C2×D412yes—
240C4×Dic79C2412yes—
241C2×Q8×C79—21no—
242C2×Q8×C79—24no—
243C2×Q8×C79—22no—
244C2×Q8×C79—82no—
245C2×Q8×C79C2×Q814yes—
246C2×Q8×C79C2412yes—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2411yescharacteristic
254C2×C8×C79—22no—
255C2×C8×C79—22no—
256C2×C8×C79C2412yes—
257C2×C8×C79C2412yes—
258C4⋊C4×C79—24no—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C4⋊C4×C79C2412yes—
266C42×C79—24no—
267C42×C79C2×D412yes—
268C42×C79C2412yes—
269C23×C79C22×D411yescharacteristic
270C22×D79—22no—
271C22×D79—22no—
272C22×D79C22⋊Q814yes—
273C22×D79C22×D412yes—
274Q8×C79—24no—
275Q8×C79—22no—
276Q8×C79—84no—
277Q8×C79C22×Q814yes—
278C2×C4×C79—24no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—42no—
286C2×C4×C79—42no—
287C2×C4×C79—42no—
288C2×C4×C79C22×D412yes—
289C2×C4×C79C22×D412yes—
290C2×C4×C79C22×D411yescharacteristic
291C2×C4×C79C22×Q812yes—
292C2×C4×C79C2×#4112yes—
293C2×C4×C79C2511yescharacteristic
294C2×Dic79—24no—
295C2×Dic79—22no—
296C2×Dic79—22no—
297C2×Dic79—22no—
298C2×Dic79—22no—
299C2×Dic79—22no—
300C2×Dic79—22no—
301C2×Dic79—42no—
302C2×Dic79—42no—
303C2×Dic79—42no—
304C2×Dic79C22⋊Q814yes—
305C2×Dic79C22×D412yes—
306C2×Dic79C22×D412yes—
307C2×Dic79C22×D412yes—
308C4×D79—216no—
309C4×D79—84no—
310C4×D79C22⋊Q818yes—
311C4×D79C22×Q814yes—
312C4×D79C2×#4114yes—
313Dic158—24no—
314Dic158—22no—
315Dic158—216no—
316Dic158—84no—
317Dic158C22×Q814yes—
318C8×C79—22no—
319C8×C79—22no—
320C79⋊C8—22no—
321C79⋊C8—22no—
322C22×C79C2×C22⋊Q812yes—
323C22×C79#57712yes—
324C22×C79#57812yes—
325C22×C79C23×D411yescharacteristic
326C2×D79—28no—
327C2×D79—22no—
328C2×D79—22no—
329C2×D79C2×C22⋊Q814yes—
330C4×C79—24no—
331C4×C79—22no—
332C4×C79—22no—
333C4×C79—42no—
334C4×C79—42no—
335C4×C79—42no—
336C4×C79C2×C22⋊Q812yes—
337C4×C79C23×Q811yescharacteristic
338C4×C79C22×#4111yescharacteristic
339Dic79—24no—
340Dic79—22no—
341Dic79—22no—
342Dic79—42no—
343Dic79—42no—
344Dic79—42no—
345Dic79C2×C22⋊Q814yes—
346C2×#3082—791nomaximal, Sylow
347C2×C79#308214yescomplemented
348C2×C79C22×C22⋊Q811yescharacteristic
349C2×C79C2×#57711yescharacteristic
350C2×C79C2×#57811yescharacteristic
351D79—24no—
352C2×#544—791no—
353C2×#519—791no—
354#3082—7916no—
355C2×#479—791no—
356C2×#479—791no—
357C2×#479—791no—
358C2×#479—791no—
359C2×#477—791no—
360C2×#477—791no—
361C2×#475—791no—
362C2×#475D7911yescharacteristic, complemented
363C2×#428—791no—
364C2×#427—791no—
365C2×#424—791no—
366C2×#419—791no—
367C22×#103—791no—
368C79C2×#308211yescharacteristic, complemented, Sylow
369C23×Q8—791no—
370C22×M16—791no—
371C23×C8—791no—
372#544—798no—
373#544—1584no—
374C2×C4⋊Q8—791no—
375C2×C4⋊Q8—1581no—
376C2×C4⋊Q8C2×D7911yescharacteristic
377C2×#125—791no—
378C2×#125—791no—
379C2×#125—1581no—
380C2×C22⋊Q8—1581no—
381C2×C22⋊Q8—1581no—
382#519—798no—
383#519—1584no—
384C2×C4×Q8—791no—
385C2×C4×Q8—791no—
386C2×C4×Q8—791no—
387C2×C4×Q8—1581no—
388C2×C4×Q8—1581no—
389C2×C4×Q8C2×D7911yescharacteristic
390C2×#117—791no—
391C2×#117—791no—
392C2×#117—791no—
393C2×#117—1581no—
394C2×#117—1581no—
395C22×C4⋊C4—791no—
396#479—798no—
397#479—798no—
398#479—798no—
399#479—798no—
400#477—798no—
401#477—798no—
402#475—798no—
403#475C2×D7918yescomplemented
404#428—798no—
405#427—798no—
406C2×#107—791no—
407C2×#107—791no—
408C2×#107—791no—
409C2×#107—791no—
410C2×#106—791no—
411C2×#106—791no—
412C2×#106C2×D7911yescharacteristic
413C2×#106C2×D7911yescharacteristic
414#424—798no—
415C2×C4⋊C8—791no—
416C2×C4⋊C8—791no—
417C2×C4⋊C8—791no—
418C2×C4⋊C8C2×D7911yescharacteristic
419#419—798no—
420C2×#103—791no—
421C2×#103—791no—
422C2×#103—791no—
423C2×#103—791no—
424C2×#103—791no—
425C2×#103—791no—
426C2×#103—798no—
427C2×#103C2×D7911yescharacteristic
428C2×#103C2×D7911yescharacteristic
429C22×Q8—21no—
430C22×Q8—798no—
431C22×Q8—794no—
432C22×Q8—791no—
433C22×Q8—1581no—
434C22×Q8—1581no—
435C22×Q8—1582no—
436C22×Q8—1584no—
437C22×Q8C22×D7911yescharacteristic
438C23×C4—791no—
439C23×C4—1581no—
440C23×C4—1581no—
441C2×M16—794no—
442C2×M16—1584no—
443C22×C8—791no—
444C22×C8—791no—
445C22×C8—794no—
446C22×C8—1584no—
447C22×C8C22×D7911yescharacteristic
448C22×C8C22×D7911yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8—794no—
451C4⋊Q8—1582no—
452C4⋊Q8—1588no—
453C4⋊Q8C22×D7914yes—
454#125—794no—
455#125—794no—
456#125—1582no—
457#125—1588no—
458#125—1582no—
459C22⋊Q8—1588no—
460C22⋊Q8—1588no—
461C4×Q8—22no—
462C4×Q8—794no—
463C4×Q8—794no—
464C4×Q8—794no—
465C4×Q8—1588no—
466C4×Q8—1582no—
467C4×Q8—1582no—
468C4×Q8—1588no—
469C4×Q8—1582no—
470C4×Q8C22×D7914yes—
471#117—794no—
472#117—794no—
473#117—794no—
474#117—794no—
475#117—1588no—
476#117—1588no—
477#117—1582no—
478#117—1582no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—791no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—791no—
484C2×C4⋊C4—791no—
485C2×C4⋊C4—791no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—1582no—
488C2×C4⋊C4—1581no—
489C2×C4⋊C4—1581no—
490C2×C4⋊C4—1581no—
491C2×C4⋊C4—1581no—
492C2×C4⋊C4—1581no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1581no—
497C2×C4⋊C4C22×D7911yescharacteristic
498C2×C4⋊C4C22×D7911yescharacteristic
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C22⋊C4—791no—
501C2×C22⋊C4—791no—
502C2×C22⋊C4—1581no—
503C2×C22⋊C4—1581no—
504C2×C42—21no—
505C2×C42—791no—
506C2×C42—1581no—
507C2×C42—1581no—
508C2×C42—1581no—
509C2×C42—1581no—
510C2×C42—1581no—
511C2×C42C22×D7911yescharacteristic
512#107—794no—
513#107—794no—
514#107—794no—
515#107—794no—
516#106—794no—
517#106—794no—
518#106C22×D7914yes—
519#106C22×D7914yes—
520C4⋊C8—794no—
521C4⋊C8—794no—
522C4⋊C8—794no—
523C4⋊C8C22×D7914yes—
524#103—794no—
525#103—794no—
526#103—794no—
527#103—794no—
528#103—794no—
529#103—794no—
530#103C22×D7914yes—
531#103C22×D7914yes—
532C24—791no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—24no—
536C2×Q8—82no—
537C2×Q8—7916no—
538C2×Q8—794no—
539C2×Q8—792no—
540C2×Q8—6322no—
541C2×Q8—1584no—
542C2×Q8—1584no—
543C2×Q8—1588no—
544C2×Q8—15816no—
545C2×Q8—1588no—
546C2×Q8—1582no—
547C2×Q8—1581no—
548C2×Q8Q8×D7914yes—
549C2×Q8C23×D7912yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—791no—
555C22×C4—794no—
556C22×C4—794no—
557C22×C4—792no—
558C22×C4—792no—
559C22×C4—791no—
560C22×C4—791no—
561C22×C4—6322no—
562C22×C4—1584no—
563C22×C4—1584no—
564C22×C4—1588no—
565C22×C4—1581no—
566C22×C4—1581no—
567C22×C4—1581no—
568C22×C4—1581no—
569C22×C4D4×D7911yescharacteristic
570C22×C4D4×D7911yescharacteristic
571C22×C4C23×D7911yescharacteristic
572M16—1588no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—792no—
576C2×C8—792no—
577C2×C8—1588no—
578C2×C8—1582no—
579C2×C8—1582no—
580C2×C8C23×D7912yes—
581C2×C8C23×D7912yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—794no—
588C4⋊C4—794no—
589C4⋊C4—792no—
590C4⋊C4—792no—
591C4⋊C4—792no—
592C4⋊C4—1584no—
593C4⋊C4—1584no—
594C4⋊C4—1584no—
595C4⋊C4—1584no—
596C4⋊C4—1584no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C4⋊C4—1584no—
601C4⋊C4—1581no—
602C4⋊C4—1581no—
603C4⋊C4—1581no—
604C4⋊C4C23×D7912yes—
605C4⋊C4C23×D7912yes—
606C4⋊C4C23×D7912yes—
607C22⋊C4—794no—
608C22⋊C4—794no—
609C22⋊C4—1584no—
610C22⋊C4—1584no—
611C42—24no—
612C42—792no—
613C42—792no—
614C42—1584no—
615C42—1584no—
616C42—1584no—
617C42—1584no—
618C42—1584no—
619C42D4×D7912yes—
620C42C23×D7912yes—
621C23—794no—
622C23—792no—
623C23—1582no—
624C23—1582no—
625C23C2×D4×D7911yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—84no—
629Q8—794no—
630Q8—6324no—
631Q8—15816no—
632Q8—1584no—
633Q8—1582no—
634Q8C2×Q8×D7914yes—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—3162no—
646C2×C4—3162no—
647C2×C4—3162no—
648C2×C4—794no—
649C2×C4—792no—
650C2×C4—798no—
651C2×C4—794no—
652C2×C4—794no—
653C2×C4—792no—
654C2×C4—792no—
655C2×C4—6324no—
656C2×C4—15816no—
657C2×C4—1582no—
658C2×C4—1582no—
659C2×C4—1582no—
660C2×C4—1584no—
661C2×C4—1582no—
662C2×C4—1582no—
663C2×C4—1582no—
664C2×C4C2×D4×D7912yes—
665C2×C4C2×D4×D7912yes—
666C2×C4C2×D4×D7911yescharacteristic
667C2×C4C2×Q8×D7912yes—
668C2×C4#41×D7912yes—
669C2×C4C24×D7911yescharacteristic
670C8—22no—
671C8—22no—
672C8—1582no—
673C8—1582no—
674C22—794no—
675C22—1588no—
676C22—1582no—
677C22—1582no—
678C22C22⋊Q8×D7912yes—
679C22#1909936912yes—
680C22#1909937912yes—
681C22C22×D4×D7911yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—3162no—
689C4—3162no—
690C4—3162no—
691C4—794no—
692C4—1582no—
693C4—1584no—
694C4—1582no—
695C4C22⋊Q8×D7912yes—
696C4C22×Q8×D7911yescharacteristic
697C4C2×#41×D7911yescharacteristic
698C2—1584no—
699C2#2377323514yesdirect product factor
700C2C2×C22⋊Q8×D7911yescharacteristic
701C2C2×#1909936911yescharacteristic
702C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#475×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenterC2×#475D79
hypocenterC79C2×#3082
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #23773235C2direct (N × H)
4. C2×#19098873C2semidirect
5. C2×#19098871C2semidirect
6. C2×#19098870C2semidirect
7. C2×#19098868C2semidirect
8. C2×#19098856C2semidirect
9. C2×#19098855C2semidirect
10. C2×#19098847C2semidirect
16. C2×#475×C79C2semidirect
42. #19098873C22semidirect
43. #19098871C22semidirect
44. #19098870C22semidirect
45. #19098868C22semidirect
46. #19098856C22semidirect
47. #19098855C22semidirect
48. #19098847C22semidirect
71. #475×C79C22semidirect
82. C2×Q8×D79Q8semidirect
191. Q8×D79C2×Q8semidirect
347. C2×C79#3082semidirect
362. C2×#475D79semidirect
368. C79C2×#3082semidirect
403. #475C2×D79semidirect
699. C2#23773235direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991902
C2×#190990392
#237732352
C2×#190988732
C2×#190988712
C2×#190988702
C2×#190988682
C2×#190988562
C2×#190988552
C2×#190988472
C2×#190986022
C2×#190985982
C2×#190985882
C2×#190985702
C2×#103×D792
C2×#475×C792
C2×#308279