Finite Group Databasebeta

← C2×#23773611 #35156529

Subgroups — C2×#23773611 #35156529

Order 20224.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099174C211yesmaximal, characteristic, complemented
2C2×#19099042C211yesmaximal, characteristic
3#23773611C2116yesmaximal, direct product factor
4C2×#19098897C211yesmaximal, characteristic, complemented
5C2×#19098892C211yesmaximal, characteristic, complemented
6C2×#19098871C211yesmaximal, characteristic, complemented
7C2×#19098863C211yesmaximal, characteristic, complemented
8C2×#19098770C211yesmaximal, characteristic, complemented
9C2×#19098722C211yesmaximal, characteristic
10C2×#19098722C211yesmaximal, characteristic
11C2×#19098667C211yesmaximal, characteristic, complemented
12C2×#19098664C211yesmaximal, characteristic, complemented
13C2×#19098655C211yesmaximal, characteristic, complemented
14C2×SD16×Dic79C211yesmaximal, characteristic, complemented
15C2×#19098623C211yesmaximal, characteristic, complemented
16C2×#461×C79C211yesmaximal, characteristic, complemented
17C22×#11929623C2211yescharacteristic
18C22×#11929614C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20#19099174—24no—
21#19099174C2218yescomplemented
22C2×#14579156—21no—
23C2×#14579156—21no—
24C2×#14579153C2211yescharacteristic
25C2×#14579151—21no—
26C2×#14579151—21no—
27C2×#14579137C2211yescharacteristic
28C2×#14579137C2211yescharacteristic
29#19099042—24no—
30#19099042C2218yes—
31C2×Q8×Dic79C2211yescharacteristic
32C2×Q8×Dic79C2211yescharacteristic
33C2×C4×Dic158C2211yescharacteristic
34C2×#14579126C2211yescharacteristic
35C2×D4×Dic79C2211yescharacteristic
36C2×C4×C22⋊D79—21no—
37C2×(C22⋊D79)⋊C4—21no—
38C2×#14579118C2211yescharacteristic
39C2×#14579117—21no—
40C22×Dic79⋊C4—21no—
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098897C2218yescomplemented
43#19098892C2218yescomplemented
44#19098871C2218yescomplemented
45#19098863C2218yescomplemented
46#19098770C2218yescomplemented
47#19098722C2218yes—
48#19098722C2218yes—
49#19098667C2218yescomplemented
50#19098664C2218yescomplemented
51#19098655C2218yescomplemented
52SD16×Dic79C2218yescomplemented
53#19098623C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×C4⋊(C79⋊C8)C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×(C2×D79)⋊C8C2211yescharacteristic
66C2×(C2×D79)⋊C8C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×SD16×C79C2211yescharacteristic
71C2×C4⋊Q8×C79C2211yescharacteristic
72C2×C4×D4×C79C2211yescharacteristic
73#461×C79C2218yescomplemented
74C2×C4⋊C8×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C2×#11929623—24no—
78C2×#11929623—24no—
79C2×#11929623—22no—
80C2×#11929623C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×C22⋊D79—21no—
83C23×Dic79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79C2311yescharacteristic
87C2×#11929614—24no—
88C2×#11929614—24no—
89C2×#11929614C2314yes—
90C2×#11929614C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93#14579156—28no—
94#14579156—28no—
95#14579153—22no—
96#14579153C2314yes—
97#14579151—28no—
98#14579151—28no—
99#14579137—22no—
100#14579137—22no—
101#14579137C2314yes—
102#14579137C2314yes—
103Q8×Dic79—22no—
104Q8×Dic79—22no—
105Q8×Dic79C2314yes—
106Q8×Dic79C2314yes—
107C4×Dic158—22no—
108C4×Dic158C2314yes—
109#14579126—22no—
110#14579126C2314yes—
111D4×Dic79—22no—
112D4×Dic79C2314yes—
113C4×C22⋊D79—28no—
114(C22⋊D79)⋊C4—28no—
115#14579118D414yes—
116#14579118C2314yes—
117#14579117—28no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×Dic79⋊C4—21no—
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—28no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C4⋊C4×D79—22no—
134C4⋊C4×D79C2314yes—
135C2×C22⋊Dic79—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4D411yescharacteristic
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579095C2314yes—
146#14579094C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149C4⋊(C79⋊C8)C2314yes—
150#14579086C2314yes—
151#14579086C2314yes—
152#14579085C2314yes—
153#14579085C2314yes—
154#14579082C2314yes—
155#14579082C2314yes—
156(C2×D79)⋊C8C2314yes—
157(C2×D79)⋊C8C2314yes—
158#14579071C2314yes—
159C8×Dic79C2314yes—
160C22×Q8×C79C2311yescharacteristic
161C22×Q8×C79C2311yescharacteristic
162C22×D4×C79C2311yescharacteristic
163C23×C4×C79—21no—
164C2×SD16×C79—24no—
165C2×SD16×C79—24no—
166C2×SD16×C79C2314yes—
167C2×SD16×C79C2314yes—
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C4⋊Q8×C79—22no—
171C4⋊Q8×C79C2314yes—
172C4×D4×C79—22no—
173C4×D4×C79C2314yes—
174C2×C4⋊C4×C79—21no—
175C2×C4⋊C4×C79—21no—
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C42×C79C2311yescharacteristic
179C4⋊C8×C79C2314yes—
180#103×C79C2314yes—
181#103×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183#11929623—216no—
184#11929623—28no—
185#11929623—28no—
186C2×Dic158—21no—
187C2×Dic158—22no—
188C2×Dic158#4114yes—
189C2×Dic158C2412yes—
190C2×C22⋊D79—28no—
191C2×C22⋊D79—24no—
192C22×Dic79—28no—
193C22×Dic79—24no—
194C22×Dic79—24no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—82no—
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C2×C4×D79—24no—
204C2×C4×D79—22no—
205C2×C4×D79—22no—
206C2×C4×D79—82no—
207C2×C4×D79C2×D412yes—
208C2×C4×D79C2412yes—
209#11929614—28no—
210#11929614—28no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8C2412yes—
214C2×C79⋊C8C2412yes—
215C4⋊Dic79—24no—
216C4⋊Dic79—24no—
217C4⋊Dic79—21no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79C2412yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4C2×D414yes—
231Dic79⋊C4C2×D414yes—
232C22⋊Dic79—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4C2×D414yes—
236(C2×D79)⋊C4C2×D414yes—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C4×Dic79—24no—
241C4×Dic79C2×D412yes—
242C4×Dic79C2412yes—
243C24×C79—21no—
244C2×Q8×C79—21no—
245C2×Q8×C79—21no—
246C2×Q8×C79—22no—
247C2×Q8×C79—22no—
248C2×Q8×C79—22no—
249C2×Q8×C79—22no—
250C2×Q8×C79C2412yes—
251C2×Q8×C79C2412yes—
252C2×D4×C79—21no—
253C2×D4×C79—22no—
254C2×D4×C79#4114yes—
255C2×D4×C79C2412yes—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—24no—
260C22×C4×C79—82no—
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2411yescharacteristic
264SD16×C79—28no—
265SD16×C79—28no—
266C2×C8×C79—22no—
267C2×C8×C79—22no—
268C2×C8×C79C2412yes—
269C2×C8×C79C2412yes—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—24no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79C2412yes—
274C22⋊C4×C79—24no—
275C42×C79C2×D412yes—
276C42×C79C2412yes—
277C23×C79—24no—
278C23×C79—22no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79C22×D411yescharacteristic
282C22×D79—22no—
283C22×D79—22no—
284C22×D79—22no—
285C22×D79C22×D412yes—
286Q8×C79—22no—
287Q8×C79—22no—
288Q8×C79—22no—
289Q8×C79—22no—
290Q8×C79—42no—
291Q8×C79—42no—
292D4×C79—24no—
293D4×C79—22no—
294D4×C79C2×#4114yes—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—42no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79—84no—
304C2×C4×C79C22×D412yes—
305C2×C4×C79C22×D412yes—
306C2×C4×C79C22×D411yescharacteristic
307C2×C4×C79C2×#4112yes—
308C2×C4×C79C2×#4112yes—
309C2×C4×C79C2511yescharacteristic
310C22⋊D79—216no—
311C2×Dic79—216no—
312C2×Dic79—22no—
313C2×Dic79—24no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—42no—
321C2×Dic79—42no—
322C2×Dic79—42no—
323C2×Dic79—84no—
324C2×Dic79C22×D412yes—
325C2×Dic79C22×D412yes—
326C2×Dic79C22×D412yes—
327C4×D79—24no—
328C4×D79—22no—
329C4×D79—22no—
330C4×D79—84no—
331Dic158—24no—
332Dic158—22no—
333Dic158C2×#4114yes—
334C8×C79—22no—
335C8×C79—22no—
336C79⋊C8—22no—
337C79⋊C8—22no—
338C22×C79—24no—
339C22×C79—48no—
340C22×C79—42no—
341C22×C79—42no—
342C22×C79#52512yes—
343C22×C79#57712yes—
344C22×C79#57812yes—
345C22×C79C23×D411yescharacteristic
346C2×D79—22no—
347C2×D79—22no—
348C2×D79—22no—
349C2×D79—44no—
350C4×C79—22no—
351C4×C79—22no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79#52512yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C22×#4111yescharacteristic
358Dic79—24no—
359Dic79—22no—
360Dic79—22no—
361Dic79—22no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365C2×#3120—791nomaximal, Sylow
366C2×C79—44no—
367C2×C79#312014yescomplemented
368C2×C79C2×#52511yescharacteristic
369C2×C79C2×#57711yescharacteristic
370C2×C79C2×#57811yescharacteristic
371D79—42no—
372C2×#541—791no—
373C2×#520—791no—
374#3120—7916no—
375C2×#484—791no—
376C2×#483—791no—
377C2×#479—791no—
378C2×#478—791no—
379C2×#462—791no—
380C2×#461D7911yescharacteristic, complemented
381C2×#452—791no—
382C2×#452—791no—
383C2×#441—791no—
384C2×#440—791no—
385C2×C4×Q16—791no—
386C2×C4×SD16—791no—
387C2×#433—791no—
388C79C2×#312011yescharacteristic, complemented, Sylow
389C22×#41—791no—
390C22×Q16—791no—
391C22×Q16—791no—
392C22×SD16C2×D7911yescharacteristic
393C22×SD16C2×D7911yescharacteristic
394#541—798no—
395#541—1584no—
396C2×C4⋊Q8C2×D7911yescharacteristic
397C2×#126—1581no—
398C2×#126—1581no—
399C2×#125—791no—
400C2×#125—1581no—
401C2×#125—1581no—
402C2×C22⋊Q8—791no—
403C2×C22⋊Q8—791no—
404#520—798no—
405#520—1584no—
406C2×C4×Q8—791no—
407C2×C4×Q8—791no—
408C2×C4×Q8—791no—
409C2×C4×Q8—791no—
410C2×C4×D4—791no—
411C2×C4×D4—1581no—
412C2×C4×D4—1581no—
413C2×C4×D4C2×D7911yescharacteristic
414C2×#117—791no—
415C2×#117—1581no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4—1581no—
418#484—798no—
419#483—798no—
420#479—798no—
421#478—798no—
422#462—798no—
423#461C2×D7918yescomplemented
424#452—798no—
425#452—798no—
426#441—798no—
427#440—798no—
428C4×Q16—798no—
429C4×SD16—798no—
430#433—798no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#106—791no—
434C2×#106—791no—
435C2×C4⋊C8—791no—
436C2×C4⋊C8C2×D7911yescharacteristic
437C2×#103—791no—
438C2×#103—791no—
439C2×#103—791no—
440C2×#103—791no—
441C2×#103C2×D7911yescharacteristic
442C2×#103C2×D7911yescharacteristic
443C2×#102—791no—
444C2×#102—791no—
445C2×C22⋊C8—791no—
446C2×C22⋊C8—791no—
447C2×#97—791no—
448C2×C4×C8—791no—
449C2×#41—794no—
450C2×#41—1582no—
451C2×#41—1584no—
452C2×#41—1584no—
453C22×Q8—791no—
454C22×Q8C22×D7911yescharacteristic
455C22×Q8C22×D7911yescharacteristic
456C22×D4—1581no—
457C22×D4C22×D7911yescharacteristic
458C23×C4—21no—
459C23×C4—791no—
460C23×C4—1581no—
461C23×C4—1581no—
462C23×C4—1581no—
463C2×Q16—794no—
464C2×Q16—794no—
465C2×Q16—1584no—
466C2×Q16—1584no—
467C2×SD16—24no—
468C2×SD16—24no—
469C2×SD16C22×D7914yes—
470C2×SD16C22×D7914yes—
471C22×C8—791no—
472C22×C8—791no—
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8C22×D7914yes—
477#126—1588no—
478#126—1588no—
479#125—794no—
480#125—1588no—
481#125—1588no—
482#125—1582no—
483C22⋊Q8—794no—
484C22⋊Q8—794no—
485C22⋊Q8—1582no—
486C22⋊Q8—1582no—
487C4×Q8—794no—
488C4×Q8—794no—
489C4×Q8—794no—
490C4×Q8—794no—
491C4×Q8—1582no—
492C4×Q8—1582no—
493C4×Q8—1582no—
494C4×Q8—1582no—
495C4×D4—22no—
496C4×D4—794no—
497C4×D4—1582no—
498C4×D4—1588no—
499C4×D4—1588no—
500C4×D4C22×D7914yes—
501#117—794no—
502#117—794no—
503#117—1588no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—794no—
512C2×C4⋊C4—1582no—
513C2×C4⋊C4—1588no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4—1581no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4C22×D7911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—791no—
526C2×C22⋊C4—791no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C42—791no—
531C2×C42—1581no—
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42—1581no—
535C2×C42C22×D7911yescharacteristic
536#107—794no—
537#107—794no—
538#106—794no—
539#106—794no—
540C4⋊C8—794no—
541C4⋊C8C22×D7914yes—
542#103—794no—
543#103—794no—
544#103—794no—
545#103—794no—
546#103C22×D7914yes—
547#103C22×D7914yes—
548#102—794no—
549#102—794no—
550C22⋊C8—794no—
551C22⋊C8—794no—
552#97—794no—
553C4×C8—794no—
554C24—21no—
555C24—791no—
556#41—1588no—
557#41—15816no—
558#41—1588no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—794no—
566C2×Q8—792no—
567C2×Q8—1582no—
568C2×Q8—1581no—
569C2×Q8C23×D7912yes—
570C2×Q8C23×D7912yes—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—1584no—
574C2×D4—1588no—
575C2×D4#1192962314yes—
576C2×D4C23×D7912yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—82no—
582C22×C4—791no—
583C22×C4—791no—
584C22×C4—791no—
585C22×C4—792no—
586C22×C4—792no—
587C22×C4—6322no—
588C22×C4—6322no—
589C22×C4—1584no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1581no—
593C22×C4—1584no—
594C22×C4—1584no—
595C22×C4—1588no—
596C22×C4—1581no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4D4×D7911yescharacteristic
600C22×C4D4×D7911yescharacteristic
601C22×C4C23×D7911yescharacteristic
602Q16—1588no—
603Q16—1588no—
604SD16—28no—
605SD16—28no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—792no—
609C2×C8—792no—
610C2×C8—1582no—
611C2×C8—1582no—
612C2×C8C23×D7912yes—
613C2×C8C23×D7912yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—794no—
618C4⋊C4—794no—
619C4⋊C4—792no—
620C4⋊C4—792no—
621C4⋊C4—792no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1581no—
632C4⋊C4—1581no—
633C4⋊C4—1581no—
634C4⋊C4C23×D7912yes—
635C22⋊C4—24no—
636C22⋊C4—794no—
637C22⋊C4—794no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C42—792no—
642C42—792no—
643C42—1584no—
644C42—1584no—
645C42—1584no—
646C42—1584no—
647C42D4×D7912yes—
648C42C23×D7912yes—
649C23—24no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—792no—
654C23—1582no—
655C23—1582no—
656C23—1582no—
657C23C2×D4×D7911yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—794no—
665Q8—1584no—
666Q8—1582no—
667D4—24no—
668D4—22no—
669D4—15816no—
670D4C2×#1192962314yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—3162no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—792no—
684C2×C4—792no—
685C2×C4—792no—
686C2×C4—6324no—
687C2×C4—6324no—
688C2×C4—1582no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—15816no—
692C2×C4—1582no—
693C2×C4—1584no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1584no—
698C2×C4—1582no—
699C2×C4—1582no—
700C2×C4C2×D4×D7912yes—
701C2×C4C2×D4×D7912yes—
702C2×C4C2×D4×D7911yescharacteristic
703C2×C4#41×D7912yes—
704C2×C4C2×#1192962312yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1582no—
709C8—1582no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—3164no—
715C22—1582no—
716C22—1582no—
717C22—1582no—
718C22#1909907312yes—
719C22#1909936912yes—
720C22#1909937912yes—
721C22C22×D4×D7911yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—1582no—
731C4—1582no—
732C4—1582no—
733C4—1584no—
734C4#1909907312yes—
735C4C2×#41×D7911yescharacteristic
736C4C22×#1192962311yescharacteristic
737C2—44no—
738C2—3162no—
739C2#2377361114yesdirect product factor
740C2C2×#1909907311yescharacteristic
741C2C2×#1909936911yescharacteristic
742C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#461×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929623C22
hypercenterC2×#461D79
hypocenterC79C2×#3120
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#19099174C2semidirect
3. #23773611C2direct (N × H)
4. C2×#19098897C2semidirect
5. C2×#19098892C2semidirect
6. C2×#19098871C2semidirect
7. C2×#19098863C2semidirect
8. C2×#19098770C2semidirect
11. C2×#19098667C2semidirect
12. C2×#19098664C2semidirect
13. C2×#19098655C2semidirect
14. C2×SD16×Dic79C2semidirect
15. C2×#19098623C2semidirect
16. C2×#461×C79C2semidirect
21. #19099174C22semidirect
42. #19098897C22semidirect
43. #19098892C22semidirect
44. #19098871C22semidirect
45. #19098863C22semidirect
46. #19098770C22semidirect
49. #19098667C22semidirect
50. #19098664C22semidirect
51. #19098655C22semidirect
52. SD16×Dic79C22semidirect
53. #19098623C22semidirect
73. #461×C79C22semidirect
367. C2×C79#3120semidirect
380. C2×#461D79semidirect
388. C79C2×#3120semidirect
423. #461C2×D79semidirect
739. C2#23773611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991742
C2×#190990422
#237736112
C2×#190988972
C2×#190988922
C2×#190988712
C2×#190988632
C2×#190987702
C2×#190987222
C2×#190986672
C2×#190986642
C2×#190986552
C2×SD16×Dic792
C2×#190986232
C2×#461×C792
C2×#312079