Finite Group Databasebeta

← C2×#23773224 #35155821

Subgroups — C2×#23773224 #35155821

Order 20224.

2234 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×#19099190C211yesmaximal, characteristic, complemented
2C2×#19099035C211yesmaximal, characteristic
3#23773224C2116yesmaximal, direct product factor
4C2×#19098866C211yesmaximal, characteristic, complemented
5C2×#19098864C211yesmaximal, characteristic, complemented
6C2×#19098863C211yesmaximal, characteristic, complemented
7C2×#19098861C211yesmaximal, characteristic, complemented
8C2×#19098851C211yesmaximal, characteristic, complemented
9C2×#19098850C211yesmaximal, characteristic, complemented
10C2×#19098842C211yesmaximal, characteristic, complemented
11C2×#19098604C211yesmaximal, characteristic, complemented
12C2×#19098600C211yesmaximal, characteristic, complemented
13C2×#19098588C211yesmaximal, characteristic, complemented
14C2×#19098566C211yesmaximal, characteristic
15C2×#102×D79C211yesmaximal, characteristic
16C2×#474×C79C211yesmaximal, characteristic, complemented
17C22×D4×D79C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099190—24no—
21#19099190C2218yescomplemented
22C2×#14579160C2211yescharacteristic, complemented
23C2×#14579159—21no—
24C2×#14579153C2211yescharacteristic, complemented
25C2×#14579152C2211yescharacteristic, complemented
26C2×#14579151—21no—
27C2×#14579139—21no—
28C2×#14579137—21no—
29#19099035—24no—
30#19099035C2218yes—
31C2×C4×D316C2211yescharacteristic
32C2×D4×Dic79C2211yescharacteristic
33C2×#14579123C2211yescharacteristic
34C2×C4×C22⋊D79—21no—
35C2×(C22⋊D79)⋊C4—21no—
36C2×#14579119C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579118C2211yescharacteristic
39C2×C4⋊C4×D79C2211yescharacteristic
40C22×(C2×D79)⋊C4—21no—
41C2×C22⋊C4×D79—21no—
42#19098866C2218yescomplemented
43#19098864C2218yescomplemented
44#19098863C2218yescomplemented
45#19098861C2218yescomplemented
46#19098851C2218yescomplemented
47#19098850C2218yescomplemented
48#19098842C2218yescomplemented
49#19098604C2218yescomplemented
50#19098600C2218yescomplemented
51C2×#14579095C2211yescharacteristic, complemented
52C2×#14579094C2211yescharacteristic, complemented
53C2×#14579093C2211yescharacteristic, complemented
54C2×#14579092C2211yescharacteristic, complemented
55C2×#14579092C2211yescharacteristic, complemented
56C2×#14579092C2211yescharacteristic, complemented
57#19098588C2218yescomplemented
58C2×C4⋊(C79⋊C8)C2211yescharacteristic, complemented
59C2×Dic79⋊C8C2211yescharacteristic, complemented
60C2×Dic79⋊C8C2211yescharacteristic, complemented
61#19098566C2218yes—
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×#14579081C2211yescharacteristic
68#102×D79C2218yes—
69C2×C4⋊Q8×C79C2211yescharacteristic, complemented
70C2×C4×D4×C79C2211yescharacteristic
71#474×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic, complemented
73C2×#107×C79C2211yescharacteristic, complemented
74C2×C4⋊C8×C79C2211yescharacteristic, complemented
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C24×D79—21no—
78C22×Dic158—21no—
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C2×D4×D79—22no—
82C2×D4×D79—24no—
83C2×D4×D79Q818yescomplemented
84C2×D4×D79C2314yes—
85C23×Dic79—21no—
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79C2311yescharacteristic
90C2×#11929607—24no—
91C2×#11929607C2314yes—
92C22×C79⋊C8C2311yescharacteristic
93C22×C79⋊C8C2311yescharacteristic
94C2×C8×D79—24no—
95C2×C8×D79C2314yes—
96#14579160—22no—
97#14579160C2314yescomplemented
98#14579159—28no—
99#14579153—22no—
100#14579153C2314yescomplemented
101#14579152—22no—
102#14579152C2314yescomplemented
103#14579151—28no—
104#14579139—28no—
105#14579137—28no—
106C4×D316—22no—
107C4×D316C2314yes—
108D4×Dic79—22no—
109D4×Dic79C2314yes—
110#14579123—22no—
111#14579123C2314yes—
112C4×C22⋊D79—28no—
113(C22⋊D79)⋊C4—28no—
114#14579119—22no—
115#14579119—22no—
116#14579119C2314yes—
117#14579119C2314yes—
118#14579118D414yes—
119#14579118C2314yes—
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⋊C4D411yescharacteristic
130C2×Dic79⋊C4D411yescharacteristic
131C4⋊C4×D79—22no—
132C4⋊C4×D79C2314yes—
133C2×C22⋊Dic79—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—28no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×(C2×D79)⋊C4D411yescharacteristic
141C22⋊C4×D79—28no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579095C2314yescomplemented
146#14579094C2314yescomplemented
147#14579093C2314yescomplemented
148#14579092C2314yescomplemented
149#14579092C2314yescomplemented
150#14579092C2314yescomplemented
151C4⋊(C79⋊C8)C2314yescomplemented
152Dic79⋊C8C2314yescomplemented
153Dic79⋊C8C2314yescomplemented
154#14579083C2314yes—
155#14579083C2314yes—
156#14579082C2314yes—
157#14579082C2314yes—
158#14579081C2314yes—
159#14579081C2314yes—
160C22×Q8×C79—21no—
161C22×D4×C79C2311yescharacteristic
162C23×C4×C79—21no—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C4⋊Q8×C79—22no—
166C4⋊Q8×C79C2314yescomplemented
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C22⋊C4×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yescomplemented
176#107×C79C2314yescomplemented
177C4⋊C8×C79C2314yescomplemented
178#102×C79C2314yes—
179#102×C79C2314yes—
180C23×D79—21no—
181C23×D79—28no—
182C23×D79—24no—
183C23×D79—82no—
184C23×D79—82no—
185C23×D79C2×D411yescharacteristic
186C2×Dic158—24no—
187C2×Dic158—82no—
188C2×D316—21no—
189C2×D316—22no—
190C2×D316C2×Q814yes—
191C2×D316C2412yes—
192C2×C22⋊D79—28no—
193C2×C22⋊D79—24no—
194D4×D79—216no—
195D4×D79—28no—
196D4×D79C2×Q8116yescomplemented
197C22×Dic79—24no—
198C22×Dic79—21no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—82no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—24no—
206C2×C4×D79—24no—
207C2×C4×D79—24no—
208C2×C4×D79—82no—
209C2×C4×D79—82no—
210C2×C4×D79—82no—
211C2×C4×D79C2×D412yes—
212C2×C4×D79C2×Q814yes—
213C2×C4×D79#4114yes—
214C2×C4×D79C2412yes—
215#11929607—28no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8—22no—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C8×D79—28no—
221C4⋊Dic79—24no—
222C4⋊Dic79—21no—
223C4⋊Dic79—21no—
224C4⋊Dic79—21no—
225C4⋊Dic79C2412yes—
226C4⋊Dic79C2412yes—
227C4⋊Dic79C2412yes—
228Dic79⋊C4—24no—
229Dic79⋊C4—24no—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4C2×D414yes—
234Dic79⋊C4C2×D414yes—
235C22⋊Dic79—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4C2×D414yes—
241(C2×D79)⋊C4C2×D414yes—
242C4×Dic79—24no—
243C4×Dic79—24no—
244C4×Dic79C2×D412yes—
245C4×Dic79C2412yes—
246C24×C79—21no—
247C2×Q8×C79—24no—
248C2×Q8×C79—82no—
249C2×D4×C79—21no—
250C2×D4×C79—22no—
251C2×D4×C79C2×Q814yes—
252C2×D4×C79C2412yes—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—24no—
257C22×C4×C79—82no—
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2411yescharacteristic
261C2×C8×C79—22no—
262C2×C8×C79—22no—
263C2×C8×C79C2412yes—
264C2×C8×C79C2412yes—
265C4⋊C4×C79—24no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79C2412yes—
270C4⋊C4×C79C2412yes—
271C4⋊C4×C79C2412yes—
272C22⋊C4×C79—24no—
273C42×C79C2×D412yes—
274C42×C79C2412yes—
275C23×C79—24no—
276C23×C79—22no—
277C23×C79—42no—
278C23×C79—42no—
279C23×C79C22×D411yescharacteristic
280C22×D79—22no—
281C22×D79—22no—
282C22×D79—24no—
283C22×D79—22no—
284C22×D79—216no—
285C22×D79—42no—
286C22×D79—42no—
287C22×D79—816no—
288C22×D79—84no—
289C22×D79—84no—
290C22×D79C22⋊Q814yes—
291C22×D79C22×D412yes—
292Q8×C79—84no—
293D4×C79—24no—
294D4×C79—22no—
295D4×C79C22×Q814yes—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79—42no—
304C2×C4×C79—84no—
305C2×C4×C79C22×D412yes—
306C2×C4×C79C22×D412yes—
307C2×C4×C79C22×D411yescharacteristic
308C2×C4×C79C22×Q812yes—
309C2×C4×C79C2×#4112yes—
310C2×C4×C79C2511yescharacteristic
311C22⋊D79—216no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—84no—
321C2×Dic79C22⋊Q814yes—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325D316—24no—
326D316—22no—
327D316C22×Q814yes—
328C4×D79—84no—
329C4×D79—84no—
330C4×D79—84no—
331C4×D79C22⋊Q818yes—
332C4×D79C22×Q814yes—
333C4×D79C2×#4114yes—
334Dic158—84no—
335C8×C79—22no—
336C8×C79—22no—
337C79⋊C8—22no—
338C79⋊C8—22no—
339C22×C79—24no—
340C22×C79—48no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79C2×C22⋊Q812yes—
344C22×C79#57612yes—
345C22×C79#57712yes—
346C22×C79C23×D411yescharacteristic
347C2×D79—28no—
348C2×D79—22no—
349C2×D79—22no—
350C2×D79—24no—
351C2×D79—48no—
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—816no—
355C2×D79C2×C22⋊Q814yes—
356C4×C79—22no—
357C4×C79—22no—
358C4×C79—42no—
359C4×C79—42no—
360C4×C79—42no—
361C4×C79C2×C22⋊Q812yes—
362C4×C79C23×Q811yescharacteristic
363C4×C79C22×#4111yescharacteristic
364Dic79—22no—
365Dic79—22no—
366Dic79—42no—
367Dic79—42no—
368Dic79—42no—
369Dic79C2×C22⋊Q814yes—
370C2×#3081—791nomaximal, Sylow
371C2×C79—44no—
372C2×C79#308114yescomplemented
373C2×C79C22×C22⋊Q811yescharacteristic
374C2×C79C2×#57611yescharacteristic
375C2×C79C2×#57711yescharacteristic
376D79—24no—
377D79—44no—
378C2×#544—791no—
379C2×#518—791no—
380#3081—7916no—
381C2×#478—791no—
382C2×#478—791no—
383C2×#478—791no—
384C2×#478—791no—
385C2×#476—791no—
386C2×#476—791no—
387C2×#474—791no—
388C2×#474D7911yescharacteristic, complemented
389C2×#428—791no—
390C2×#427—791no—
391C2×#424—791no—
392C2×#418—791no—
393C22×#102—791no—
394C79C2×#308111yescharacteristic, complemented, Sylow
395C23×D4—791no—
396C22×M16—791no—
397C23×C8—791no—
398#544—798no—
399#544—1584no—
400C2×C4⋊Q8—791no—
401C2×C4⋊Q8—1581no—
402C2×C4⋊Q8C2×D7911yescharacteristic, complemented
403C2×#125—791no—
404C2×#125—791no—
405C2×#125—1581no—
406C2×C22⋊Q8—1581no—
407C2×C22⋊Q8—1581no—
408#518—798no—
409#518—1584no—
410C2×C4×D4—791no—
411C2×C4×D4—791no—
412C2×C4×D4—791no—
413C2×C4×D4—1581no—
414C2×C4×D4—1581no—
415C2×C4×D4C2×D7911yescharacteristic
416C2×#117—791no—
417C2×#117—791no—
418C2×#117—791no—
419C22×C4⋊C4—791no—
420C22×C22⋊C4—1581no—
421C22×C22⋊C4—1581no—
422#478—798no—
423#478—798no—
424#478—798no—
425#478—798no—
426#476—798no—
427#476—798no—
428#474—798no—
429#474C2×D7918yescomplemented
430#428—798no—
431#427—798no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107C2×D7911yescharacteristic, complemented
435C2×#107C2×D7911yescharacteristic, complemented
436C2×#106—791no—
437C2×#106—791no—
438C2×#106—791no—
439C2×#106—791no—
440#424—798no—
441C2×C4⋊C8—791no—
442C2×C4⋊C8—791no—
443C2×C4⋊C8—791no—
444C2×C4⋊C8C2×D7911yescharacteristic, complemented
445#418—798no—
446C2×#102—791no—
447C2×#102—791no—
448C2×#102—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#102—798no—
453C2×#102C2×D7911yescharacteristic
454C2×#102C2×D7911yescharacteristic
455C25—1581no—
456C22×Q8—21no—
457C22×Q8—1581no—
458C22×D4—798no—
459C22×D4—794no—
460C22×D4—791no—
461C22×D4—1582no—
462C22×D4—1584no—
463C22×D4—1581no—
464C22×D4C22×D7911yescharacteristic
465C23×C4—21no—
466C23×C4—791no—
467C23×C4—1581no—
468C23×C4—1581no—
469C23×C4—1581no—
470C23×C4—1581no—
471C2×M16—794no—
472C2×M16—1584no—
473C22×C8—791no—
474C22×C8—791no—
475C22×C8—794no—
476C22×C8—1584no—
477C22×C8C22×D7911yescharacteristic
478C22×C8C22×D7911yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—794no—
481C4⋊Q8—1582no—
482C4⋊Q8—1588no—
483C4⋊Q8C22×D7914yescomplemented
484#125—794no—
485#125—794no—
486#125—1582no—
487#125—1588no—
488#125—1582no—
489C22⋊Q8—1588no—
490C22⋊Q8—1588no—
491C4×D4—22no—
492C4×D4—794no—
493C4×D4—794no—
494C4×D4—794no—
495C4×D4—1582no—
496C4×D4—1582no—
497C4×D4—1588no—
498C4×D4—1588no—
499C4×D4—1582no—
500C4×D4C22×D7914yes—
501#117—794no—
502#117—794no—
503#117—794no—
504#117—794no—
505#117—1582no—
506#117—1582no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—794no—
514C2×C4⋊C4—1582no—
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⋊C4C22×D7911yescharacteristic
522C2×C4⋊C4C22×D7911yescharacteristic
523C2×C4⋊C4C22×D7911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—791no—
526C2×C22⋊C4—791no—
527C2×C22⋊C4—1588no—
528C2×C22⋊C4—1588no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C42—791no—
535C2×C42—1581no—
536C2×C42—1581no—
537C2×C42C22×D7911yescharacteristic
538#107—794no—
539#107—794no—
540#107C22×D7914yescomplemented
541#107C22×D7914yescomplemented
542#106—794no—
543#106—794no—
544#106—794no—
545#106—794no—
546C4⋊C8—794no—
547C4⋊C8—794no—
548C4⋊C8—794no—
549C4⋊C8C22×D7914yescomplemented
550#102—794no—
551#102—794no—
552#102—794no—
553#102—794no—
554#102—794no—
555#102—794no—
556#102C22×D7914yes—
557#102C22×D7914yes—
558C24—21no—
559C24—791no—
560C24—6322no—
561C24—6322no—
562C24—1584no—
563C24—1588no—
564C24—1581no—
565C2×Q8—24no—
566C2×Q8—82no—
567C2×Q8—6322no—
568C2×Q8—1584no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—7916no—
572C2×D4—794no—
573C2×D4—792no—
574C2×D4—15816no—
575C2×D4—1588no—
576C2×D4—1584no—
577C2×D4—1588no—
578C2×D4—1582no—
579C2×D4—1581no—
580C2×D4Q8×D7914yes—
581C2×D4C23×D7912yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—791no—
588C22×C4—794no—
589C22×C4—794no—
590C22×C4—792no—
591C22×C4—792no—
592C22×C4—791no—
593C22×C4—791no—
594C22×C4—6322no—
595C22×C4—6322no—
596C22×C4—6322no—
597C22×C4—6322no—
598C22×C4—1584no—
599C22×C4—1584no—
600C22×C4—1581no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1584no—
604C22×C4—1584no—
605C22×C4D4×D7911yescharacteristic
606C22×C4D4×D7911yescharacteristic
607C22×C4C23×D7911yescharacteristic
608M16—1588no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—792no—
612C2×C8—792no—
613C2×C8—1588no—
614C2×C8—1582no—
615C2×C8—1582no—
616C2×C8C23×D7912yes—
617C2×C8C23×D7912yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—794no—
623C4⋊C4—794no—
624C4⋊C4—792no—
625C4⋊C4—792no—
626C4⋊C4—792no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1584no—
632C4⋊C4—1584no—
633C4⋊C4—1581no—
634C4⋊C4—1581no—
635C4⋊C4—1581no—
636C4⋊C4C23×D7912yes—
637C4⋊C4C23×D7912yes—
638C4⋊C4C23×D7912yes—
639C22⋊C4—24no—
640C22⋊C4—794no—
641C22⋊C4—794no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C42—792no—
648C42—792no—
649C42—1584no—
650C42—1584no—
651C42D4×D7912yes—
652C42C23×D7912yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—3162no—
658C23—3162no—
659C23—794no—
660C23—792no—
661C23—63216no—
662C23—6324no—
663C23—6324no—
664C23—15816no—
665C23—1584no—
666C23—1582no—
667C23—1582no—
668C23—1582no—
669C23C2×D4×D7911yescharacteristic
670Q8—84no—
671Q8—6324no—
672D4—24no—
673D4—22no—
674D4—794no—
675D4—15816no—
676D4—1584no—
677D4—1582no—
678D4C2×Q8×D7914yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—3162no—
689C2×C4—3162no—
690C2×C4—3162no—
691C2×C4—794no—
692C2×C4—792no—
693C2×C4—798no—
694C2×C4—794no—
695C2×C4—794no—
696C2×C4—792no—
697C2×C4—792no—
698C2×C4—6324no—
699C2×C4—6324no—
700C2×C4—6324no—
701C2×C4—6324no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4C2×D4×D7912yes—
708C2×C4C2×D4×D7912yes—
709C2×C4C2×D4×D7911yescharacteristic
710C2×C4C2×Q8×D7912yes—
711C2×C4#41×D7912yes—
712C2×C4C24×D7911yescharacteristic
713C8—22no—
714C8—22no—
715C8—1582no—
716C8—1582no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—3168no—
722C22—3162no—
723C22—3162no—
724C22—794no—
725C22—63216no—
726C22—1584no—
727C22—1588no—
728C22—1582no—
729C22—1582no—
730C22C22⋊Q8×D7912yes—
731C22#1909936412yes—
732C22#1909937212yes—
733C22C22×D4×D7911yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—3162no—
740C4—3162no—
741C4—3162no—
742C4—794no—
743C4—1582no—
744C4—1582no—
745C4C22⋊Q8×D7912yes—
746C4C22×Q8×D7911yescharacteristic
747C4C2×#41×D7911yescharacteristic
748C2—44no—
749C2—3164no—
750C2—1584no—
751C2#2377322414yesdirect product factor
752C2C2×C22⋊Q8×D7911yescharacteristic
753C2C2×#1909936411yescharacteristic
754C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#474×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×D79C22
hypercenterC2×#474D79
hypocenterC79C2×#3081
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#19099190C2semidirect
3. #23773224C2direct (N × H)
4. C2×#19098866C2semidirect
5. C2×#19098864C2semidirect
6. C2×#19098863C2semidirect
7. C2×#19098861C2semidirect
8. C2×#19098851C2semidirect
9. C2×#19098850C2semidirect
10. C2×#19098842C2semidirect
11. C2×#19098604C2semidirect
12. C2×#19098600C2semidirect
13. C2×#19098588C2semidirect
16. C2×#474×C79C2semidirect
21. #19099190C22semidirect
22. C2×#14579160C22semidirect
24. C2×#14579153C22semidirect
25. C2×#14579152C22semidirect
42. #19098866C22semidirect
43. #19098864C22semidirect
44. #19098863C22semidirect
45. #19098861C22semidirect
46. #19098851C22semidirect
47. #19098850C22semidirect
48. #19098842C22semidirect
49. #19098604C22semidirect
50. #19098600C22semidirect
51. C2×#14579095C22semidirect
52. C2×#14579094C22semidirect
53. C2×#14579093C22semidirect
54. C2×#14579092C22semidirect
55. C2×#14579092C22semidirect
56. C2×#14579092C22semidirect
57. #19098588C22semidirect
58. C2×C4⋊(C79⋊C8)C22semidirect
59. C2×Dic79⋊C8C22semidirect
60. C2×Dic79⋊C8C22semidirect
69. C2×C4⋊Q8×C79C22semidirect
71. #474×C79C22semidirect
72. C2×#107×C79C22semidirect
73. C2×#107×C79C22semidirect
74. C2×C4⋊C8×C79C22semidirect
83. C2×D4×D79Q8semidirect
97. #14579160C23semidirect
100. #14579153C23semidirect
102. #14579152C23semidirect
145. #14579095C23semidirect
146. #14579094C23semidirect
147. #14579093C23semidirect
148. #14579092C23semidirect
149. #14579092C23semidirect
150. #14579092C23semidirect
151. C4⋊(C79⋊C8)C23semidirect
152. Dic79⋊C8C23semidirect
153. Dic79⋊C8C23semidirect
166. C4⋊Q8×C79C23semidirect
175. #107×C79C23semidirect
176. #107×C79C23semidirect
177. C4⋊C8×C79C23semidirect
196. D4×D79C2×Q8semidirect
372. C2×C79#3081semidirect
388. C2×#474D79semidirect
394. C79C2×#3081semidirect
402. C2×C4⋊Q8C2×D79semidirect
429. #474C2×D79semidirect
434. C2×#107C2×D79semidirect
435. C2×#107C2×D79semidirect
444. C2×C4⋊C8C2×D79semidirect
483. C4⋊Q8C22×D79semidirect
540. #107C22×D79semidirect
541. #107C22×D79semidirect
549. C4⋊C8C22×D79semidirect
751. C2#23773224direct (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×#190990352
#237732242
C2×#190988662
C2×#190988642
C2×#190988632
C2×#190988612
C2×#190988512
C2×#190988502
C2×#190988422
C2×#190986042
C2×#190986002
C2×#190985882
C2×#190985662
C2×#102×D792
C2×#474×C792
C2×#308179