Finite Group Databasebeta

← C2×#23776215 #35168005

Subgroups — C2×#23776215 #35168005

Order 20224.

1906 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099296C211yesmaximal, characteristic
2C2×Q8×Dic158C211yesmaximal, characteristic, complemented
3#23776215C2116yesmaximal, direct product factor
4C2×#19098923C211yesmaximal, characteristic, complemented
5C2×#19098921C211yesmaximal, characteristic, complemented
6C2×#19098908C211yesmaximal, characteristic
7C2×#19098857C211yesmaximal, characteristic, complemented
8C2×#19098843C211yesmaximal, characteristic, complemented
9C2×#19098842C211yesmaximal, characteristic, complemented
10C2×#19098785C211yesmaximal, characteristic, complemented
11C2×#19098783C211yesmaximal, characteristic, complemented
12C2×#19098761C211yesmaximal, characteristic
13C2×#19098691C211yesmaximal, characteristic, complemented
14C2×#19098666C211yesmaximal, characteristic, complemented
15C2×#19098655C211yesmaximal, characteristic, complemented
16C2×#440×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19#19099296—24no—
20#19099296C2218yes—
21Q8×Dic158—24no—
22Q8×Dic158C2218yescomplemented
23C2×#14579161—21no—
24C2×#14579161C2211yescharacteristic
25C2×#14579160—21no—
26C2×#14579160—21no—
27C2×#14579160C2211yescharacteristic
28C2×#14579160C2211yescharacteristic
29C2×#14579157C2211yescharacteristic
30C2×#14579149C2211yescharacteristic
31C2×#14579148C2211yescharacteristic
32C2×#14579147—21no—
33C2×#14579144—21no—
34C2×#14579143—21no—
35C2×Q8×Dic79C2211yescharacteristic
36C2×Q8×Dic79C2211yescharacteristic
37C2×C4×Dic158—21no—
38C2×C4×Dic158C2211yescharacteristic
39C2×#14579126C2211yescharacteristic
40C2×#14579123C2211yescharacteristic
41C2×C4×C22⋊D79—21no—
42#19098923C2218yescomplemented
43#19098921C2218yescomplemented
44#19098908C2218yes—
45#19098857C2218yescomplemented
46#19098843C2218yescomplemented
47#19098842C2218yescomplemented
48#19098785C2218yescomplemented
49#19098783C2218yescomplemented
50#19098761C2218yes—
51#19098691C2218yescomplemented
52#19098666C2218yescomplemented
53#19098655C2218yescomplemented
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×C4⋊(C79⋊C8)C2211yescharacteristic
57C2×Dic79⋊C8C2211yescharacteristic
58C2×Dic79⋊C8C2211yescharacteristic
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579083C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C2×C4×Q8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#440×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158—21no—
80C22×Dic158D411yescharacteristic
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C22⋊D79—21no—
85C22×C4×D79—21no—
86C2×#11929614—24no—
87C2×#11929614C2314yes—
88C2×#11929611—24no—
89C2×#11929611C2314yes—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92#14579161—22no—
93#14579161—28no—
94#14579161C2314yes—
95#14579160—28no—
96#14579160—28no—
97#14579160—22no—
98#14579160—22no—
99#14579160C2314yes—
100#14579160C2314yes—
101#14579157—22no—
102#14579157C2314yes—
103#14579149—22no—
104#14579149C2314yes—
105#14579148—22no—
106#14579148C2314yes—
107#14579147—28no—
108#14579144—28no—
109#14579143—28no—
110Q8×Dic79—22no—
111Q8×Dic79—22no—
112Q8×Dic79C2314yes—
113Q8×Dic79C2314yes—
114C4×Dic158—28no—
115C4×Dic158D414yes—
116C4×Dic158C2314yes—
117#14579126—22no—
118#14579126C2314yes—
119#14579123—22no—
120#14579123C2314yes—
121C4×C22⋊D79—28no—
122C2×C4⋊Dic79—21no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79D411yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4D411yescharacteristic
132C2×Dic79⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142C2×C4×Dic79C2311yescharacteristic
143#14579094C2314yes—
144#14579094C2314yes—
145C4⋊(C79⋊C8)C2314yes—
146Dic79⋊C8C2314yes—
147Dic79⋊C8C2314yes—
148#14579086C2314yes—
149#14579086C2314yes—
150#14579084C2314yes—
151#14579083C2314yes—
152#14579083C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155#14579081C2314yes—
156#14579071C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79C2311yescharacteristic
160C23×C4×C79—21no—
161C2×SD16×C79—24no—
162C2×SD16×C79C2314yes—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C4×Q8×C79—22no—
166C4×Q8×C79C2314yes—
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C42×C79—21no—
174C2×C42×C79C2311yescharacteristic
175#107×C79C2314yes—
176#103×C79C2314yes—
177#102×C79C2314yes—
178#97×C79C2314yes—
179C23×D79—21no—
180C2×Dic158—24no—
181C2×Dic158—24no—
182C2×Dic158—24no—
183C2×Dic158—21no—
184C2×Dic158—24no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—82no—
188C2×Dic158—82no—
189C2×Dic158—82no—
190C2×Dic158C2×D414yes—
191C2×Dic158C2412yes—
192C2×D316—21no—
193C2×D316—22no—
194C2×D316—22no—
195C2×D316C2412yes—
196C2×C22⋊D79—24no—
197C2×C22⋊D79—24no—
198C2×C22⋊D79—44no—
199C2×C22⋊D79—82no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D411yescharacteristic
207C2×C4×D79—24no—
208C2×C4×D79—82no—
209#11929614—28no—
210#11929611—28no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8C2412yes—
214C2×C79⋊C8C2412yes—
215C4⋊Dic79—24no—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79C2×D414yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4C2×D414yes—
227Dic79⋊C4C2×D414yes—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79C2×D412yes—
237C4×Dic79C2×D412yes—
238C4×Dic79C2412yes—
239C4×Dic79C2412yes—
240C24×C79—21no—
241C2×Q8×C79—21no—
242C2×Q8×C79—22no—
243C2×Q8×C79#4114yes—
244C2×Q8×C79C2412yes—
245C2×D4×C79—21no—
246C2×D4×C79—22no—
247C2×D4×C79—22no—
248C2×D4×C79C2412yes—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—24no—
253C22×C4×C79—82no—
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2411yescharacteristic
257SD16×C79—28no—
258C2×C8×C79—22no—
259C2×C8×C79—22no—
260C2×C8×C79C2412yes—
261C2×C8×C79C2412yes—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79C2412yes—
266C4⋊C4×C79C2412yes—
267C22⋊C4×C79—24no—
268C42×C79—24no—
269C42×C79C2×D412yes—
270C42×C79C2412yes—
271C23×C79—22no—
272C23×C79—42no—
273C23×C79—42no—
274C23×C79—42no—
275C23×C79C22×D411yescharacteristic
276C22×D79—22no—
277C22×D79—42no—
278C22×D79—42no—
279C22×D79—42no—
280Q8×C79—24no—
281Q8×C79—22no—
282Q8×C79C2×#4114yes—
283D4×C79—22no—
284D4×C79—22no—
285D4×C79—42no—
286C2×C4×C79—24no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—42no—
293C2×C4×C79—42no—
294C2×C4×C79—84no—
295C2×C4×C79C22×D412yes—
296C2×C4×C79C22×D412yes—
297C2×C4×C79C22×D411yescharacteristic
298C2×C4×C79C2×#4112yes—
299C2×C4×C792−1+412yes—
300C2×C4×C79C2511yescharacteristic
301C22⋊D79—48no—
302C22⋊D79—84no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79#13714yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315C2×Dic79C22×D412yes—
316C2×Dic79C22×D412yes—
317D316—22no—
318D316—22no—
319D316—42no—
320C4×D79—84no—
321Dic158—28no—
322Dic158—22no—
323Dic158—22no—
324Dic158—42no—
325Dic158—84no—
326Dic158—84no—
327Dic158—84no—
328C8×C79—22no—
329C8×C79—22no—
330C79⋊C8—22no—
331C79⋊C8—22no—
332C22×C79—42no—
333C22×C79—42no—
334C22×C79—42no—
335C22×C79—84no—
336C22×C79#54812yes—
337C22×C79C2×#13712yes—
338C22×C79#57612yes—
339C22×C79C23×D411yescharacteristic
340C2×D79—42no—
341C2×D79—42no—
342C2×D79—42no—
343C2×D79—84no—
344C4×C79—24no—
345C4×C79—22no—
346C4×C79—22no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79#54812yes—
350C4×C79C22×#4111yescharacteristic
351C4×C79C2×2−1+411yescharacteristic
352Dic79—22no—
353Dic79—22no—
354Dic79—22no—
355Dic79—42no—
356Dic79—42no—
357Dic79—42no—
358Dic79C2×#13714yes—
359C2×#3375—791nomaximal, Sylow
360C2×C79—82no—
361C2×C79#337514yescomplemented
362C2×C79C2×#54811yescharacteristic
363C2×C79C22×#13711yescharacteristic
364C2×C79C2×#57611yescharacteristic
365D79—82no—
366C2×#559—791no—
367C2×Q82—791no—
368#3375—7916no—
369C2×#489—791no—
370C2×#489—791no—
371C2×#486—791no—
372C2×#477—791no—
373C2×#474—791no—
374C2×#474—791no—
375C2×#464—791no—
376C2×#464—791no—
377C2×#460—791no—
378C2×#446—791no—
379C2×#440—791no—
380C2×#440D7911yescharacteristic, complemented
381C2×C4×Q16—791no—
382C79C2×#337511yescharacteristic, complemented, Sylow
383C22×Q16—791no—
384C22×SD16—791no—
385C22×SD16C2×D7911yescharacteristic
386#559—798no—
387#559—1584no—
388Q82—798no—
389Q82—1584no—
390C2×C4⋊Q8—791no—
391C2×C4⋊Q8—791no—
392C2×C4⋊Q8—791no—
393C2×C4⋊Q8—1581no—
394C2×C4⋊Q8—1581no—
395C2×C4⋊Q8—1581no—
396C2×#127—791no—
397C2×#124—791no—
398C2×#124—791no—
399C2×#124—1581no—
400C2×#123—1581no—
401C2×#123—1581no—
402C2×C4×Q8—791no—
403C2×C4×Q8—791no—
404C2×C4×Q8—791no—
405C2×C4×Q8—791no—
406C2×C4×Q8—1581no—
407C2×C4×Q8C2×D7911yescharacteristic
408C2×C4×D4—791no—
409C2×C4×D4—1581no—
410C2×C4×D4C2×D7911yescharacteristic
411#489—798no—
412#489—798no—
413#486—798no—
414#477—798no—
415#474—798no—
416#474—798no—
417#464—798no—
418#464—798no—
419#460—798no—
420#446—798no—
421#440—798no—
422#440C2×D7918yescomplemented
423C4×Q16—798no—
424C2×#107—791no—
425C2×#107—791no—
426C2×#107C2×D7911yescharacteristic
427C2×C4⋊C8—791no—
428C2×C4⋊C8—791no—
429C2×C4⋊C8—791no—
430C2×#103—791no—
431C2×#103—791no—
432C2×#103—791no—
433C2×#103C2×D7911yescharacteristic
434C2×#102—791no—
435C2×#102—791no—
436C2×#102—791no—
437C2×#102—791no—
438C2×#102—791no—
439C2×#102C2×D7911yescharacteristic
440C2×#97—791no—
441C2×#97C2×D7911yescharacteristic
442C2×C4×C8—791no—
443C22×Q8—791no—
444C22×Q8—791no—
445C22×Q8—1581no—
446C22×Q8—1581no—
447C22×Q8—1581no—
448C22×Q8C22×D7911yescharacteristic
449C22×D4—791no—
450C22×D4—1581no—
451C22×D4—1581no—
452C22×D4C22×D7911yescharacteristic
453C23×C4—21no—
454C23×C4—1581no—
455C2×Q16—794no—
456C2×Q16—1584no—
457C2×SD16—24no—
458C2×SD16—794no—
459C2×SD16—1584no—
460C2×SD16C22×D7914yes—
461C22×C8—791no—
462C22×C8—791no—
463C22×C8C22×D7911yescharacteristic
464C22×C8C22×D7911yescharacteristic
465C4⋊Q8—794no—
466C4⋊Q8—794no—
467C4⋊Q8—794no—
468C4⋊Q8—1588no—
469C4⋊Q8—1582no—
470C4⋊Q8—1582no—
471C4⋊Q8—1588no—
472C4⋊Q8—1588no—
473C4⋊Q8—1582no—
474#127—794no—
475#127—1582no—
476#124—794no—
477#124—794no—
478#124—1582no—
479#124—1588no—
480#124—1582no—
481#123—1588no—
482#123—1588no—
483C4×Q8—22no—
484C4×Q8—794no—
485C4×Q8—794no—
486C4×Q8—794no—
487C4×Q8—794no—
488C4×Q8—794no—
489C4×Q8—1588no—
490C4×Q8—1582no—
491C4×Q8—1582no—
492C4×Q8—1582no—
493C4×Q8C22×D7914yes—
494C4×D4—22no—
495C4×D4—794no—
496C4×D4—1582no—
497C4×D4—1588no—
498C4×D4C22×D7914yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—791no—
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⋊C4C22×D7911yescharacteristic
512C2×C4⋊C4C22×D7911yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1581no—
515C2×C22⋊C4—1581no—
516C2×C22⋊C4—1581no—
517C2×C22⋊C4—1581no—
518C2×C22⋊C4—1581no—
519C2×C42—21no—
520C2×C42—791no—
521C2×C42—791no—
522C2×C42—1581no—
523C2×C42—1581no—
524C2×C42—1581no—
525C2×C42C22×D7911yescharacteristic
526#107—794no—
527#107—794no—
528#107C22×D7914yes—
529C4⋊C8—794no—
530C4⋊C8—794no—
531C4⋊C8—794no—
532#103—794no—
533#103—794no—
534#103—794no—
535#103C22×D7914yes—
536#102—794no—
537#102—794no—
538#102—794no—
539#102—794no—
540#102—794no—
541#102C22×D7914yes—
542#97—794no—
543#97C22×D7914yes—
544C4×C8—794no—
545C24—21no—
546C24—1581no—
547C2×Q8—22no—
548C2×Q8—21no—
549C2×Q8—794no—
550C2×Q8—792no—
551C2×Q8—6322no—
552C2×Q8—6322no—
553C2×Q8—6322no—
554C2×Q8—1584no—
555C2×Q8—1584no—
556C2×Q8—1584no—
557C2×Q8—1582no—
558C2×Q8—1582no—
559C2×Q8—1581no—
560C2×Q8—1584no—
561C2×Q8#1192962414yes—
562C2×Q8C23×D7912yes—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—3164no—
567C2×D4—792no—
568C2×D4—6322no—
569C2×D4—1584no—
570C2×D4—1584no—
571C2×D4—1582no—
572C2×D4—1582no—
573C2×D4—1581no—
574C2×D4C23×D7912yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—791no—
581C22×C4—791no—
582C22×C4—791no—
583C22×C4—791no—
584C22×C4—6322no—
585C22×C4—1584no—
586C22×C4—1581no—
587C22×C4—1581no—
588C22×C4—1581no—
589C22×C4D4×D7911yescharacteristic
590C22×C4D4×D7911yescharacteristic
591C22×C4C23×D7911yescharacteristic
592Q16—1588no—
593SD16—28no—
594SD16—1588no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—792no—
598C2×C8—792no—
599C2×C8—1582no—
600C2×C8—1582no—
601C2×C8C23×D7912yes—
602C2×C8C23×D7912yes—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—794no—
607C4⋊C4—794no—
608C4⋊C4—794no—
609C4⋊C4—792no—
610C4⋊C4—792no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1584no—
614C4⋊C4—1584no—
615C4⋊C4—1584no—
616C4⋊C4—1581no—
617C4⋊C4—1581no—
618C4⋊C4—1584no—
619C4⋊C4C23×D7912yes—
620C4⋊C4C23×D7912yes—
621C22⋊C4—24no—
622C22⋊C4—1584no—
623C22⋊C4—1584no—
624C22⋊C4—1584no—
625C22⋊C4—1584no—
626C22⋊C4—1584no—
627C42—24no—
628C42—792no—
629C42—792no—
630C42—792no—
631C42—792no—
632C42—1584no—
633C42—1584no—
634C42—1584no—
635C42D4×D7912yes—
636C42C23×D7912yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—3162no—
642C23—3162no—
643C23—3162no—
644C23—1582no—
645C23C2×D4×D7911yescharacteristic
646Q8—22no—
647Q8—24no—
648Q8—3162no—
649Q8—6324no—
650Q8—6324no—
651Q8—6324no—
652Q8—1588no—
653Q8—1582no—
654Q8—1582no—
655Q8C2×#1192962414yes—
656D4—22no—
657D4—22no—
658D4—42no—
659D4—3168no—
660D4—3162no—
661D4—6324no—
662D4—1582no—
663D4—1582no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—3162no—
674C2×C4—3162no—
675C2×C4—3162no—
676C2×C4—794no—
677C2×C4—792no—
678C2×C4—792no—
679C2×C4—792no—
680C2×C4—792no—
681C2×C4—6324no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4C2×D4×D7912yes—
689C2×C4C2×D4×D7912yes—
690C2×C4C2×D4×D7911yescharacteristic
691C2×C4C2×#1192962412yes—
692C2×C4#1457920812yes—
693C2×C4C24×D7911yescharacteristic
694C8—22no—
695C8—22no—
696C8—1582no—
697C8—1582no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—3162no—
703C22—3162no—
704C22—3162no—
705C22—6324no—
706C22#1909922212yes—
707C22#137×D7912yes—
708C22#1909936712yes—
709C22C22×D4×D7911yescharacteristic
710C4—22no—
711C4—24no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—3162no—
716C4—3162no—
717C4—3162no—
718C4—794no—
719C4—1582no—
720C4—1582no—
721C4—1582no—
722C4#1909922212yes—
723C4C22×#1192962411yescharacteristic
724C4C2×#1457920811yescharacteristic
725C2—82no—
726C2—6322no—
727C2#2377621514yesdirect product factor
728C2C2×#1909922211yescharacteristic
729C2C2×#137×D7911yescharacteristic
730C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#440×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579157C22
hypercenterC2×#440D79
hypocenterC79C2×#3375
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic158C2semidirect
3. #23776215C2direct (N × H)
4. C2×#19098923C2semidirect
5. C2×#19098921C2semidirect
7. C2×#19098857C2semidirect
8. C2×#19098843C2semidirect
9. C2×#19098842C2semidirect
10. C2×#19098785C2semidirect
11. C2×#19098783C2semidirect
13. C2×#19098691C2semidirect
14. C2×#19098666C2semidirect
15. C2×#19098655C2semidirect
16. C2×#440×C79C2semidirect
22. Q8×Dic158C22semidirect
42. #19098923C22semidirect
43. #19098921C22semidirect
45. #19098857C22semidirect
46. #19098843C22semidirect
47. #19098842C22semidirect
48. #19098785C22semidirect
49. #19098783C22semidirect
51. #19098691C22semidirect
52. #19098666C22semidirect
53. #19098655C22semidirect
72. #440×C79C22semidirect
361. C2×C79#3375semidirect
380. C2×#440D79semidirect
382. C79C2×#3375semidirect
422. #440C2×D79semidirect
727. C2#23776215direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992962
C2×Q8×Dic1582
#237762152
C2×#190989232
C2×#190989212
C2×#190989082
C2×#190988572
C2×#190988432
C2×#190988422
C2×#190987852
C2×#190987832
C2×#190987612
C2×#190986912
C2×#190986662
C2×#190986552
C2×#440×C792
C2×#337579