Finite Group Databasebeta

← #2502×D79 #34457445

Subgroups — #2502×D79 #34457445

Order 20224.

3094 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D79C211yesmaximal, characteristic
2C22×C4⋊C4×D79C211yesmaximal, characteristic
3#23767879C211yesmaximal, characteristic, complemented
4#23767878C211yesmaximal, characteristic, complemented
5#23767877C212yesmaximal, complemented
6#23767876C214yesmaximal, complemented
7#23767875C212yesmaximal, complemented
8#23767874C211yesmaximal, characteristic, complemented
9#23767873C214yesmaximal, complemented
10#398×D79C214yesmaximal, complemented
11#391×D79C212yesmaximal, complemented
12#385×D79C214yesmaximal
13#384×D79C212yesmaximal, complemented
14C4×C22⋊C4×D79C211yesmaximal, characteristic
15C79×#2502C211yesmaximal, characteristic, complemented
16C22×Q8×D79C2211yescharacteristic
17C23×C4×D79C2211yescharacteristic
18C23×C4×D79C2212yes—
19C2×#14579141C2211yescharacteristic
20C2×#14579140C2211yescharacteristic
21C2×#14579139C2212yes—
22C2×#14579138C2212yes—
23C2×#14579137C2211yescharacteristic
24C22⋊Q8×D79—28no—
25C22×C4⋊Dic79C2211yescharacteristic
26C22×Dic79⋊C4C2212yes—
27C2×C4⋊C4×D79—28no—
28C2×C4⋊C4×D79C2211yescharacteristic
29C2×C4⋊C4×D79C2212yes—
30C2×C4⋊C4×D79C2212yes—
31C2×C4⋊C4×D79C2212yes—
32C2×C4⋊C4×D79C2212yes—
33C2×C4⋊C4×D79C2212yes—
34C2×C4⋊C4×D79C2218yes—
35C2×C22⋊C4×D79C2212yes—
36C2×C22⋊C4×D79C2212yes—
37C2×C42×D79C2212yes—
38#19098497C2218yescomplemented
39#19098496C2218yescomplemented
40#19098495C2214yescomplemented
41#19098494C2214yescomplemented
42#19098493C2214yescomplemented
43#19098470C2212yescomplemented
44#19098469C2212yescomplemented
45#19098468C2212yescomplemented
46#19098467C2218yescomplemented
47#19098438C2214yes—
48#19098437C2218yes—
49#19098436C2214yes—
50#19098435C2214yes—
51#19098434C2218yes—
52#19098433C2212yescomplemented
53#19098432C2218yescomplemented
54#19098432C2212yescomplemented
55#19098432C2212yescomplemented
56C22⋊C4×Dic79C2212yes—
57C4×(C2×D79)⋊C4C2212yes—
58C4×C22⋊Dic79C2211yescharacteristic
59#19098410C2212yes—
60#95×D79C2218yes—
61#95×D79C2212yes—
62C2×C22⋊Q8×C79C2211yescharacteristic
63C22×C4⋊C4×C79C2211yescharacteristic
64#398×C79C2214yescomplemented
65#391×C79C2212yescomplemented
66#385×C79C2214yes—
67#384×C79C2212yescomplemented
68C4×C22⋊C4×C79C2211yescharacteristic
69C24×D79C2311yescharacteristic
70C22×Dic158C2312yes—
71C22×Dic158C2311yescharacteristic
72C2×Q8×D79—24no—
73C2×Q8×D79—28no—
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2312yes—
76C22×C4×D79—28no—
77C22×C4×D79—28no—
78C22×C4×D79—48no—
79C22×C4×D79D418yes—
80C22×C4×D79C2312yes—
81C22×C4×D79C2314yes—
82C22×C4×D79C2312yes—
83C22×C4×D79C2311yescharacteristic
84C22×C4×D79C2311yescharacteristic
85C22×C4×D79C2311yescharacteristic
86C22×C4×D79C2314yes—
87C22×C4×D79C2314yes—
88C22×C4×D79C2311yescharacteristic
89#14579141—24no—
90#14579140—24no—
91#14579139—28no—
92#14579138—28no—
93#14579137—24no—
94C2×C4⋊Dic79—24no—
95C2×C4⋊Dic79C2311yescharacteristic
96C2×C4⋊Dic79C2312yes—
97C2×C4⋊Dic79C2312yes—
98C2×C4⋊Dic79C2312yes—
99C2×C4⋊Dic79C2318yes—
100C2×Dic79⋊C4—28no—
101C2×Dic79⋊C4C2312yes—
102C2×Dic79⋊C4C2314yes—
103C2×Dic79⋊C4C2312yes—
104C2×Dic79⋊C4C2314yes—
105C2×Dic79⋊C4C2312yes—
106C2×Dic79⋊C4C2318yes—
107C2×Dic79⋊C4C2318yes—
108C4⋊C4×D79—28no—
109C4⋊C4×D79—28no—
110C4⋊C4×D79—28no—
111C4⋊C4×D79—28no—
112C4⋊C4×D79—28no—
113C4⋊C4×D79—24no—
114C4⋊C4×D79—416no—
115C2×C22⋊Dic79C2312yes—
116C2×C22⋊Dic79C2312yes—
117C2×(C2×D79)⋊C4C2312yes—
118C2×(C2×D79)⋊C4C2312yes—
119C2×(C2×D79)⋊C4C2314yes—
120C22⋊C4×D79—28no—
121C22⋊C4×D79Q8116yescomplemented
122C2×C4×Dic79C2314yes—
123C2×C4×Dic79C2312yes—
124C42×D79—28no—
125C79⋊#95C2312yes—
126C79⋊#95C2314yes—
127C79⋊#95C2318yes—
128C79⋊#95C2318yes—
129C79⋊#95C2318yes—
130C22×Q8×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2312yes—
133C22⋊Q8×C79—24no—
134C2×C4⋊C4×C79—24no—
135C2×C4⋊C4×C79C2311yescharacteristic
136C2×C4⋊C4×C79C2312yes—
137C2×C4⋊C4×C79C2312yes—
138C2×C4⋊C4×C79C2312yes—
139C2×C4⋊C4×C79C2318yes—
140C2×C22⋊C4×C79C2312yes—
141C2×C22⋊C4×C79C2312yes—
142C2×C42×C79C2312yes—
143#95×C79C2312yes—
144#95×C79C2318yes—
145C23×D79—24no—
146C23×D79—24no—
147C23×D79C2×D414yes—
148C23×D79C2×Q818yes—
149C23×D79C2411yescharacteristic
150C23×D79C2411yescharacteristic
151C2×Dic158—24no—
152C2×Dic158—28no—
153C2×Dic158—22no—
154C2×Dic158—24no—
155Q8×D79—416no—
156C22×Dic79—24no—
157C22×Dic79—24no—
158C22×Dic79—44no—
159C22×Dic79C2×D414yes—
160C22×Dic79C2412yes—
161C22×Dic79C2414yes—
162C22×Dic79C2412yes—
163C22×Dic79C2411yescharacteristic
164C22×Dic79C2414yes—
165C22×Dic79C2411yescharacteristic
166C2×C4×D79—24no—
167C2×C4×D79—232no—
168C2×C4×D79—24no—
169C2×C4×D79—24no—
170C2×C4×D79—28no—
171C2×C4×D79—28no—
172C2×C4×D79—28no—
173C2×C4×D79—24no—
174C2×C4×D79—28no—
175C2×C4×D79—28no—
176C2×C4×D79—28no—
177C2×C4×D79—216no—
178C2×C4×D79—24no—
179C2×C4×D79—48no—
180C2×C4×D79—432no—
181C2×C4×D79C2×D414yes—
182C2×C4×D79C2×D414yes—
183C2×C4×D79C2×D414yes—
184C2×C4×D79C2×D414yes—
185C2×C4×D79C2×Q8116yes—
186C2×C4×D79#4118yes—
187C4⋊Dic79—24no—
188C4⋊Dic79—24no—
189C4⋊Dic79—24no—
190C4⋊Dic79—22no—
191C4⋊Dic79—48no—
192Dic79⋊C4—28no—
193Dic79⋊C4—28no—
194Dic79⋊C4—24no—
195Dic79⋊C4—24no—
196Dic79⋊C4—24no—
197Dic79⋊C4—48no—
198Dic79⋊C4—48no—
199C22⋊Dic79—24no—
200C22⋊Dic79C2×Q818yescomplemented
201(C2×D79)⋊C4—24no—
202(C2×D79)⋊C4—24no—
203(C2×D79)⋊C4C2×Q8116yescomplemented
204C4×Dic79—28no—
205C4×Dic79—24no—
206C24×C79C2411yescharacteristic
207C2×Q8×C79—22no—
208C2×Q8×C79—24no—
209C22×C4×C79—24no—
210C22×C4×C79—24no—
211C22×C4×C79—44no—
212C22×C4×C79C2×D414yes—
213C22×C4×C79C2412yes—
214C22×C4×C79C2414yes—
215C22×C4×C79C2412yes—
216C22×C4×C79C2411yescharacteristic
217C22×C4×C79C2414yes—
218C22×C4×C79C2411yescharacteristic
219C4⋊C4×C79—24no—
220C4⋊C4×C79—24no—
221C4⋊C4×C79—24no—
222C4⋊C4×C79—22no—
223C4⋊C4×C79—48no—
224C22⋊C4×C79—24no—
225C22⋊C4×C79C2×Q818yescomplemented
226C42×C79—24no—
227C23×C79—22no—
228C23×C79—22no—
229C23×C79C22×D412yes—
230C23×C79C22×Q814yes—
231C23×C79C2511yescharacteristic
232C22×D79—22no—
233C22×D79—22no—
234C22×D79—28no—
235C22×D79—28no—
236C22×D79—232no—
237C22×D79C4⋊Q8116yes—
238C22×D79C22×D412yes—
239C22×D79C22×D412yes—
240C22×D79C22×Q814yes—
241C22×D79C22×Q814yes—
242C22×D79C2×#4114yes—
243C22×D79H(5,𝔽2)14yes—
244Q8×C79—44no—
245C2×C4×C79—24no—
246C2×C4×C79—22no—
247C2×C4×C79—24no—
248C2×C4×C79—28no—
249C2×C4×C79—22no—
250C2×C4×C79—22no—
251C2×C4×C79—24no—
252C2×C4×C79—24no—
253C2×C4×C79—24no—
254C2×C4×C79—28no—
255C2×C4×C79—48no—
256C2×C4×C79C22×D412yes—
257C2×C4×C79C22×D412yes—
258C2×C4×C79C22×Q818yes—
259C2×C4×C79C2×#4114yes—
260C2×Dic79—24no—
261C2×Dic79—22no—
262C2×Dic79—24no—
263C2×Dic79—28no—
264C2×Dic79—22no—
265C2×Dic79—22no—
266C2×Dic79—24no—
267C2×Dic79—24no—
268C2×Dic79—24no—
269C2×Dic79—28no—
270C2×Dic79—48no—
271C2×Dic79C22×D412yes—
272C2×Dic79C22×D412yes—
273C2×Dic79C22×Q818yes—
274C2×Dic79C2×#4114yes—
275C4×D79—28no—
276C4×D79—232no—
277C4×D79—28no—
278C4×D79—28no—
279C4×D79—416no—
280C4×D79—48no—
281C4×D79—48no—
282C4×D79—416no—
283C4×D79#123116yes—
284Dic158—44no—
285Dic158—48no—
286C22×C79—22no—
287C22×C79—22no—
288C22×C79—28no—
289C22×C79C2×C4⋊Q814yes—
290C22×C79C23×D411yescharacteristic
291C22×C79C23×Q812yes—
292C22×C79C22×#4112yes—
293C22×C79C2×H(5,𝔽2)12yes—
294C2×D79—22no—
295C2×D79—22no—
296C2×D79—28no—
297C2×D79—232no—
298C2×D79C2×#12314yes—
299C2×D79C2×C4⋊Q814yes—
300C2×D79C2×C4⋊Q814yes—
301C2×D79#53514yes—
302C2×D79#554116yes—
303C4×C79—22no—
304C4×C79—28no—
305C4×C79—42no—
306C4×C79—44no—
307C4×C79—42no—
308C4×C79C2×#12314yes—
309Dic79—22no—
310Dic79—28no—
311Dic79—42no—
312Dic79—44no—
313Dic79—42no—
314Dic79C2×#12314yes—
315C2×#2502—791nomaximal, Sylow
316C2×C79—24no—
317C2×C79C22×#12311yescharacteristic
318C2×C79C22×C4⋊Q811yescharacteristic
319C2×C79C2×#53511yescharacteristic
320C2×C79C2×#55414yes—
321D79—24no—
322D79#250218yesdirect product factor
323C22×C22⋊Q8—791no—
324C23×C4⋊C4—791no—
325#2502—794no—
326#2502—792no—
327#2502—794no—
328#2502—792no—
329#2502—791no—
330#2502—791no—
331#2502—791no—
332#2502D7911yescharacteristic, direct product factor
333C2×#398—794no—
334C2×#391—792no—
335C2×#385—794no—
336C2×#384—792no—
337C2×C4×C22⋊C4—791no—
338C79C2×#250211yescharacteristic, complemented, Sylow
339C23×Q8—791no—
340C24×C4—792no—
341C24×C4—791no—
342C2×C22⋊Q8—791no—
343C2×C22⋊Q8—791no—
344C2×C22⋊Q8—792no—
345C2×C22⋊Q8—791no—
346C2×C22⋊Q8—792no—
347C2×C22⋊Q8—1588no—
348C2×C22⋊Q8C2×D7911yescharacteristic
349C22×C4⋊C4—798no—
350C22×C4⋊C4—792no—
351C22×C4⋊C4—791no—
352C22×C4⋊C4—792no—
353C22×C4⋊C4—792no—
354C22×C4⋊C4—792no—
355C22×C4⋊C4—792no—
356C22×C4⋊C4—792no—
357C22×C4⋊C4—791no—
358C22×C4⋊C4—1588no—
359C22×C4⋊C4C2×D7911yescharacteristic
360C22×C22⋊C4—792no—
361C22×C22⋊C4—792no—
362C22×C42—792no—
363#398—794no—
364#398—794no—
365#398—798no—
366#398—794no—
367#398—798no—
368#398C2×D7914yescomplemented
369#391—792no—
370#391—792no—
371#391—792no—
372#391—798no—
373#391C2×D7912yescomplemented
374#385—794no—
375#385—798no—
376#385—794no—
377#385—794no—
378#385—798no—
379#385C2×D7914yes—
380#384—792no—
381#384—792no—
382#384—798no—
383#384—792no—
384#384C2×D7912yescomplemented
385C4×C22⋊C4—791no—
386C4×C22⋊C4—792no—
387C4×C22⋊C4—792no—
388C4×C22⋊C4—792no—
389C4×C22⋊C4C2×D7911yescharacteristic
390C2×#95—792no—
391C2×#95—798no—
392C25—791no—
393C22×Q8—792no—
394C22×Q8—791no—
395C22×Q8—1584no—
396C22×Q8—1588no—
397C22×Q8C22×D7911yescharacteristic
398C23×C4—3168no—
399C23×C4—792no—
400C23×C4—794no—
401C23×C4—791no—
402C23×C4—791no—
403C23×C4—798no—
404C23×C4—794no—
405C23×C4—791no—
406C23×C4—791no—
407C23×C4—791no—
408C23×C4—792no—
409C23×C4—792no—
410C23×C4—794no—
411C23×C4—1588no—
412C23×C4—1588no—
413C23×C4C22×D7911yescharacteristic
414C23×C4C22×D7912yes—
415C22⋊Q8—24no—
416C22⋊Q8—1588no—
417C22⋊Q8—1588no—
418C22⋊Q8—1584no—
419C22⋊Q8—1584no—
420C22⋊Q8—1584no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—31616no—
423C2×C4⋊C4—798no—
424C2×C4⋊C4—798no—
425C2×C4⋊C4—798no—
426C2×C4⋊C4—794no—
427C2×C4⋊C4—792no—
428C2×C4⋊C4—794no—
429C2×C4⋊C4—792no—
430C2×C4⋊C4—792no—
431C2×C4⋊C4—791no—
432C2×C4⋊C4—792no—
433C2×C4⋊C4—792no—
434C2×C4⋊C4—792no—
435C2×C4⋊C4—1588no—
436C2×C4⋊C4—1588no—
437C2×C4⋊C4—1588no—
438C2×C4⋊C4—1588no—
439C2×C4⋊C4—1584no—
440C2×C4⋊C4—1588no—
441C2×C4⋊C4—1588no—
442C2×C4⋊C4—1584no—
443C2×C4⋊C4C22×D7912yes—
444C2×C4⋊C4C22×D7912yes—
445C2×C4⋊C4C22×D7911yescharacteristic
446C2×C4⋊C4C22×D7912yes—
447C2×C4⋊C4C22×D7918yes—
448C2×C22⋊C4—792no—
449C2×C22⋊C4—794no—
450C2×C22⋊C4—7916no—
451C2×C22⋊C4—792no—
452C2×C22⋊C4—792no—
453C2×C22⋊C4—792no—
454C2×C22⋊C4—1588no—
455C2×C22⋊C4C22×D7912yes—
456C2×C22⋊C4C22×D7912yes—
457C2×C42—794no—
458C2×C42—792no—
459C2×C42—1588no—
460C2×C42C22×D7912yes—
461#95—792no—
462#95—794no—
463#95—798no—
464#95—798no—
465#95—798no—
466#95C22×D7912yes—
467#95C22×D7918yes—
468C24—791no—
469C24—798no—
470C24—791no—
471C24—794no—
472C24—1584no—
473C24—1584no—
474C24C23×D7911yescharacteristic
475C2×Q8—24no—
476C2×Q8—22no—
477C2×Q8—31616no—
478C2×Q8—1584no—
479C2×Q8—1588no—
480C2×Q8—1584no—
481C2×Q8—1582no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—44no—
485C22×C4—3168no—
486C22×C4—31632no—
487C22×C4—3164no—
488C22×C4—791no—
489C22×C4—798no—
490C22×C4—794no—
491C22×C4—794no—
492C22×C4—791no—
493C22×C4—794no—
494C22×C4—7916no—
495C22×C4—794no—
496C22×C4—794no—
497C22×C4—794no—
498C22×C4—792no—
499C22×C4—794no—
500C22×C4—792no—
501C22×C4—1584no—
502C22×C4—1584no—
503C22×C4—1588no—
504C22×C4—15816no—
505C22×C4—1588no—
506C22×C4—1588no—
507C22×C4—1588no—
508C22×C4—1584no—
509C22×C4—15832no—
510C22×C4—1588no—
511C22×C4—1588no—
512C22×C4—1584no—
513C22×C4—1584no—
514C22×C4—1584no—
515C22×C4—1584no—
516C22×C4D4×D7914yes—
517C22×C4C23×D7912yes—
518C22×C4C23×D7914yes—
519C22×C4C23×D7912yes—
520C22×C4C23×D7914yes—
521C22×C4C23×D7911yescharacteristic
522C22×C4C23×D7911yescharacteristic
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—22no—
526C4⋊C4—24no—
527C4⋊C4—48no—
528C4⋊C4—3168no—
529C4⋊C4—3168no—
530C4⋊C4—3168no—
531C4⋊C4—1588no—
532C4⋊C4—1588no—
533C4⋊C4—1584no—
534C4⋊C4—1584no—
535C4⋊C4—1584no—
536C4⋊C4—1584no—
537C4⋊C4—1584no—
538C4⋊C4—1584no—
539C4⋊C4—1582no—
540C22⋊C4—24no—
541C22⋊C4—798no—
542C22⋊C4—7916no—
543C22⋊C4—1584no—
544C22⋊C4—1584no—
545C22⋊C4—1584no—
546C22⋊C4Q8×D7918yescomplemented
547C42—24no—
548C42—1588no—
549C42—1584no—
550C23—22no—
551C23—22no—
552C23—794no—
553C23—792no—
554C23—794no—
555C23—794no—
556C23—7916no—
557C23—792no—
558C23—794no—
559C23—1588no—
560C23—1588no—
561C23—15832no—
562C23—1582no—
563C23—1582no—
564C23C2×D4×D7912yes—
565C23C2×Q8×D7914yes—
566C23C24×D7911yescharacteristic
567Q8—44no—
568Q8—3168no—
569Q8—3164no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—28no—
574C2×C4—24no—
575C2×C4—28no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—48no—
581C2×C4—31616no—
582C2×C4—3168no—
583C2×C4—3168no—
584C2×C4—31616no—
585C2×C4—3168no—
586C2×C4—792no—
587C2×C4—794no—
588C2×C4—7916no—
589C2×C4—792no—
590C2×C4—798no—
591C2×C4—1588no—
592C2×C4—1588no—
593C2×C4—15832no—
594C2×C4—1584no—
595C2×C4—1588no—
596C2×C4—1582no—
597C2×C4—1582no—
598C2×C4—1584no—
599C2×C4—1584no—
600C2×C4—1588no—
601C2×C4—1584no—
602C2×C4—1584no—
603C2×C4—1582no—
604C2×C4—1588no—
605C2×C4C2×D4×D7912yes—
606C2×C4C2×D4×D7912yes—
607C2×C4C2×Q8×D7918yes—
608C2×C4#41×D7914yes—
609C22—22no—
610C22—28no—
611C22—22no—
612C22—794no—
613C22—7916no—
614C22—794no—
615C22—794no—
616C22—794no—
617C22—15832no—
618C22—1582no—
619C22—1588no—
620C22—1582no—
621C22C4⋊Q8×D7914yes—
622C22C22×D4×D7911yescharacteristic
623C22C22×Q8×D7912yes—
624C22C2×#41×D7912yes—
625C22H(5,𝔽2)×D7912yes—
626C4—22no—
627C4—28no—
628C4—42no—
629C4—44no—
630C4—42no—
631C4—3162no—
632C4—3164no—
633C4—3162no—
634C4—794no—
635C4—1582no—
636C4—1588no—
637C4#123×D7914yes—
638C2—24no—
639C2—798no—
640C2—1584no—
641C2C2×#123×D7911yescharacteristic
642C2C2×C4⋊Q8×D7911yescharacteristic
643C2#535×D7911yescharacteristic
644C2#554×D7914yes—
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2502C2
prime radicalC24×D79C23
hypercenter#2502D79
hypocenterC79C2×#2502
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2502

Complements

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

NH ≅ G/Ntype
3. #23767879C2semidirect
4. #23767878C2semidirect
5. #23767877C2semidirect
6. #23767876C2semidirect
7. #23767875C2semidirect
8. #23767874C2semidirect
9. #23767873C2semidirect
10. #398×D79C2semidirect
11. #391×D79C2semidirect
13. #384×D79C2semidirect
15. C79×#2502C2semidirect
38. #19098497C22semidirect
39. #19098496C22semidirect
40. #19098495C22semidirect
41. #19098494C22semidirect
42. #19098493C22semidirect
43. #19098470C22semidirect
44. #19098469C22semidirect
45. #19098468C22semidirect
46. #19098467C22semidirect
52. #19098433C22semidirect
53. #19098432C22semidirect
54. #19098432C22semidirect
55. #19098432C22semidirect
64. #398×C79C22semidirect
65. #391×C79C22semidirect
67. #384×C79C22semidirect
121. C22⋊C4×D79Q8semidirect
200. C22⋊Dic79C2×Q8semidirect
203. (C2×D79)⋊C4C2×Q8semidirect
225. C22⋊C4×C79C2×Q8semidirect
322. D79#2502direct (N × H)
332. #2502D79direct (N × H)
338. C79C2×#2502semidirect
368. #398C2×D79semidirect
373. #391C2×D79semidirect
384. #384C2×D79semidirect
546. C22⋊C4Q8×D79semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D792
C22×C4⋊C4×D792
#237678792
#237678782
#237678772
#237678762
#237678752
#237678742
#237678732
#398×D792
#391×D792
#385×D792
#384×D792
C4×C22⋊C4×D792
C79×#25022
C2×#250279