Finite Group Databasebeta

← C2×#23772345 #35152647

Subgroups — C2×#23772345 #35152647

Order 20224.

1938 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099117C211yesmaximal, characteristic
2#23772345C2116yesmaximal, direct product factor
3C2×#19098694C211yesmaximal, characteristic, complemented
4C2×#19098692C211yesmaximal, characteristic, complemented
5C2×#19098692C211yesmaximal, characteristic, complemented
6C2×#19098691C211yesmaximal, characteristic, complemented
7C2×#19098691C211yesmaximal, characteristic, complemented
8C2×C8×Dic158C211yesmaximal, characteristic, complemented
9C2×#19098687C211yesmaximal, characteristic, complemented
10C2×#19098588C211yesmaximal, characteristic
11C2×#19098588C211yesmaximal, characteristic
12C2×C4⋊C8×D79C211yesmaximal, characteristic
13C2×#19098520C211yesmaximal, characteristic
14C2×#19098517C211yesmaximal, characteristic
15C2×#19098515C211yesmaximal, characteristic
16C2×#446×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099117C418yes—
22#19099117C2218yes—
23C2×#14579160C411yescharacteristic
24C2×#14579159C411yescharacteristic
25C2×#14579151C411yescharacteristic
26C2×#14579151C411yescharacteristic
27C2×#14579141C411yescharacteristic
28C2×#14579139C411yescharacteristic
29C2×#14579139C411yescharacteristic
30C2×#14579137C411yescharacteristic
31C2×C4×Dic158C2211yescharacteristic
32C2×C4×Dic158C2211yescharacteristic
33C2×C4×Dic158C2211yescharacteristic
34C2×#14579118C2211yescharacteristic
35C2×#14579118C2211yescharacteristic
36C2×C42×D79C2211yescharacteristic
37#19098694C2218yescomplemented
38#19098692C2218yescomplemented
39#19098692C2218yescomplemented
40#19098691C2218yescomplemented
41#19098691C2218yescomplemented
42C8×Dic158C2218yescomplemented
43#19098687C2218yescomplemented
44#19098588C2218yes—
45#19098588C2218yes—
46C2×C4⋊(C79⋊C8)C2211yescharacteristic
47C2×C4⋊(C79⋊C8)C2211yescharacteristic
48C2×C4⋊(C79⋊C8)C2211yescharacteristic
49C2×Dic79⋊C8C2211yescharacteristic
50C2×Dic79⋊C8C2211yescharacteristic
51C2×Dic79⋊C8C2211yescharacteristic
52C2×Dic79⋊C8C2211yescharacteristic
53C2×Dic79⋊C8C2211yescharacteristic
54C2×Dic79⋊C8C2211yescharacteristic
55C4⋊C8×D79C2218yes—
56#19098520C2218yes—
57#19098517C2218yes—
58#19098515C2218yes—
59C2×#14579072C2211yescharacteristic
60C2×#14579072C2211yescharacteristic
61C2×#14579071C2211yescharacteristic
62C2×#14579071C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64C2×C8×Dic79C2211yescharacteristic
65C2×C8×Dic79C2211yescharacteristic
66C2×C8×Dic79C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
68C2×C4×Q8×C79C2211yescharacteristic
69#446×C79C2218yescomplemented
70C2×C4⋊C8×C79C2211yescharacteristic
71C2×C4⋊C8×C79C2211yescharacteristic
72C2×C4⋊C8×C79C2211yescharacteristic
73C2×#97×C79C2211yescharacteristic
74C2×#97×C79C2211yescharacteristic
75C2×C4×C8×C79C2211yescharacteristic
76C22×Dic158C2×C411yescharacteristic
77C22×Dic158C2×C411yescharacteristic
78C22×Dic158C2×C411yescharacteristic
79C22×C4×D79C2×C411yescharacteristic
80C22×C4×D79C2×C411yescharacteristic
81C22×C4×D79C2311yescharacteristic
82C2×#11929607—24no—
83C2×#11929607Q818yescomplemented
84C2×#11929607C2314yes—
85C2×#11929607C2314yes—
86C22×C79⋊C8C2311yescharacteristic
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90C2×C8×D79—24no—
91C2×C8×D79—24no—
92C2×C8×D79C2314yes—
93C2×C8×D79C2314yes—
94#14579160C2×C418yes—
95#14579159C2×C418yes—
96#14579151C2×C418yes—
97#14579151C2×C418yes—
98#14579141C2×C418yes—
99#14579139C2×C418yes—
100#14579139C2×C418yes—
101#14579137C2×C418yes—
102C4×Dic158C2×C414yes—
103C4×Dic158C2×C414yes—
104C4×Dic158C2×C414yes—
105C4×Dic158C2314yes—
106C4×Dic158C2314yes—
107C4×Dic158C2314yes—
108#14579118C2×C414yes—
109#14579118C2×C414yes—
110#14579118C2314yes—
111#14579118C2314yes—
112C2×C4⋊Dic79C2×C411yescharacteristic
113C2×C4⋊Dic79C2×C411yescharacteristic
114C2×C4⋊Dic79C2×C411yescharacteristic
115C2×Dic79⋊C4C2×C411yescharacteristic
116C2×Dic79⋊C4C2×C411yescharacteristic
117C2×Dic79⋊C4C2×C411yescharacteristic
118C2×Dic79⋊C4C2×C411yescharacteristic
119C2×Dic79⋊C4C2×C411yescharacteristic
120C2×Dic79⋊C4C2×C411yescharacteristic
121C2×Dic79⋊C4C2×C411yescharacteristic
122C2×Dic79⋊C4C2×C411yescharacteristic
123C2×Dic79⋊C4C2×C411yescharacteristic
124C2×Dic79⋊C4C2×C411yescharacteristic
125C2×(C2×D79)⋊C4C2×C411yescharacteristic
126C2×(C2×D79)⋊C4C2×C411yescharacteristic
127C2×(C2×D79)⋊C4C2×C411yescharacteristic
128C2×(C2×D79)⋊C4C2×C411yescharacteristic
129C2×C4×Dic79C2×C411yescharacteristic
130C2×C4×Dic79C2×C411yescharacteristic
131C2×C4×Dic79C2311yescharacteristic
132C2×C4×Dic79C2311yescharacteristic
133C2×C4×Dic79C2311yescharacteristic
134C42×D79C2×C414yes—
135C42×D79C2314yes—
136C4⋊(C79⋊C8)C2314yes—
137C4⋊(C79⋊C8)C2314yes—
138C4⋊(C79⋊C8)C2314yes—
139Dic79⋊C8C2314yes—
140Dic79⋊C8C2314yes—
141Dic79⋊C8C2314yes—
142Dic79⋊C8C2314yes—
143Dic79⋊C8C2314yes—
144Dic79⋊C8C2314yes—
145#14579072C2314yes—
146#14579072C2314yes—
147#14579071C2314yes—
148#14579071C2314yes—
149C4×C79⋊C8C2314yes—
150C8×Dic79C2314yes—
151C8×Dic79C2314yes—
152C8×Dic79C2314yes—
153C8×Dic79C2314yes—
154C22×Q8×C79C2×C411yescharacteristic
155C22×C8×C79C2311yescharacteristic
156C22×C8×C79C2311yescharacteristic
157C22×C8×C79C2311yescharacteristic
158C22×C8×C79C2311yescharacteristic
159C4×Q8×C79C2×C414yes—
160C4×Q8×C79C2314yes—
161C2×C4⋊C4×C79C2×C411yescharacteristic
162C2×C4⋊C4×C79C2×C411yescharacteristic
163C2×C4⋊C4×C79C2×C411yescharacteristic
164C2×C42×C79C2311yescharacteristic
165C2×C42×C79C2311yescharacteristic
166C2×C42×C79C2311yescharacteristic
167C4⋊C8×C79C2314yes—
168C4⋊C8×C79C2314yes—
169C4⋊C8×C79C2314yes—
170#97×C79C2314yes—
171#97×C79C2314yes—
172C4×C8×C79C2314yes—
173C23×D79C22×C411yescharacteristic
174C2×Dic158—24no—
175C2×Dic158—24no—
176C2×Dic158—42no—
177C2×Dic158C22×C414yes—
178C2×Dic158C22×C414yes—
179C2×Dic158C22×C414yes—
180C22×Dic79C22×C411yescharacteristic
181C22×Dic79C22×C411yescharacteristic
182C22×Dic79C22×C411yescharacteristic
183C22×Dic79C22×C411yescharacteristic
184C22×Dic79C22×C411yescharacteristic
185C22×Dic79C22×C411yescharacteristic
186C22×Dic79C22×C411yescharacteristic
187C2×C4×D79—24no—
188C2×C4×D79—42no—
189C2×C4×D79C22×C414yes—
190C2×C4×D79C22×C414yes—
191C2×C4×D79C22×C412yes—
192C2×C4×D79C2×Q814yes—
193C2×C4×D79#4114yes—
194C2×C4×D79C2412yes—
195#11929607—28no—
196#11929607C2×Q8116yescomplemented
197C2×C79⋊C8—22no—
198C2×C79⋊C8—22no—
199C2×C79⋊C8—22no—
200C2×C79⋊C8C2×Q814yes—
201C2×C79⋊C8C2412yes—
202C2×C79⋊C8C2412yes—
203C2×C79⋊C8C2412yes—
204C2×C79⋊C8C2412yes—
205C8×D79—28no—
206C8×D79—28no—
207C4⋊Dic79C22×C414yes—
208C4⋊Dic79C22×C414yes—
209C4⋊Dic79C22×C414yes—
210Dic79⋊C4C22×C414yes—
211Dic79⋊C4C22×C414yes—
212Dic79⋊C4C22×C414yes—
213Dic79⋊C4C22×C414yes—
214Dic79⋊C4C22×C414yes—
215Dic79⋊C4C22×C414yes—
216Dic79⋊C4C22×C414yes—
217Dic79⋊C4C22×C414yes—
218Dic79⋊C4C22×C414yes—
219Dic79⋊C4C22×C414yes—
220(C2×D79)⋊C4C22×C414yes—
221(C2×D79)⋊C4C22×C414yes—
222(C2×D79)⋊C4C22×C414yes—
223(C2×D79)⋊C4C22×C414yes—
224C4×Dic79C22×C412yes—
225C4×Dic79C22×C414yes—
226C4×Dic79C22×C414yes—
227C4×Dic79C22×C412yes—
228C4×Dic79C22×C412yes—
229C4×Dic79C2412yes—
230C4×Dic79C2412yes—
231C4×Dic79C2412yes—
232C2×Q8×C79—42no—
233C2×Q8×C79C22×C414yes—
234C22×C4×C79C22×C411yescharacteristic
235C22×C4×C79C22×C411yescharacteristic
236C22×C4×C79C22×C411yescharacteristic
237C22×C4×C79C22×C411yescharacteristic
238C22×C4×C79C22×C411yescharacteristic
239C22×C4×C79C22×C411yescharacteristic
240C22×C4×C79C2411yescharacteristic
241C2×C8×C79—22no—
242C2×C8×C79—22no—
243C2×C8×C79—22no—
244C2×C8×C79C2×Q814yes—
245C2×C8×C79C2412yes—
246C2×C8×C79C2412yes—
247C2×C8×C79C2412yes—
248C2×C8×C79C2412yes—
249C4⋊C4×C79C22×C414yes—
250C4⋊C4×C79C22×C414yes—
251C4⋊C4×C79C22×C414yes—
252C42×C79C22×C412yes—
253C42×C79C22×C412yes—
254C42×C79C22×C412yes—
255C42×C79C2412yes—
256C42×C79C2412yes—
257C42×C79C2412yes—
258C23×C79C23×C411yescharacteristic
259C22×D79—22no—
260C22×D79—22no—
261C22×D79C4×Q814yes—
262C22×D79C23×C412yes—
263Q8×C79—44no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
270C2×C4×C79C23×C412yes—
271C2×C4×C79C23×C412yes—
272C2×C4×C79C23×C412yes—
273C2×C4×C79C23×C412yes—
274C2×C4×C79C23×C412yes—
275C2×C4×C79C23×C412yes—
276C2×C4×C79C23×C411yescharacteristic
277C2×C4×C79C22×Q812yes—
278C2×C4×C79C2×#4112yes—
279C2×C4×C79C2511yescharacteristic
280C2×Dic79—22no—
281C2×Dic79—22no—
282C2×Dic79—22no—
283C2×Dic79—22no—
284C2×Dic79—22no—
285C2×Dic79C4×Q814yes—
286C2×Dic79#13114yes—
287C2×Dic79C23×C412yes—
288C2×Dic79C23×C412yes—
289C2×Dic79C23×C412yes—
290C2×Dic79C23×C412yes—
291C2×Dic79C23×C412yes—
292C2×Dic79C23×C412yes—
293C2×Dic79C23×C412yes—
294C4×D79—28no—
295C4×D79—44no—
296C4×D79C4×Q818yes—
297C4×D79C22×Q814yes—
298C4×D79C2×#4114yes—
299Dic158—28no—
300Dic158—28no—
301Dic158—44no—
302C8×C79—22no—
303C8×C79—22no—
304C8×C79—22no—
305C8×C79C22×Q814yes—
306C79⋊C8—22no—
307C79⋊C8—22no—
308C79⋊C8—22no—
309C79⋊C8C22×Q814yes—
310C22×C79C2×C4×Q812yes—
311C22×C79C2×#13112yes—
312C22×C79#56812yes—
313C22×C79C24×C411yescharacteristic
314C2×D79—28no—
315C2×D79—22no—
316C2×D79—22no—
317C2×D79C2×C4×Q814yes—
318C4×C79—22no—
319C4×C79—22no—
320C4×C79—22no—
321C4×C79—22no—
322C4×C79—22no—
323C4×C79—22no—
324C4×C79C2×C4×Q812yes—
325C4×C79C23×Q811yescharacteristic
326C4×C79C22×#4111yescharacteristic
327Dic79—22no—
328Dic79—22no—
329Dic79—22no—
330Dic79—22no—
331Dic79—22no—
332Dic79C2×C4×Q814yes—
333Dic79C2×#13114yes—
334C2×#2962—791nomaximal, Sylow
335C2×C79#296214yescomplemented
336C2×C79C22×C4×Q811yescharacteristic
337C2×C79C22×#13111yescharacteristic
338C2×C79C2×#56811yescharacteristic
339D79—24no—
340C2×#533—791no—
341#2962—7916no—
342C2×#446—791no—
343C2×#446—791no—
344C2×#446—791no—
345C2×#446—791no—
346C2×#446—791no—
347C2×#446D7911yescharacteristic, complemented
348C2×C8×Q8—791no—
349C2×C8×Q8—791no—
350C2×#424—791no—
351C2×#424—791no—
352C22×C4⋊C8—791no—
353C2×#405—791no—
354C2×#405—791no—
355C2×C4×M16—791no—
356C79C2×#296211yescharacteristic, complemented, Sylow
357C22×M16—791no—
358C22×M16—791no—
359C23×C8—791no—
360C23×C8—791no—
361#533—798no—
362#533—798no—
363C2×C4⋊Q8—791no—
364C2×C4⋊Q8—791no—
365C2×#125—791no—
366C2×#125—791no—
367C2×C22⋊Q8—791no—
368C2×C22⋊Q8—791no—
369C2×C22⋊Q8—791no—
370C2×C22⋊Q8—791no—
371C2×C4×Q8—791no—
372C2×C4×Q8—791no—
373C2×C4×Q8—791no—
374C2×C4×Q8C2×D7911yescharacteristic
375C2×#117—791no—
376C2×#117—791no—
377C22×C42—791no—
378#446—798no—
379#446—798no—
380#446—798no—
381#446—798no—
382#446—798no—
383#446C2×D7918yescomplemented
384C8×Q8—798no—
385C8×Q8—798no—
386#424—798no—
387#424—798no—
388C2×C4⋊C8—791no—
389C2×C4⋊C8—791no—
390C2×C4⋊C8—791no—
391C2×C4⋊C8—791no—
392C2×C4⋊C8—791no—
393C2×C4⋊C8—791no—
394C2×C4⋊C8—791no—
395C2×C4⋊C8—791no—
396C2×C4⋊C8—791no—
397C2×C4⋊C8—798no—
398C2×C4⋊C8C2×D7911yescharacteristic
399C2×C4⋊C8C2×D7911yescharacteristic
400C2×C4⋊C8C2×D7911yescharacteristic
401#405—798no—
402#405—798no—
403C4×M16—798no—
404C2×#97—791no—
405C2×#97—791no—
406C2×#97—791no—
407C2×#97—791no—
408C2×#97C2×D7911yescharacteristic
409C2×#97C2×D7911yescharacteristic
410C2×C4×C8—791no—
411C2×C4×C8—791no—
412C2×C4×C8—791no—
413C2×C4×C8—791no—
414C2×C4×C8—791no—
415C2×C4×C8C2×D7911yescharacteristic
416C22×Q8—791no—
417C22×Q8—791no—
418C22×Q8—791no—
419C22×Q8C4×D7911yescharacteristic
420C23×C4—791no—
421C23×C4—791no—
422C23×C4—791no—
423C2×M16—798no—
424C2×M16—794no—
425C2×M16—794no—
426C2×M16—1584no—
427C22×C8—791no—
428C22×C8—791no—
429C22×C8—791no—
430C22×C8—791no—
431C22×C8—794no—
432C22×C8—794no—
433C22×C8—1584no—
434C22×C8—1584no—
435C22×C8C22×D7911yescharacteristic
436C22×C8C22×D7911yescharacteristic
437C22×C8C22×D7911yescharacteristic
438C22×C8C22×D7911yescharacteristic
439C4⋊Q8—798no—
440C4⋊Q8—798no—
441#125—798no—
442#125—798no—
443C22⋊Q8—798no—
444C22⋊Q8—798no—
445C22⋊Q8—798no—
446C22⋊Q8—798no—
447C4×Q8—794no—
448C4×Q8—794no—
449C4×Q8—794no—
450C4×Q8—794no—
451C4×Q8—794no—
452C4×Q8—794no—
453C4×Q8C4×D7914yes—
454C4×Q8C22×D7914yes—
455#117—794no—
456#117—794no—
457#117—794no—
458#117—794no—
459C2×C4⋊C4—791no—
460C2×C4⋊C4—791no—
461C2×C4⋊C4—791no—
462C2×C4⋊C4—791no—
463C2×C4⋊C4—791no—
464C2×C4⋊C4—791no—
465C2×C4⋊C4—791no—
466C2×C4⋊C4—791no—
467C2×C4⋊C4—791no—
468C2×C4⋊C4—791no—
469C2×C4⋊C4—791no—
470C2×C4⋊C4—791no—
471C2×C4⋊C4—791no—
472C2×C4⋊C4C4×D7911yescharacteristic
473C2×C4⋊C4C4×D7911yescharacteristic
474C2×C4⋊C4C4×D7911yescharacteristic
475C2×C22⋊C4—791no—
476C2×C22⋊C4—791no—
477C2×C22⋊C4—791no—
478C2×C22⋊C4—791no—
479C2×C42—791no—
480C2×C42—791no—
481C2×C42—791no—
482C2×C42—791no—
483C2×C42—791no—
484C2×C42—794no—
485C2×C42—794no—
486C2×C42C22×D7911yescharacteristic
487C2×C42C22×D7911yescharacteristic
488C2×C42C22×D7911yescharacteristic
489C4⋊C8—794no—
490C4⋊C8—794no—
491C4⋊C8—794no—
492C4⋊C8—794no—
493C4⋊C8—794no—
494C4⋊C8—794no—
495C4⋊C8—794no—
496C4⋊C8—794no—
497C4⋊C8—794no—
498C4⋊C8C22×D7914yes—
499C4⋊C8C22×D7914yes—
500C4⋊C8C22×D7914yes—
501#97—794no—
502#97—794no—
503#97—794no—
504#97—794no—
505#97C22×D7914yes—
506#97C22×D7914yes—
507C4×C8—794no—
508C4×C8—794no—
509C4×C8—794no—
510C4×C8—794no—
511C4×C8—794no—
512C4×C8C22×D7914yes—
513C24—791no—
514C2×Q8—42no—
515C2×Q8—3162no—
516C2×Q8—794no—
517C2×Q8—794no—
518C2×Q8—794no—
519C2×Q8—1584no—
520C2×Q8—1584no—
521C2×Q8C2×C4×D7914yes—
522C22×C4—3162no—
523C22×C4—794no—
524C22×C4—791no—
525C22×C4—791no—
526C22×C4—794no—
527C22×C4—794no—
528C22×C4—792no—
529C22×C4—792no—
530C22×C4—791no—
531C22×C4—791no—
532C22×C4—791no—
533C22×C4—791no—
534C22×C4—791no—
535C22×C4—794no—
536C22×C4—1584no—
537C22×C4C2×C4×D7911yescharacteristic
538C22×C4C2×C4×D7911yescharacteristic
539C22×C4C2×C4×D7911yescharacteristic
540C22×C4C2×C4×D7911yescharacteristic
541C22×C4C2×C4×D7911yescharacteristic
542C22×C4C2×C4×D7911yescharacteristic
543C22×C4C23×D7911yescharacteristic
544M16—7916no—
545M16—1588no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—794no—
550C2×C8—792no—
551C2×C8—792no—
552C2×C8—792no—
553C2×C8—792no—
554C2×C8—1588no—
555C2×C8—1588no—
556C2×C8—1582no—
557C2×C8—1582no—
558C2×C8—1582no—
559C2×C8Q8×D7914yes—
560C2×C8C23×D7912yes—
561C2×C8C23×D7912yes—
562C2×C8C23×D7912yes—
563C2×C8C23×D7912yes—
564C4⋊C4—794no—
565C4⋊C4—794no—
566C4⋊C4—794no—
567C4⋊C4—794no—
568C4⋊C4—794no—
569C4⋊C4—794no—
570C4⋊C4—794no—
571C4⋊C4—794no—
572C4⋊C4—794no—
573C4⋊C4—794no—
574C4⋊C4—794no—
575C4⋊C4—794no—
576C4⋊C4—794no—
577C4⋊C4C2×C4×D7914yes—
578C4⋊C4C2×C4×D7914yes—
579C4⋊C4C2×C4×D7914yes—
580C22⋊C4—794no—
581C22⋊C4—794no—
582C22⋊C4—794no—
583C22⋊C4—794no—
584C42—792no—
585C42—792no—
586C42—792no—
587C42—792no—
588C42—794no—
589C42—794no—
590C42—792no—
591C42—792no—
592C42C2×C4×D7912yes—
593C42C2×C4×D7912yes—
594C42C2×C4×D7912yes—
595C42C23×D7912yes—
596C42C23×D7912yes—
597C42C23×D7912yes—
598C23—794no—
599C23—792no—
600C23—1582no—
601C23—1582no—
602C23C22×C4×D7911yescharacteristic
603Q8—44no—
604Q8—3164no—
605Q8—1588no—
606Q8—1588no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—3164no—
614C2×C4—794no—
615C2×C4—794no—
616C2×C4—792no—
617C2×C4—792no—
618C2×C4—798no—
619C2×C4—794no—
620C2×C4—794no—
621C2×C4—792no—
622C2×C4—792no—
623C2×C4—792no—
624C2×C4—792no—
625C2×C4—792no—
626C2×C4—1588no—
627C2×C4—1582no—
628C2×C4—1582no—
629C2×C4—1582no—
630C2×C4—1582no—
631C2×C4—1582no—
632C2×C4C22×C4×D7912yes—
633C2×C4C22×C4×D7912yes—
634C2×C4C22×C4×D7912yes—
635C2×C4C22×C4×D7912yes—
636C2×C4C22×C4×D7912yes—
637C2×C4C22×C4×D7912yes—
638C2×C4C22×C4×D7911yescharacteristic
639C2×C4C2×Q8×D7912yes—
640C2×C4#41×D7912yes—
641C2×C4C24×D7911yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—794no—
646C8—1582no—
647C8—1582no—
648C8—1582no—
649C8C2×Q8×D7914yes—
650C22—794no—
651C22—1582no—
652C22—1582no—
653C22—1588no—
654C22C4×Q8×D7912yes—
655C22#131×D7912yes—
656C22#1909932912yes—
657C22C23×C4×D7911yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—794no—
665C4—794no—
666C4—1582no—
667C4—1582no—
668C4—1582no—
669C4—1582no—
670C4—1582no—
671C4C4×Q8×D7912yes—
672C4C22×Q8×D7911yescharacteristic
673C4C2×#41×D7911yescharacteristic
674C2—1584no—
675C2#2377234514yesdirect product factor
676C2C2×C4×Q8×D7911yescharacteristic
677C2C2×#131×D7911yescharacteristic
678C2C2×#1909932911yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC2×C4C24×D79
FittingC2×#446×C79C2
socleC23×C79C23×C4
prime radicalC23×D79C22×C4
cosocleC2×C4×C79C25
hypercenterC2×#446D79
hypocenterC79C2×#2962
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #23772345C2direct (N × H)
3. C2×#19098694C2semidirect
4. C2×#19098692C2semidirect
5. C2×#19098692C2semidirect
6. C2×#19098691C2semidirect
7. C2×#19098691C2semidirect
8. C2×C8×Dic158C2semidirect
9. C2×#19098687C2semidirect
16. C2×#446×C79C2semidirect
37. #19098694C22semidirect
38. #19098692C22semidirect
39. #19098692C22semidirect
40. #19098691C22semidirect
41. #19098691C22semidirect
42. C8×Dic158C22semidirect
43. #19098687C22semidirect
69. #446×C79C22semidirect
83. C2×#11929607Q8semidirect
196. #11929607C2×Q8semidirect
335. C2×C79#2962semidirect
347. C2×#446D79semidirect
356. C79C2×#2962semidirect
383. #446C2×D79semidirect
675. C2#23772345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991172
#237723452
C2×#190986942
C2×#190986922
C2×#190986912
C2×C8×Dic1582
C2×#190986872
C2×#190985882
C2×C4⋊C8×D792
C2×#190985202
C2×#190985172
C2×#190985152
C2×#446×C792
C2×#296279