Finite Group Databasebeta

← C2×#23772468 #35153043

Subgroups — C2×#23772468 #35153043

Order 20224.

2186 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099110C211yesmaximal, characteristic
2#23772468C2116yesmaximal, direct product factor
3C2×#19098637C211yesmaximal, characteristic, complemented
4C2×#19098636C211yesmaximal, characteristic, complemented
5C2×#19098635C211yesmaximal, characteristic, complemented
6C2×#19098634C211yesmaximal, characteristic, complemented
7C2×#19098633C211yesmaximal, characteristic, complemented
8C2×#19098632C211yesmaximal, characteristic, complemented
9C2×#19098631C211yesmaximal, characteristic, complemented
10C2×#19098619C211yesmaximal, characteristic, complemented
11C2×#19098618C211yesmaximal, characteristic, complemented
12C2×#19098531C211yesmaximal, characteristic, complemented
13C2×#19098529C211yesmaximal, characteristic, complemented
14C2×#19098528C211yesmaximal, characteristic, complemented
15C2×#19098528C211yesmaximal, characteristic, complemented
16C2×#435×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929624C2211yescharacteristic
19C22×#11929608C2211yescharacteristic
20C22×#11929607C2211yescharacteristic
21C22×#11929607C2211yescharacteristic
22C23×C79⋊C8C2211yescharacteristic
23C22×C8×D79C2211yescharacteristic
24C22×C8×D79C2211yescharacteristic
25#19099110C418yes—
26#19099110C2218yes—
27C2×#14579160C411yescharacteristic
28C2×#14579157C411yescharacteristic
29C2×#14579147C411yescharacteristic
30C2×#14579147C411yescharacteristic
31C2×#14579136C411yescharacteristic
32C2×#14579134C411yescharacteristic
33C2×#14579134C411yescharacteristic
34C2×#14579132C411yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×C4×C22⋊D79C2211yescharacteristic
37C2×C4×C22⋊D79C2211yescharacteristic
38C2×C42×D79C2211yescharacteristic
39#19098637C2218yescomplemented
40#19098636C2218yescomplemented
41#19098635C2218yescomplemented
42#19098634C2218yescomplemented
43#19098633C2218yescomplemented
44#19098632C2218yescomplemented
45#19098631C2218yescomplemented
46#19098619C2218yescomplemented
47#19098618C2218yescomplemented
48C2×C4⋊(C79⋊C8)C2211yescharacteristic
49C2×Dic79⋊C8C2211yescharacteristic
50C2×Dic79⋊C8C2211yescharacteristic
51#19098531C2218yescomplemented
52#19098529C2218yescomplemented
53#19098528C2218yescomplemented
54#19098528C2218yescomplemented
55C2×C22⋊(C79⋊C8)C2211yescharacteristic
56C2×C22⋊(C79⋊C8)C2211yescharacteristic
57C2×(C2×D79)⋊C8C2211yescharacteristic
58C2×(C2×D79)⋊C8C2211yescharacteristic
59C2×(C2×D79)⋊C8C2211yescharacteristic
60C2×(C2×D79)⋊C8C2211yescharacteristic
61C2×(C2×D79)⋊C8C2211yescharacteristic
62C2×(C2×D79)⋊C8C2211yescharacteristic
63C2×(C2×D79)⋊C8C2211yescharacteristic
64C2×(C2×D79)⋊C8C2211yescharacteristic
65C2×#14579072C2211yescharacteristic
66C2×#14579071C2211yescharacteristic
67C2×#14579071C2211yescharacteristic
68C22×M16×C79C2211yescharacteristic
69C23×C8×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71#435×C79C2218yescomplemented
72C2×C4⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×#97×C79C2211yescharacteristic
76C2×#11929624—42no—
77C2×#11929624—42no—
78C2×#11929624—42no—
79C2×#11929624—42no—
80C2×#11929624C2×C414yes—
81C2×#11929624C2×C414yes—
82C2×#11929624C2314yes—
83C2×#11929624C2314yes—
84C22×Dic158C2×C411yescharacteristic
85C22×Dic158C2×C411yescharacteristic
86C22×D316C2×C411yescharacteristic
87C22×D316C2×C411yescharacteristic
88C22×D316C2×C411yescharacteristic
89C22×C22⋊D79C2×C411yescharacteristic
90C22×C22⋊D79C2×C411yescharacteristic
91C22×C22⋊D79C2×C411yescharacteristic
92C22×C22⋊D79C2×C411yescharacteristic
93C22×C22⋊D79C2×C411yescharacteristic
94C22×C22⋊D79C2×C411yescharacteristic
95C22×C4×D79C2×C411yescharacteristic
96C22×C4×D79C2×C411yescharacteristic
97C22×C4×D79C2311yescharacteristic
98C22×C4×D79C2311yescharacteristic
99C22×C4×D79C2311yescharacteristic
100C2×#11929608—42no—
101C2×#11929608C2314yes—
102C2×#11929607—42no—
103C2×#11929607—42no—
104C2×#11929607C2314yes—
105C2×#11929607C2314yes—
106C22×C79⋊C8—42no—
107C22×C79⋊C8C2311yescharacteristic
108C22×C79⋊C8C2311yescharacteristic
109C22×C79⋊C8C2311yescharacteristic
110C22×C79⋊C8C2311yescharacteristic
111C22×C79⋊C8C2314yes—
112C2×C8×D79—42no—
113C2×C8×D79—42no—
114C2×C8×D79C2314yes—
115C2×C8×D79C2314yes—
116#14579160C2×C418yes—
117#14579157C2×C418yes—
118#14579147C2×C418yes—
119#14579147C2×C418yes—
120#14579136C2×C418yes—
121#14579134C2×C418yes—
122#14579134C2×C418yes—
123#14579132C2×C418yes—
124C4×D316C2×C414yes—
125C4×D316C2314yes—
126C4×C22⋊D79C2×C414yes—
127C4×C22⋊D79C2×C414yes—
128C4×C22⋊D79C2314yes—
129C4×C22⋊D79C2314yes—
130C2×C4⋊Dic79C2×C411yescharacteristic
131C2×Dic79⋊C4C2×C411yescharacteristic
132C2×Dic79⋊C4C2×C411yescharacteristic
133C2×C22⋊Dic79C2×C411yescharacteristic
134C2×C22⋊Dic79C2×C411yescharacteristic
135C2×(C2×D79)⋊C4C2×C411yescharacteristic
136C2×(C2×D79)⋊C4C2×C411yescharacteristic
137C2×(C2×D79)⋊C4C2×C411yescharacteristic
138C2×(C2×D79)⋊C4C2×C411yescharacteristic
139C2×C4×Dic79C2×C411yescharacteristic
140C2×C4×Dic79C2×C411yescharacteristic
141C2×C4×Dic79C2311yescharacteristic
142C42×D79C2×C414yes—
143C42×D79C2314yes—
144C4⋊(C79⋊C8)C2314yes—
145Dic79⋊C8C2314yes—
146Dic79⋊C8C2314yes—
147C22⋊(C79⋊C8)C2314yes—
148C22⋊(C79⋊C8)C2314yes—
149(C2×D79)⋊C8C2314yes—
150(C2×D79)⋊C8C2314yes—
151(C2×D79)⋊C8C2314yes—
152(C2×D79)⋊C8C2314yes—
153(C2×D79)⋊C8C2314yes—
154(C2×D79)⋊C8C2314yes—
155(C2×D79)⋊C8C2314yes—
156(C2×D79)⋊C8C2314yes—
157#14579072C2314yes—
158#14579071C2314yes—
159#14579071C2314yes—
160C22×D4×C79C2×C411yescharacteristic
161C23×C4×C79C2311yescharacteristic
162C23×C4×C79C2311yescharacteristic
163C2×M16×C79—42no—
164C2×M16×C79C2314yes—
165C22×C8×C79—42no—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C22×C8×C79C2314yes—
171C4×D4×C79C2×C414yes—
172C4×D4×C79C2314yes—
173C2×C4⋊C4×C79C2×C411yescharacteristic
174C2×C22⋊C4×C79C2×C411yescharacteristic
175C2×C22⋊C4×C79C2×C411yescharacteristic
176C2×C42×C79C2311yescharacteristic
177C4⋊C8×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C22⋊C8×C79C2314yes—
180#97×C79C2314yes—
181C23×D79C22×C411yescharacteristic
182C23×D79C22×C411yescharacteristic
183C23×D79C22×C411yescharacteristic
184#11929624—48no—
185#11929624—48no—
186#11929624—44no—
187#11929624—44no—
188#11929624—44no—
189#11929624—44no—
190C2×Dic158—42no—
191C2×Dic158—42no—
192C2×Dic158C22×C414yes—
193C2×Dic158C22×C414yes—
194C2×D316—42no—
195C2×D316—42no—
196C2×D316—42no—
197C2×D316C22×C414yes—
198C2×D316C22×C414yes—
199C2×D316C22×C414yes—
200C2×C22⋊D79—42no—
201C2×C22⋊D79—42no—
202C2×C22⋊D79—42no—
203C2×C22⋊D79—42no—
204C2×C22⋊D79—42no—
205C2×C22⋊D79—42no—
206C2×C22⋊D79C22×C414yes—
207C2×C22⋊D79C22×C414yes—
208C2×C22⋊D79C22×C414yes—
209C2×C22⋊D79C22×C414yes—
210C2×C22⋊D79C22×C414yes—
211C2×C22⋊D79C22×C414yes—
212C22×Dic79C22×C411yescharacteristic
213C22×Dic79C22×C411yescharacteristic
214C22×Dic79C22×C411yescharacteristic
215C22×Dic79C22×C411yescharacteristic
216C22×Dic79C22×C411yescharacteristic
217C2×C4×D79—22no—
218C2×C4×D79—22no—
219C2×C4×D79—22no—
220C2×C4×D79—22no—
221C2×C4×D79—22no—
222C2×C4×D79—22no—
223C2×C4×D79—42no—
224C2×C4×D79—42no—
225C2×C4×D79C22×C412yes—
226C2×C4×D79C22×C412yes—
227C2×C4×D79C22×C412yes—
228C2×C4×D79C22×C414yes—
229C2×C4×D79C22×C414yes—
230C2×C4×D79C2412yes—
231C2×C4×D79C2412yes—
232C2×C4×D79C2412yes—
233#11929608—44no—
234#11929607—44no—
235#11929607—44no—
236C2×C79⋊C8—22no—
237C2×C79⋊C8—22no—
238C2×C79⋊C8—22no—
239C2×C79⋊C8—22no—
240C2×C79⋊C8—44no—
241C2×C79⋊C8C2412yes—
242C2×C79⋊C8C2412yes—
243C2×C79⋊C8C2412yes—
244C2×C79⋊C8C2412yes—
245C8×D79—44no—
246C8×D79—44no—
247C4⋊Dic79C22×C414yes—
248Dic79⋊C4C22×C414yes—
249Dic79⋊C4C22×C414yes—
250C22⋊Dic79C22×C414yes—
251C22⋊Dic79C22×C414yes—
252(C2×D79)⋊C4C22×C414yes—
253(C2×D79)⋊C4C22×C414yes—
254(C2×D79)⋊C4C22×C414yes—
255(C2×D79)⋊C4C22×C414yes—
256C4×Dic79C22×C412yes—
257C4×Dic79C22×C414yes—
258C4×Dic79C22×C414yes—
259C4×Dic79C2412yes—
260C24×C79C22×C411yescharacteristic
261C24×C79C22×C411yescharacteristic
262C2×D4×C79—42no—
263C2×D4×C79C22×C414yes—
264C22×C4×C79—22no—
265C22×C4×C79—22no—
266C22×C4×C79—22no—
267C22×C4×C79—22no—
268C22×C4×C79C22×C411yescharacteristic
269C22×C4×C79C22×C411yescharacteristic
270C22×C4×C79C22×C412yes—
271C22×C4×C79C22×C412yes—
272C22×C4×C79C22×C411yescharacteristic
273C22×C4×C79C22×C411yescharacteristic
274C22×C4×C79C2412yes—
275C22×C4×C79C2412yes—
276C22×C4×C79C2411yescharacteristic
277M16×C79—44no—
278C2×C8×C79—22no—
279C2×C8×C79—22no—
280C2×C8×C79—22no—
281C2×C8×C79—22no—
282C2×C8×C79—44no—
283C2×C8×C79C2412yes—
284C2×C8×C79C2412yes—
285C2×C8×C79C2412yes—
286C2×C8×C79C2412yes—
287C4⋊C4×C79C22×C414yes—
288C22⋊C4×C79C22×C414yes—
289C22⋊C4×C79C22×C414yes—
290C42×C79C22×C412yes—
291C42×C79C2412yes—
292C23×C79—22no—
293C23×C79—22no—
294C23×C79—22no—
295C23×C79—22no—
296C23×C79—22no—
297C23×C79—22no—
298C23×C79C23×C412yes—
299C23×C79C23×C412yes—
300C23×C79C23×C411yescharacteristic
301C22×D79—22no—
302C22×D79—22no—
303C22×D79—22no—
304C22×D79—22no—
305C22×D79—22no—
306C22×D79—22no—
307C22×D79—22no—
308C22×D79—22no—
309C22×D79—22no—
310C22×D79C23×C412yes—
311C22×D79C23×C412yes—
312C22×D79C23×C412yes—
313D4×C79—44no—
314C2×C4×C79—22no—
315C2×C4×C79—22no—
316C2×C4×C79—22no—
317C2×C4×C79—22no—
318C2×C4×C79—24no—
319C2×C4×C79—24no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79C23×C412yes—
325C2×C4×C79C23×C412yes—
326C2×C4×C79C23×C412yes—
327C2×C4×C79C23×C412yes—
328C2×C4×C79C23×C411yescharacteristic
329C2×C4×C79H(5,𝔽2)12yes—
330C2×C4×C79H(5,𝔽2)12yes—
331C2×C4×C79C2511yescharacteristic
332C22⋊D79—44no—
333C22⋊D79—44no—
334C22⋊D79—44no—
335C22⋊D79—44no—
336C22⋊D79—44no—
337C22⋊D79—44no—
338C2×Dic79—22no—
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—22no—
342C2×Dic79—22no—
343C2×Dic79C23×C412yes—
344C2×Dic79C23×C412yes—
345C2×Dic79C23×C412yes—
346C2×Dic79C23×C412yes—
347C2×Dic79C23×C412yes—
348D316—44no—
349D316—44no—
350D316—44no—
351C4×D79—24no—
352C4×D79—24no—
353C4×D79—24no—
354C4×D79—22no—
355C4×D79—22no—
356C4×D79—22no—
357C4×D79—22no—
358C4×D79—22no—
359C4×D79—22no—
360C4×D79—44no—
361C4×D79—44no—
362Dic158—44no—
363Dic158—44no—
364C8×C79—22no—
365C8×C79—22no—
366C8×C79—22no—
367C8×C79—22no—
368C79⋊C8—22no—
369C79⋊C8—22no—
370C79⋊C8—22no—
371C79⋊C8—22no—
372C22×C79—22no—
373C22×C79—22no—
374C22×C79—22no—
375C22×C79—22no—
376C22×C79—22no—
377C22×C79—22no—
378C22×C79—44no—
379C22×C79—44no—
380C22×C79#51812yes—
381C22×C79#56812yes—
382C22×C79#56812yes—
383C22×C79C24×C411yescharacteristic
384C2×D79—22no—
385C2×D79—22no—
386C2×D79—22no—
387C2×D79—22no—
388C2×D79—22no—
389C2×D79—22no—
390C2×D79—22no—
391C2×D79—22no—
392C2×D79—22no—
393C2×D79—44no—
394C2×D79—44no—
395C2×D79—44no—
396C4×C79—22no—
397C4×C79—22no—
398C4×C79—22no—
399C4×C79—22no—
400C4×C79#51812yes—
401C4×C79C2×H(5,𝔽2)11yescharacteristic
402C4×C79C2×H(5,𝔽2)11yescharacteristic
403Dic79—22no—
404Dic79—22no—
405Dic79—22no—
406Dic79—22no—
407Dic79—22no—
408C2×#2980—791nomaximal, Sylow
409C2×C79—42no—
410C2×C79—42no—
411C2×C79#298014yescomplemented
412C2×C79C2×#51811yescharacteristic
413C2×C79C2×#56811yescharacteristic
414C2×C79C2×#56811yescharacteristic
415D79—42no—
416D79—42no—
417D79—42no—
418C2×#532—791no—
419#2980—7916no—
420C2×#435—791no—
421C2×#435—791no—
422C2×#435—791no—
423C2×#435—791no—
424C2×#435—791no—
425C2×#435—791no—
426C2×#435—791no—
427C2×#435D7911yescharacteristic, complemented
428C2×#432—791no—
429C2×#432—791no—
430C2×#408—791no—
431C2×#408—791no—
432C2×#408—791no—
433C2×#408—791no—
434C79C2×#298011yescharacteristic, complemented, Sylow
435C22×#41—791no—
436C22×#41—791no—
437C22×M16—791no—
438C22×M16—791no—
439C22×M16—791no—
440C22×M16C2×D7911yescharacteristic
441C23×C8—791no—
442C23×C8—791no—
443C23×C8—791no—
444C23×C8C2×D7911yescharacteristic
445#532—798no—
446#532—798no—
447C2×C4⋊Q8—791no—
448C2×#127—791no—
449C2×#124—791no—
450C2×#124—791no—
451C2×#121—791no—
452C2×#121—791no—
453C2×#121—791no—
454C2×#121—791no—
455C2×C4×D4—791no—
456C2×C4×D4—791no—
457C2×C4×D4—791no—
458C2×C4×D4C2×D7911yescharacteristic
459C22×C42—791no—
460#435—798no—
461#435—798no—
462#435—798no—
463#435—798no—
464#435—798no—
465#435—798no—
466#435—798no—
467#435C2×D7918yescomplemented
468#432—798no—
469#432—798no—
470C2×C4⋊C8—791no—
471C2×C4⋊C8—791no—
472C2×C4⋊C8—791no—
473C2×C4⋊C8C2×D7911yescharacteristic
474#408—798no—
475#408—798no—
476#408—798no—
477#408—798no—
478C2×C22⋊C8—791no—
479C2×C22⋊C8—791no—
480C2×C22⋊C8—791no—
481C2×C22⋊C8—791no—
482C2×C22⋊C8—791no—
483C2×C22⋊C8—791no—
484C2×C22⋊C8—791no—
485C2×C22⋊C8—791no—
486C2×C22⋊C8—791no—
487C2×C22⋊C8—791no—
488C2×C22⋊C8C2×D7911yescharacteristic
489C2×C22⋊C8C2×D7911yescharacteristic
490C2×#97—791no—
491C2×#97—791no—
492C2×#97—791no—
493C2×#97C2×D7911yescharacteristic
494C2×#41—3162no—
495C2×#41—3162no—
496C2×#41—3162no—
497C2×#41—3162no—
498C2×#41—794no—
499C2×#41—794no—
500C2×#41—794no—
501C2×#41—794no—
502C22×Q8—791no—
503C22×Q8—791no—
504C22×D4—791no—
505C22×D4—791no—
506C22×D4—791no—
507C22×D4—791no—
508C22×D4—791no—
509C22×D4—791no—
510C22×D4—791no—
511C22×D4—791no—
512C22×D4—791no—
513C22×D4C4×D7911yescharacteristic
514C23×C4—791no—
515C23×C4—791no—
516C23×C4—791no—
517C23×C4—791no—
518C23×C4—791no—
519C23×C4C22×D7911yescharacteristic
520C23×C4C22×D7911yescharacteristic
521C2×M16—42no—
522C2×M16—3162no—
523C2×M16—3162no—
524C2×M16—3162no—
525C2×M16—794no—
526C2×M16—794no—
527C2×M16—794no—
528C2×M16C22×D7914yes—
529C22×C8—42no—
530C22×C8—3162no—
531C22×C8—3162no—
532C22×C8—3162no—
533C22×C8—794no—
534C22×C8—794no—
535C22×C8—794no—
536C22×C8—791no—
537C22×C8—791no—
538C22×C8—791no—
539C22×C8—791no—
540C22×C8C22×D7911yescharacteristic
541C22×C8C22×D7911yescharacteristic
542C22×C8C22×D7911yescharacteristic
543C22×C8C22×D7911yescharacteristic
544C22×C8C22×D7914yes—
545C4⋊Q8—798no—
546#127—798no—
547#124—798no—
548#124—798no—
549#121—798no—
550#121—798no—
551#121—798no—
552#121—798no—
553C4×D4—794no—
554C4×D4—794no—
555C4×D4—794no—
556C4×D4—794no—
557C4×D4—794no—
558C4×D4—794no—
559C4×D4C4×D7914yes—
560C4×D4C22×D7914yes—
561C2×C4⋊C4—791no—
562C2×C4⋊C4—791no—
563C2×C4⋊C4—791no—
564C2×C4⋊C4C4×D7911yescharacteristic
565C2×C22⋊C4—791no—
566C2×C22⋊C4—791no—
567C2×C22⋊C4—791no—
568C2×C22⋊C4—791no—
569C2×C22⋊C4—791no—
570C2×C22⋊C4—791no—
571C2×C22⋊C4C4×D7911yescharacteristic
572C2×C22⋊C4C4×D7911yescharacteristic
573C2×C42—791no—
574C2×C42—791no—
575C2×C42—791no—
576C2×C42—794no—
577C2×C42—794no—
578C2×C42C22×D7911yescharacteristic
579C4⋊C8—794no—
580C4⋊C8—794no—
581C4⋊C8—794no—
582C4⋊C8C22×D7914yes—
583C22⋊C8—794no—
584C22⋊C8—794no—
585C22⋊C8—794no—
586C22⋊C8—794no—
587C22⋊C8—794no—
588C22⋊C8—794no—
589C22⋊C8—794no—
590C22⋊C8—794no—
591C22⋊C8—794no—
592C22⋊C8—794no—
593C22⋊C8C22×D7914yes—
594C22⋊C8C22×D7914yes—
595#97—794no—
596#97—794no—
597#97—794no—
598#97C22×D7914yes—
599C24—791no—
600C24—791no—
601C24—791no—
602C24C2×C4×D7911yescharacteristic
603C24C2×C4×D7911yescharacteristic
604#41—3164no—
605#41—3164no—
606#41—3164no—
607#41—3164no—
608#41—3168no—
609#41—3168no—
610C2×Q8—3162no—
611C2×Q8—3162no—
612C2×Q8—794no—
613C2×Q8—794no—
614C2×D4—42no—
615C2×D4—3162no—
616C2×D4—3162no—
617C2×D4—3162no—
618C2×D4—3162no—
619C2×D4—3162no—
620C2×D4—3162no—
621C2×D4—3162no—
622C2×D4—3162no—
623C2×D4—3162no—
624C2×D4—794no—
625C2×D4—794no—
626C2×D4—794no—
627C2×D4—794no—
628C2×D4—794no—
629C2×D4—794no—
630C2×D4—794no—
631C2×D4—794no—
632C2×D4—794no—
633C2×D4C2×C4×D7914yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—3162no—
639C22×C4—3162no—
640C22×C4—794no—
641C22×C4—794no—
642C22×C4—791no—
643C22×C4—791no—
644C22×C4—791no—
645C22×C4—791no—
646C22×C4—791no—
647C22×C4—792no—
648C22×C4—792no—
649C22×C4—792no—
650C22×C4—792no—
651C22×C4—792no—
652C22×C4—792no—
653C22×C4—1582no—
654C22×C4—1582no—
655C22×C4—1582no—
656C22×C4—1582no—
657C22×C4—1582no—
658C22×C4—1582no—
659C22×C4C2×C4×D7911yescharacteristic
660C22×C4C2×C4×D7911yescharacteristic
661C22×C4C2×C4×D7911yescharacteristic
662C22×C4C2×C4×D7911yescharacteristic
663C22×C4C2×C4×D7912yes—
664C22×C4C2×C4×D7912yes—
665C22×C4C23×D7912yes—
666C22×C4C23×D7912yes—
667C22×C4C23×D7911yescharacteristic
668M16—44no—
669M16—3164no—
670M16—3164no—
671M16—3164no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—3164no—
678C2×C8—3164no—
679C2×C8—3164no—
680C2×C8—792no—
681C2×C8—792no—
682C2×C8—792no—
683C2×C8—792no—
684C2×C8—1582no—
685C2×C8—1582no—
686C2×C8—1582no—
687C2×C8—1582no—
688C2×C8C23×D7912yes—
689C2×C8C23×D7912yes—
690C2×C8C23×D7912yes—
691C2×C8C23×D7912yes—
692C4⋊C4—794no—
693C4⋊C4—794no—
694C4⋊C4—794no—
695C4⋊C4C2×C4×D7914yes—
696C22⋊C4—794no—
697C22⋊C4—794no—
698C22⋊C4—794no—
699C22⋊C4—794no—
700C22⋊C4—794no—
701C22⋊C4—794no—
702C22⋊C4C2×C4×D7914yes—
703C22⋊C4C2×C4×D7914yes—
704C42—792no—
705C42—792no—
706C42—794no—
707C42—794no—
708C42C2×C4×D7912yes—
709C42C23×D7912yes—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—792no—
717C23—792no—
718C23—792no—
719C23—1582no—
720C23—1582no—
721C23—1582no—
722C23—1582no—
723C23—1582no—
724C23—1582no—
725C23—1582no—
726C23—1582no—
727C23—1582no—
728C23C22×C4×D7912yes—
729C23C22×C4×D7912yes—
730C23C22×C4×D7911yescharacteristic
731Q8—3164no—
732Q8—3164no—
733D4—44no—
734D4—3164no—
735D4—3164no—
736D4—3164no—
737D4—3164no—
738D4—3164no—
739D4—3164no—
740D4—3164no—
741D4—3164no—
742D4—3164no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—3164no—
754C2×C4—3164no—
755C2×C4—792no—
756C2×C4—792no—
757C2×C4—792no—
758C2×C4—792no—
759C2×C4—792no—
760C2×C4—1582no—
761C2×C4—1582no—
762C2×C4—1582no—
763C2×C4—1582no—
764C2×C4—1582no—
765C2×C4—1582no—
766C2×C4—1582no—
767C2×C4—1582no—
768C2×C4—1582no—
769C2×C4—1582no—
770C2×C4—1582no—
771C2×C4—1584no—
772C2×C4—1584no—
773C2×C4—1584no—
774C2×C4C22×C4×D7912yes—
775C2×C4C22×C4×D7912yes—
776C2×C4C22×C4×D7912yes—
777C2×C4C22×C4×D7912yes—
778C2×C4C22×C4×D7911yescharacteristic
779C2×C4#1457920612yes—
780C2×C4#1457920712yes—
781C2×C4C24×D7911yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1582no—
787C8—1582no—
788C8—1582no—
789C8—1582no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—3164no—
799C22—3164no—
800C22—3164no—
801C22—1582no—
802C22—1582no—
803C22—1582no—
804C22—1582no—
805C22—1582no—
806C22—1582no—
807C22—1582no—
808C22—1582no—
809C22—1582no—
810C22#1909903512yes—
811C22#1909932812yes—
812C22#1909932912yes—
813C22C23×C4×D7911yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—1582no—
819C4—1582no—
820C4—1582no—
821C4—1582no—
822C4—1582no—
823C4#1909903512yes—
824C4C2×#1457920611yescharacteristic
825C4C2×#1457920711yescharacteristic
826C2—42no—
827C2—42no—
828C2—3162no—
829C2—3162no—
830C2—3162no—
831C2#2377246814yesdirect product factor
832C2C2×#1909903511yescharacteristic
833C2C2×#1909932811yescharacteristic
834C2C2×#1909932911yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC2×C4C24×D79
FittingC2×#435×C79C2
socleC23×C79C23×C4
prime radicalC2×#19099110C2
cosocleC2×C4×C79C25
hypercenterC2×#435D79
hypocenterC79C2×#2980
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #23772468C2direct (N × H)
3. C2×#19098637C2semidirect
4. C2×#19098636C2semidirect
5. C2×#19098635C2semidirect
6. C2×#19098634C2semidirect
7. C2×#19098633C2semidirect
8. C2×#19098632C2semidirect
9. C2×#19098631C2semidirect
10. C2×#19098619C2semidirect
11. C2×#19098618C2semidirect
12. C2×#19098531C2semidirect
13. C2×#19098529C2semidirect
14. C2×#19098528C2semidirect
15. C2×#19098528C2semidirect
16. C2×#435×C79C2semidirect
39. #19098637C22semidirect
40. #19098636C22semidirect
41. #19098635C22semidirect
42. #19098634C22semidirect
43. #19098633C22semidirect
44. #19098632C22semidirect
45. #19098631C22semidirect
46. #19098619C22semidirect
47. #19098618C22semidirect
51. #19098531C22semidirect
52. #19098529C22semidirect
53. #19098528C22semidirect
54. #19098528C22semidirect
71. #435×C79C22semidirect
411. C2×C79#2980semidirect
427. C2×#435D79semidirect
434. C79C2×#2980semidirect
467. #435C2×D79semidirect
831. C2#23772468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991102
#237724682
C2×#190986372
C2×#190986362
C2×#190986352
C2×#190986342
C2×#190986332
C2×#190986322
C2×#190986312
C2×#190986192
C2×#190986182
C2×#190985312
C2×#190985292
C2×#190985282
C2×#435×C792
C2×#298079