Finite Group Databasebeta

← C2×#23775638 #35165106

Subgroups — C2×#23775638 #35165106

Order 20224.

2630 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099276C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
3#23775638C2116yesmaximal, direct product factor
4C2×#19098908C211yesmaximal, characteristic, complemented
5C2×#19098887C211yesmaximal, characteristic, complemented
6C2×#19098886C211yesmaximal, characteristic, complemented
7C2×#19098851C211yesmaximal, characteristic, complemented
8C2×#19098816C211yesmaximal, characteristic, complemented
9C2×#19098815C211yesmaximal, characteristic, complemented
10C2×#19098757C211yesmaximal, characteristic, complemented
11C2×#19098698C211yesmaximal, characteristic, complemented
12C2×#19098697C211yesmaximal, characteristic, complemented
13C2×#19098643C211yesmaximal, characteristic, complemented
14C2×#19098639C211yesmaximal, characteristic, complemented
15C2×#19098566C211yesmaximal, characteristic, complemented
16C2×#418×C79C211yesmaximal, characteristic, complemented
17C23×C22⋊D79—21no—
18C22×D4×D79C2211yescharacteristic
19C22×D632C2211yescharacteristic, complemented
20C22×#11929609C2211yescharacteristic
21C22×#11929609C2211yescharacteristic, complemented
22C22×#11929607C2211yescharacteristic, complemented
23#19099276—24no—
24#19099276C2218yescomplemented
25D4×C22⋊D79—24no—
26D4×C22⋊D79C2218yescomplemented
27C2×#14579160C2211yescharacteristic, complemented
28C2×#14579157C2211yescharacteristic
29C2×#14579149—21no—
30C2×#14579147—21no—
31C2×#14579136C2211yescharacteristic, complemented
32C2×#14579135C2211yescharacteristic
33C2×#14579135C2211yescharacteristic, complemented
34C2×#14579134—21no—
35C2×#14579133—21no—
36C2×#14579132C2211yescharacteristic
37C2×#14579130—21no—
38C2×#14579129—21no—
39C2×D4×Dic79C2211yescharacteristic
40C2×#14579123C2211yescharacteristic, complemented
41C2×C4×C22⋊D79C2211yescharacteristic
42C2×#14579119C2211yescharacteristic, complemented
43C2×#14579118—21no—
44#19098908C2218yescomplemented
45#19098887C2218yescomplemented
46#19098886C2218yescomplemented
47#19098851C2218yescomplemented
48#19098816C2218yescomplemented
49#19098815C2218yescomplemented
50#19098757C2218yescomplemented
51#19098698C2218yescomplemented
52#19098697C2218yescomplemented
53#19098643C2218yescomplemented
54#19098639C2218yescomplemented
55C2×#14579094C2211yescharacteristic, complemented
56C2×#14579093C2211yescharacteristic, complemented
57C2×#14579092C2211yescharacteristic, complemented
58C2×Dic79⋊C8C2211yescharacteristic, complemented
59#19098566C2218yescomplemented
60C2×#14579083C2211yescharacteristic, complemented
61C2×#14579083C2211yescharacteristic, complemented
62C2×#14579082C2211yescharacteristic
63C2×#14579082C2211yescharacteristic, complemented
64C2×#14579081C2211yescharacteristic, complemented
65C2×#14579081C2211yescharacteristic, complemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D79)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic79C2211yescharacteristic, complemented
69C23×D4×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic, complemented
71C2×#117×C79C2211yescharacteristic, complemented
72#418×C79C2218yescomplemented
73C2×#102×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic, complemented
76C2×#102×C79C2211yescharacteristic, complemented
77C24×D79—21no—
78C22×Dic158—21no—
79C22×D316—21no—
80C22×D316C2311yescharacteristic
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C22×C22⋊D79—21no—
84C22×C22⋊D79—21no—
85C22×C22⋊D79—28no—
86C22×C22⋊D79—21no—
87C22×C22⋊D79—21no—
88C22×C22⋊D79—21no—
89C22×C22⋊D79—48no—
90C22×C22⋊D79D411yescharacteristic
91C2×D4×D79—24no—
92C2×D4×D79—22no—
93C2×D4×D79—42no—
94C2×D4×D79C2314yes—
95C23×Dic79—21no—
96C22×C4×D79—21no—
97C22×C4×D79C2311yescharacteristic
98C2×D632—42no—
99C2×D632C2314yescomplemented
100C2×#11929609—24no—
101C2×#11929609—42no—
102C2×#11929609C2314yes—
103C2×#11929609C2314yescomplemented
104C2×#11929607—42no—
105C2×#11929607C2314yescomplemented
106C22×C79⋊C8C2311yescharacteristic
107C22×C79⋊C8C2311yescharacteristic
108#14579160—22no—
109#14579160C2314yescomplemented
110#14579157—22no—
111#14579157C2314yes—
112#14579149—28no—
113#14579147—28no—
114#14579136—22no—
115#14579136C2314yescomplemented
116#14579135—22no—
117#14579135—22no—
118#14579135C2314yes—
119#14579135C2314yescomplemented
120#14579134—28no—
121#14579133—28no—
122#14579132—22no—
123#14579132C2314yes—
124#14579130—28no—
125#14579129—28no—
126D4×Dic79—22no—
127D4×Dic79C2314yes—
128#14579123—22no—
129#14579123C2314yescomplemented
130C4×C22⋊D79D414yes—
131C4×C22⋊D79C2314yes—
132#14579119—22no—
133#14579119C2314yescomplemented
134#14579118—28no—
135C2×C4⋊Dic79C2311yescharacteristic
136C2×C4⋊Dic79C2311yescharacteristic
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4D411yescharacteristic
139C2×C22⋊Dic79—21no—
140C2×C22⋊Dic79—21no—
141C2×C22⋊Dic79D411yescharacteristic
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4D411yescharacteristic
148C2×C4×Dic79—21no—
149C2×C4×Dic79C2311yescharacteristic
150#14579094C2314yescomplemented
151#14579093C2314yescomplemented
152#14579092C2314yescomplemented
153Dic79⋊C8C2314yescomplemented
154#14579083C2314yescomplemented
155#14579083C2314yescomplemented
156#14579082C2314yes—
157#14579082C2314yescomplemented
158#14579081C2314yescomplemented
159#14579081C2314yescomplemented
160C22⋊(C79⋊C8)C2314yescomplemented
161(C2×D79)⋊C8C2314yescomplemented
162C8×Dic79C2314yescomplemented
163C25×C79—21no—
164C22×D4×C79—24no—
165C22×D4×C79—22no—
166C22×D4×C79—21no—
167C22×D4×C79—42no—
168C22×D4×C79C2311yescharacteristic
169C22×D4×C79C2314yes—
170C22×D4×C79C2311yescharacteristic
171C23×C4×C79C2311yescharacteristic
172C2×M16×C79—42no—
173C2×M16×C79C2314yescomplemented
174C22×C8×C79C2311yescharacteristic
175C22×C8×C79C2311yescharacteristic
176#117×C79—22no—
177#117×C79C2314yescomplemented
178C2×C4⋊C4×C79C2311yescharacteristic
179C2×C4⋊C4×C79C2311yescharacteristic
180C2×C22⋊C4×C79—21no—
181C2×C42×C79—21no—
182#102×C79C2314yes—
183#102×C79C2314yes—
184#102×C79C2314yescomplemented
185#102×C79C2314yescomplemented
186C23×D79—21no—
187C23×D79—21no—
188C23×D79—24no—
189C23×D79—44no—
190C23×D79—44no—
191C23×D79—82no—
192C23×D79C2×D411yescharacteristic
193C2×Dic158—24no—
194C2×Dic158—82no—
195C2×D316—24no—
196C2×D316—21no—
197C2×D316—21no—
198C2×D316—22no—
199C2×D316—22no—
200C2×D316—22no—
201C2×D316—22no—
202C2×D316—82no—
203C2×D316C2412yes—
204C2×D316C2412yes—
205C2×C22⋊D79—24no—
206C2×C22⋊D79—24no—
207C2×C22⋊D79—24no—
208C2×C22⋊D79—24no—
209C2×C22⋊D79—24no—
210C2×C22⋊D79—24no—
211C2×C22⋊D79—24no—
212C2×C22⋊D79—432no—
213C2×C22⋊D79—44no—
214C2×C22⋊D79—44no—
215C2×C22⋊D79—44no—
216C2×C22⋊D79—44no—
217C2×C22⋊D79—82no—
218C2×C22⋊D79—82no—
219C2×C22⋊D79C2×D414yes—
220D4×D79—28no—
221D4×D79—44no—
222D4×D79—48no—
223C22×Dic79—24no—
224C22×Dic79—21no—
225C22×Dic79—21no—
226C22×Dic79—44no—
227C22×Dic79C2×D411yescharacteristic
228C22×Dic79C2×D411yescharacteristic
229C22×Dic79C2×D411yescharacteristic
230C2×C4×D79—24no—
231C2×C4×D79—22no—
232C2×C4×D79—22no—
233C2×C4×D79—44no—
234C2×C4×D79C2×D412yes—
235C2×C4×D79C2412yes—
236D632—44no—
237#11929609—28no—
238#11929609—44no—
239#11929607—44no—
240C2×C79⋊C8—22no—
241C2×C79⋊C8—22no—
242C2×C79⋊C8C2412yes—
243C2×C79⋊C8C2412yes—
244C4⋊Dic79—21no—
245C4⋊Dic79—21no—
246C4⋊Dic79C2412yes—
247C4⋊Dic79C2412yes—
248Dic79⋊C4—24no—
249Dic79⋊C4C2×D414yes—
250C22⋊Dic79—24no—
251C22⋊Dic79—24no—
252C22⋊Dic79C2×D414yes—
253(C2×D79)⋊C4—24no—
254(C2×D79)⋊C4—24no—
255(C2×D79)⋊C4—24no—
256(C2×D79)⋊C4—24no—
257(C2×D79)⋊C4—24no—
258(C2×D79)⋊C4C2×D414yes—
259C4×Dic79—24no—
260C4×Dic79C2×D412yes—
261C4×Dic79C2412yes—
262C24×C79—21no—
263C24×C79—21no—
264C24×C79—24no—
265C24×C79—44no—
266C24×C79—44no—
267C24×C79—82no—
268C24×C79C2×D411yescharacteristic
269C2×D4×C79—28no—
270C2×D4×C79—21no—
271C2×D4×C79—24no—
272C2×D4×C79—21no—
273C2×D4×C79—22no—
274C2×D4×C79—22no—
275C2×D4×C79—22no—
276C2×D4×C79—44no—
277C2×D4×C79—48no—
278C2×D4×C79—44no—
279C2×D4×C79#4114yes—
280C2×D4×C79C2412yes—
281C2×D4×C79C2412yes—
282C22×C4×C79—22no—
283C22×C4×C79—22no—
284C22×C4×C79—21no—
285C22×C4×C79—21no—
286C22×C4×C79C2×D411yescharacteristic
287C22×C4×C79C2×D412yes—
288C22×C4×C79C2412yes—
289C22×C4×C79C2411yescharacteristic
290M16×C79—44no—
291C2×C8×C79—22no—
292C2×C8×C79—22no—
293C2×C8×C79C2412yes—
294C2×C8×C79C2412yes—
295C4⋊C4×C79—21no—
296C4⋊C4×C79—21no—
297C4⋊C4×C79C2412yes—
298C4⋊C4×C79C2412yes—
299C22⋊C4×C79—24no—
300C42×C79—24no—
301C23×C79—24no—
302C23×C79—22no—
303C23×C79—22no—
304C23×C79—22no—
305C23×C79—22no—
306C23×C79—22no—
307C23×C79—48no—
308C23×C79—48no—
309C23×C79—42no—
310C23×C79—42no—
311C23×C79—42no—
312C23×C79—42no—
313C23×C79—42no—
314C23×C79—84no—
315C23×C79—816no—
316C23×C79C22×D412yes—
317C23×C79C22×D411yescharacteristic
318C22×D79—22no—
319C22×D79—22no—
320C22×D79—22no—
321C22×D79—22no—
322C22×D79—22no—
323C22×D79—48no—
324C22×D79—48no—
325C22×D79—42no—
326C22×D79—42no—
327C22×D79—42no—
328C22×D79—42no—
329C22×D79—42no—
330C22×D79—42no—
331C22×D79—84no—
332C22×D79—816no—
333C22×D79C22×D412yes—
334D4×C79—24no—
335D4×C79—22no—
336D4×C79—22no—
337D4×C79—22no—
338D4×C79—48no—
339D4×C79—42no—
340D4×C79C2×#4114yes—
341C2×C4×C79—22no—
342C2×C4×C79—24no—
343C2×C4×C79—22no—
344C2×C4×C79—22no—
345C2×C4×C79—22no—
346C2×C4×C79—22no—
347C2×C4×C79—42no—
348C2×C4×C79—42no—
349C2×C4×C79C22×D412yes—
350C2×C4×C79C22×D411yescharacteristic
351C2×C4×C79C2×#4112yes—
352C2×C4×C79H(5,𝔽2)12yes—
353C2×C4×C79C2511yescharacteristic
354C22⋊D79—28no—
355C22⋊D79—48no—
356C22⋊D79—48no—
357C22⋊D79—48no—
358C22⋊D79—48no—
359C22⋊D79—84no—
360C22⋊D79—84no—
361C2×Dic79—22no—
362C2×Dic79—22no—
363C2×Dic79—22no—
364C2×Dic79—22no—
365C2×Dic79—42no—
366C2×Dic79—42no—
367C2×Dic79—48no—
368C2×Dic79AGL(1,ℤ/8)14yes—
369C2×Dic79C22×D412yes—
370C2×Dic79C22×D412yes—
371C2×Dic79C22×D412yes—
372D316—22no—
373D316—22no—
374D316—22no—
375D316—22no—
376D316—42no—
377D316—42no—
378D316—84no—
379C4×D79—24no—
380C4×D79—22no—
381C4×D79—22no—
382C4×D79—48no—
383Dic158—84no—
384C8×C79—22no—
385C8×C79—22no—
386C79⋊C8—22no—
387C79⋊C8—22no—
388C22×C79—24no—
389C22×C79—22no—
390C22×C79—22no—
391C22×C79—22no—
392C22×C79—42no—
393C22×C79—48no—
394C22×C79—44no—
395C22×C79—42no—
396C22×C79—42no—
397C22×C79—42no—
398C22×C79—42no—
399C22×C79—816no—
400C22×C79—84no—
401C22×C79#54612yes—
402C22×C79C2×AGL(1,ℤ/8)12yes—
403C22×C79#57612yes—
404C22×C79C23×D411yescharacteristic
405C2×D79—22no—
406C2×D79—22no—
407C2×D79—22no—
408C2×D79—44no—
409C2×D79—42no—
410C2×D79—42no—
411C2×D79—42no—
412C2×D79—42no—
413C2×D79—42no—
414C2×D79—42no—
415C2×D79—816no—
416C2×D79—84no—
417C2×D79—84no—
418C4×C79—22no—
419C4×C79—42no—
420C4×C79—42no—
421C4×C79#54612yes—
422C4×C79C22×#4111yescharacteristic
423C4×C79C2×H(5,𝔽2)11yescharacteristic
424Dic79—22no—
425Dic79—22no—
426Dic79—42no—
427Dic79—42no—
428Dic79C2×AGL(1,ℤ/8)14yes—
429C2×#3325—791nomaximal, Sylow
430C2×C79—44no—
431C2×C79—42no—
432C2×C79—82no—
433C2×C79#332514yescomplemented
434C2×C79C2×#54611yescharacteristic
435C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
436C2×C79C2×#57611yescharacteristic
437D79—42no—
438D79—82no—
439D79—82no—
440C2×#555—791no—
441C2×D42—791no—
442#3325—7916no—
443C2×#486—791no—
444C2×#482—791no—
445C2×#482—791no—
446C2×#476—791no—
447C2×#469—791no—
448C2×#469—791no—
449C2×#459—791no—
450C2×#447—791no—
451C2×#447—791no—
452C2×C4×D8—791no—
453C2×#436—791no—
454C2×#418—791no—
455C2×#418D7911yescharacteristic, complemented
456C79C2×#332511yescharacteristic, complemented, Sylow
457C23×D4—791no—
458C23×D4—1581no—
459C23×D4C2×D7911yescharacteristic
460C22×D8—791no—
461C22×D8—791no—
462C22×D8—791no—
463C22×M16—791no—
464C22×M16C2×D7911yescharacteristic, complemented
465#555—798no—
466#555—1584no—
467D42—798no—
468D42—1584no—
469C2×C4⋊Q8—791no—
470C2×#127—791no—
471C2×#124—1581no—
472C2×#124—1581no—
473C2×#121—791no—
474C2×#121—791no—
475C2×#121—791no—
476C2×#121—791no—
477C2×#121—1581no—
478C2×#121—1581no—
479C2×#120—1581no—
480C2×#120—1581no—
481C2×C4×D4—791no—
482C2×C4×D4—791no—
483C2×C4×D4—791no—
484C2×#117—791no—
485C2×#117—1581no—
486C2×#117C2×D7911yescharacteristic, complemented
487#486—798no—
488#482—798no—
489#482—798no—
490#476—798no—
491#469—798no—
492#469—798no—
493#459—798no—
494#447—798no—
495#447—798no—
496C4×D8—798no—
497#436—798no—
498C2×#107—791no—
499C2×#106—791no—
500C2×#106—791no—
501C2×C4⋊C8—791no—
502#418—798no—
503#418C2×D7918yescomplemented
504C2×#102—791no—
505C2×#102—791no—
506C2×#102—791no—
507C2×#102—791no—
508C2×#102—791no—
509C2×#102—791no—
510C2×#102C2×D7911yescharacteristic
511C2×#102C2×D7911yescharacteristic
512C2×#102C2×D7911yescharacteristic, complemented
513C2×#102C2×D7911yescharacteristic, complemented
514C2×C22⋊C8—791no—
515C2×C22⋊C8—791no—
516C2×C4×C8—791no—
517C25—21no—
518C25—1581no—
519C22×Q8—1581no—
520C22×D4—24no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—42no—
524C22×D4—3168no—
525C22×D4—3162no—
526C22×D4—794no—
527C22×D4—791no—
528C22×D4—791no—
529C22×D4—791no—
530C22×D4—1581no—
531C22×D4—1582no—
532C22×D4—1581no—
533C22×D4—1581no—
534C22×D4—1581no—
535C22×D4—1588no—
536C22×D4—1581no—
537C22×D4—1581no—
538C22×D4—1584no—
539C22×D4—1581no—
540C22×D4C22×D7911yescharacteristic
541C22×D4C22×D7914yes—
542C22×D4C22×D7911yescharacteristic
543C23×C4—791no—
544C23×C4—1581no—
545C23×C4—1581no—
546C23×C4C22×D7911yescharacteristic
547C2×D8—3162no—
548C2×D8—3162no—
549C2×D8—794no—
550C2×D8—794no—
551C2×D8—794no—
552C2×D8—1584no—
553C2×M16—42no—
554C2×M16—3162no—
555C2×M16—794no—
556C2×M16C22×D7914yescomplemented
557C22×C8—791no—
558C22×C8—791no—
559C22×C8C22×D7911yescharacteristic
560C22×C8C22×D7911yescharacteristic
561C4⋊Q8—794no—
562C4⋊Q8—1582no—
563#127—794no—
564#127—1582no—
565#124—1588no—
566#124—1588no—
567#121—794no—
568#121—794no—
569#121—794no—
570#121—794no—
571#121—1588no—
572#121—1582no—
573#121—1588no—
574#121—1582no—
575#121—1582no—
576#121—1582no—
577#120—1588no—
578#120—1588no—
579C4×D4—794no—
580C4×D4—794no—
581C4×D4—794no—
582C4×D4—794no—
583C4×D4—1582no—
584C4×D4—1582no—
585#117—22no—
586#117—794no—
587#117—1588no—
588#117—1582no—
589#117C22×D7914yescomplemented
590C2×C4⋊C4—791no—
591C2×C4⋊C4—791no—
592C2×C4⋊C4—791no—
593C2×C4⋊C4—1581no—
594C2×C4⋊C4C22×D7911yescharacteristic
595C2×C4⋊C4C22×D7911yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—791no—
598C2×C22⋊C4—791no—
599C2×C22⋊C4—1581no—
600C2×C22⋊C4—1581no—
601C2×C22⋊C4—1581no—
602C2×C22⋊C4—1581no—
603C2×C22⋊C4—1581no—
604C2×C22⋊C4—1581no—
605C2×C22⋊C4—1581no—
606C2×C42—21no—
607C2×C42—791no—
608C2×C42—1581no—
609#107—794no—
610#106—794no—
611#106—794no—
612C4⋊C8—794no—
613#102—794no—
614#102—794no—
615#102—794no—
616#102—794no—
617#102—794no—
618#102—794no—
619#102C22×D7914yes—
620#102C22×D7914yes—
621#102C22×D7914yescomplemented
622#102C22×D7914yescomplemented
623C22⋊C8—794no—
624C22⋊C8—794no—
625C4×C8—794no—
626C24—21no—
627C24—21no—
628C24—24no—
629C24—44no—
630C24—44no—
631C24—82no—
632C24—3164no—
633C24—3164no—
634C24—791no—
635C24—6322no—
636C24—1584no—
637C24—1581no—
638C24—1581no—
639C24D4×D7911yescharacteristic
640C2×Q8—6322no—
641C2×Q8—1584no—
642C2×D4—28no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—21no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—44no—
650C2×D4—48no—
651C2×D4—44no—
652C2×D4—3164no—
653C2×D4—3164no—
654C2×D4—31632no—
655C2×D4—3164no—
656C2×D4—3168no—
657C2×D4—3164no—
658C2×D4—3164no—
659C2×D4—794no—
660C2×D4—792no—
661C2×D4—792no—
662C2×D4—6322no—
663C2×D4—6322no—
664C2×D4—6322no—
665C2×D4—1584no—
666C2×D4—1584no—
667C2×D4—1584no—
668C2×D4—1584no—
669C2×D4—1584no—
670C2×D4—1584no—
671C2×D4—1584no—
672C2×D4—1588no—
673C2×D4—1584no—
674C2×D4—1582no—
675C2×D4—1582no—
676C2×D4—1582no—
677C2×D4—1582no—
678C2×D4—1581no—
679C2×D4—1581no—
680C2×D4#1192962414yes—
681C2×D4C23×D7912yes—
682C2×D4C23×D7912yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—3164no—
688C22×C4—3164no—
689C22×C4—791no—
690C22×C4—791no—
691C22×C4—791no—
692C22×C4—792no—
693C22×C4—792no—
694C22×C4—1584no—
695C22×C4—1584no—
696C22×C4—1581no—
697C22×C4—1581no—
698C22×C4—1582no—
699C22×C4—1582no—
700C22×C4D4×D7912yes—
701C22×C4D4×D7911yescharacteristic
702C22×C4C23×D7912yes—
703C22×C4C23×D7911yescharacteristic
704D8—3164no—
705D8—3164no—
706D8—1588no—
707M16—44no—
708M16—3164no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—792no—
712C2×C8—792no—
713C2×C8—1582no—
714C2×C8—1582no—
715C2×C8C23×D7912yes—
716C2×C8C23×D7912yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—794no—
720C4⋊C4—792no—
721C4⋊C4—792no—
722C4⋊C4—1584no—
723C4⋊C4—1581no—
724C4⋊C4—1581no—
725C4⋊C4C23×D7912yes—
726C4⋊C4C23×D7912yes—
727C22⋊C4—24no—
728C22⋊C4—794no—
729C22⋊C4—794no—
730C22⋊C4—1584no—
731C22⋊C4—1584no—
732C22⋊C4—1584no—
733C22⋊C4—1584no—
734C22⋊C4—1584no—
735C22⋊C4—1584no—
736C22⋊C4—1584no—
737C42—24no—
738C42—792no—
739C42—792no—
740C42—1584no—
741C23—22no—
742C23—24no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—48no—
748C23—48no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—84no—
755C23—816no—
756C23—3168no—
757C23—3168no—
758C23—3162no—
759C23—3162no—
760C23—3162no—
761C23—3162no—
762C23—3162no—
763C23—3162no—
764C23—792no—
765C23—63216no—
766C23—6324no—
767C23—1582no—
768C23—1582no—
769C23—1582no—
770C23—1582no—
771C23—1582no—
772C23C2×D4×D7912yes—
773C23C2×D4×D7911yescharacteristic
774Q8—6324no—
775D4—22no—
776D4—22no—
777D4—24no—
778D4—22no—
779D4—48no—
780D4—42no—
781D4—3168no—
782D4—3168no—
783D4—3168no—
784D4—3168no—
785D4—3162no—
786D4—3162no—
787D4—6324no—
788D4—6324no—
789D4—6324no—
790D4—1588no—
791D4—1582no—
792D4—1582no—
793D4—1582no—
794D4—1582no—
795D4C2×#1192962414yes—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—3168no—
805C2×C4—3162no—
806C2×C4—3162no—
807C2×C4—3168no—
808C2×C4—794no—
809C2×C4—792no—
810C2×C4—792no—
811C2×C4—792no—
812C2×C4—1582no—
813C2×C4—1582no—
814C2×C4—1582no—
815C2×C4—1582no—
816C2×C4—1582no—
817C2×C4—1584no—
818C2×C4—1582no—
819C2×C4C2×D4×D7912yes—
820C2×C4C2×D4×D7911yescharacteristic
821C2×C4C2×#1192962412yes—
822C2×C4#1457920612yes—
823C2×C4C24×D7911yescharacteristic
824C8—22no—
825C8—22no—
826C8—1582no—
827C8—1582no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—48no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—84no—
841C22—3164no—
842C22—3162no—
843C22—3162no—
844C22—3162no—
845C22—3162no—
846C22—3162no—
847C22—3162no—
848C22—63216no—
849C22—6324no—
850C22—6324no—
851C22—1582no—
852C22—1582no—
853C22—1582no—
854C22#1909920312yes—
855C22AGL(1,ℤ/8)×D7912yes—
856C22#1909936712yes—
857C22C22×D4×D7911yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—3162no—
862C4—3162no—
863C4—794no—
864C4—1582no—
865C4—1582no—
866C4#1909920312yes—
867C4C22×#1192962411yescharacteristic
868C4C2×#1457920611yescharacteristic
869C2—42no—
870C2—44no—
871C2—82no—
872C2—3162no—
873C2—6322no—
874C2—6322no—
875C2#2377563814yesdirect product factor
876C2C2×#1909920311yescharacteristic
877C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
878C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#418×C79C2
socleC23×C79C22×D4
hypercenterC2×#418D79
hypocenterC79C2×#3325
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#19099276C2semidirect
2. C2×D4×C22⋊D79C2semidirect
3. #23775638C2direct (N × H)
4. C2×#19098908C2semidirect
5. C2×#19098887C2semidirect
6. C2×#19098886C2semidirect
7. C2×#19098851C2semidirect
8. C2×#19098816C2semidirect
9. C2×#19098815C2semidirect
10. C2×#19098757C2semidirect
11. C2×#19098698C2semidirect
12. C2×#19098697C2semidirect
13. C2×#19098643C2semidirect
14. C2×#19098639C2semidirect
15. C2×#19098566C2semidirect
16. C2×#418×C79C2semidirect
19. C22×D632C22semidirect
21. C22×#11929609C22semidirect
22. C22×#11929607C22semidirect
24. #19099276C22semidirect
26. D4×C22⋊D79C22semidirect
27. C2×#14579160C22semidirect
31. C2×#14579136C22semidirect
33. C2×#14579135C22semidirect
40. C2×#14579123C22semidirect
42. C2×#14579119C22semidirect
44. #19098908C22semidirect
45. #19098887C22semidirect
46. #19098886C22semidirect
47. #19098851C22semidirect
48. #19098816C22semidirect
49. #19098815C22semidirect
50. #19098757C22semidirect
51. #19098698C22semidirect
52. #19098697C22semidirect
53. #19098643C22semidirect
54. #19098639C22semidirect
55. C2×#14579094C22semidirect
56. C2×#14579093C22semidirect
57. C2×#14579092C22semidirect
58. C2×Dic79⋊C8C22semidirect
59. #19098566C22semidirect
60. C2×#14579083C22semidirect
61. C2×#14579083C22semidirect
63. C2×#14579082C22semidirect
64. C2×#14579081C22semidirect
65. C2×#14579081C22semidirect
66. C2×C22⋊(C79⋊C8)C22semidirect
67. C2×(C2×D79)⋊C8C22semidirect
68. C2×C8×Dic79C22semidirect
70. C22×M16×C79C22semidirect
71. C2×#117×C79C22semidirect
72. #418×C79C22semidirect
75. C2×#102×C79C22semidirect
76. C2×#102×C79C22semidirect
99. C2×D632C23semidirect
103. C2×#11929609C23semidirect
105. C2×#11929607C23semidirect
109. #14579160C23semidirect
115. #14579136C23semidirect
119. #14579135C23semidirect
129. #14579123C23semidirect
133. #14579119C23semidirect
150. #14579094C23semidirect
151. #14579093C23semidirect
152. #14579092C23semidirect
153. Dic79⋊C8C23semidirect
154. #14579083C23semidirect
155. #14579083C23semidirect
157. #14579082C23semidirect
158. #14579081C23semidirect
159. #14579081C23semidirect
160. C22⋊(C79⋊C8)C23semidirect
161. (C2×D79)⋊C8C23semidirect
162. C8×Dic79C23semidirect
173. C2×M16×C79C23semidirect
177. #117×C79C23semidirect
184. #102×C79C23semidirect
185. #102×C79C23semidirect
433. C2×C79#3325semidirect
455. C2×#418D79semidirect
456. C79C2×#3325semidirect
464. C22×M16C2×D79semidirect
486. C2×#117C2×D79semidirect
503. #418C2×D79semidirect
512. C2×#102C2×D79semidirect
513. C2×#102C2×D79semidirect
556. C2×M16C22×D79semidirect
589. #117C22×D79semidirect
621. #102C22×D79semidirect
622. #102C22×D79semidirect
875. C2#23775638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992762
C2×D4×C22⋊D792
#237756382
C2×#190989082
C2×#190988872
C2×#190988862
C2×#190988512
C2×#190988162
C2×#190988152
C2×#190987572
C2×#190986982
C2×#190986972
C2×#190986432
C2×#190986392
C2×#190985662
C2×#418×C792
C2×#332579