Finite Group Databasebeta

← C2×#23776022 #35167015

Subgroups — C2×#23776022 #35167015

Order 20224.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099276C211yesmaximal, characteristic
2C2×#19099268C211yesmaximal, characteristic, complemented
3#23776022C2116yesmaximal, direct product factor
4C2×#19098967C211yesmaximal, characteristic, complemented
5C2×#19098907C211yesmaximal, characteristic, complemented
6C2×#19098904C211yesmaximal, characteristic, complemented
7C2×#19098878C211yesmaximal, characteristic, complemented
8C2×#19098876C211yesmaximal, characteristic, complemented
9C2×#19098857C211yesmaximal, characteristic, complemented
10C2×#19098852C211yesmaximal, characteristic, complemented
11C2×#19098810C211yesmaximal, characteristic, complemented
12C2×#19098809C211yesmaximal, characteristic, complemented
13C2×#19098650C211yesmaximal, characteristic, complemented
14C2×#19098639C211yesmaximal, characteristic, complemented
15C2×#19098602C211yesmaximal, characteristic, complemented
16C2×#428×C79C211yesmaximal, characteristic, complemented
17C22×#11929613C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19#19099276—24no—
20#19099276C2218yes—
21#19099268—24no—
22#19099268C2218yescomplemented
23C2×#14579160C2211yescharacteristic
24C2×#14579160C2211yescharacteristic
25C2×#14579151—21no—
26C2×#14579149—21no—
27C2×#14579147—21no—
28C2×#14579141C2211yescharacteristic
29C2×#14579140—21no—
30C2×#14579140C2211yescharacteristic
31C2×#14579139—21no—
32C2×#14579136C2211yescharacteristic
33C2×#14579135C2211yescharacteristic
34C2×#14579134—21no—
35C2×#14579126C2211yescharacteristic
36C2×#14579123C2211yescharacteristic
37C2×C4×C22⋊D79—21no—
38C2×C4×C22⋊D79C2211yescharacteristic
39C2×#14579119C2211yescharacteristic
40C2×#14579118—21no—
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098967C2218yescomplemented
43#19098907C2218yescomplemented
44#19098904C2218yescomplemented
45#19098878C2218yescomplemented
46#19098876C2218yescomplemented
47#19098857C2218yescomplemented
48#19098852C2218yescomplemented
49#19098810C2218yescomplemented
50#19098809C2218yescomplemented
51#19098650C2218yescomplemented
52#19098639C2218yescomplemented
53#19098602C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×Dic79⋊C8C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579081C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71C22×C4⋊C4×C79C2211yescharacteristic
72#428×C79C2218yescomplemented
73C2×#107×C79C2211yescharacteristic
74C2×#107×C79C2211yescharacteristic
75C2×#106×C79C2211yescharacteristic
76C2×#106×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×Dic158C2311yescharacteristic
80C22×D316—21no—
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C22×C22⋊D79D411yescharacteristic
84C22×C4×D79—21no—
85C22×C4×D79—21no—
86C22×C4×D79C2311yescharacteristic
87C2×#11929613—24no—
88C2×#11929613C2314yes—
89C2×#11929607—24no—
90C2×#11929607C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93#14579160—22no—
94#14579160—22no—
95#14579160C2314yes—
96#14579160C2314yes—
97#14579151—28no—
98#14579149—28no—
99#14579147—28no—
100#14579141—22no—
101#14579141C2314yes—
102#14579140—22no—
103#14579140—28no—
104#14579140C2314yes—
105#14579139—28no—
106#14579136—22no—
107#14579136C2314yes—
108#14579135—22no—
109#14579135C2314yes—
110#14579134—28no—
111#14579126—22no—
112#14579126C2314yes—
113#14579123—22no—
114#14579123C2314yes—
115C4×C22⋊D79—28no—
116C4×C22⋊D79D414yes—
117C4×C22⋊D79C2314yes—
118#14579119—22no—
119#14579119C2314yes—
120#14579118—28no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4D411yescharacteristic
130C4⋊C4×D79—22no—
131C4⋊C4×D79C2314yes—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79D411yescharacteristic
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79C2311yescharacteristic
143#14579095C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579094C2314yes—
147#14579092C2314yes—
148Dic79⋊C8C2314yes—
149#14579086C2314yes—
150#14579084C2314yes—
151#14579084C2314yes—
152#14579083C2314yes—
153#14579081C2314yes—
154#14579081C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157C8×Dic79C2314yes—
158C23×C4×C79—21no—
159C23×C4×C79C2311yescharacteristic
160C2×M16×C79—24no—
161C2×M16×C79C2314yes—
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164#117×C79—22no—
165#117×C79C2314yes—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2314yes—
173C2×C22⋊C4×C79—21no—
174C2×C42×C79—21no—
175#107×C79C2314yes—
176#107×C79C2314yes—
177#106×C79C2314yes—
178#106×C79C2314yes—
179C23×D79—21no—
180C23×D79C2×D411yescharacteristic
181C2×Dic158—24no—
182C2×Dic158—24no—
183C2×Dic158—21no—
184C2×Dic158—22no—
185C2×Dic158—22no—
186C2×Dic158—82no—
187C2×Dic158—82no—
188C2×Dic158C2412yes—
189C2×D316—24no—
190C2×D316—21no—
191C2×D316—22no—
192C2×D316—22no—
193C2×D316—82no—
194C2×D316C2412yes—
195C2×C22⋊D79—24no—
196C2×C22⋊D79—24no—
197C2×C22⋊D79—82no—
198C2×C22⋊D79C2×D414yes—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—24no—
206C2×C4×D79—24no—
207C2×C4×D79—22no—
208C2×C4×D79—22no—
209C2×C4×D79—44no—
210C2×C4×D79—82no—
211C2×C4×D79C2×D412yes—
212C2×C4×D79C2412yes—
213#11929613—28no—
214#11929607—28no—
215C2×C79⋊C8—22no—
216C2×C79⋊C8—22no—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C4⋊Dic79—24no—
220C4⋊Dic79—21no—
221C4⋊Dic79—21no—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4—24no—
229Dic79⋊C4C2×D414yes—
230C22⋊Dic79—24no—
231C22⋊Dic79C2×D414yes—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4C2×D414yes—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C4×Dic79C2×D412yes—
241C4×Dic79C2412yes—
242C24×C79C2×D411yescharacteristic
243C22×C4×C79—22no—
244C22×C4×C79—22no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—24no—
250C22×C4×C79—82no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D412yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2411yescharacteristic
255M16×C79—28no—
256C2×C8×C79—22no—
257C2×C8×C79#4114yes—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79C2412yes—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C22⋊C4×C79—24no—
270C42×C79—24no—
271C23×C79—22no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79C22×D412yes—
275C23×C79C22×D411yescharacteristic
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—42no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79C22×D412yes—
284C2×C4×C79—22no—
285C2×C4×C79—24no—
286C2×C4×C79—22no—
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—42no—
295C2×C4×C79—42no—
296C2×C4×C79—84no—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D411yescharacteristic
299C2×C4×C79C2×#4112yes—
300C2×C4×C792−1+412yes—
301C2×C4×C79C2511yescharacteristic
302C22⋊D79—28no—
303C22⋊D79—84no—
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—
316D316—22no—
317D316—22no—
318D316—42no—
319D316—84no—
320C4×D79—24no—
321C4×D79—22no—
322C4×D79—22no—
323C4×D79—48no—
324C4×D79—84no—
325Dic158—22no—
326Dic158—22no—
327Dic158—42no—
328Dic158—84no—
329Dic158—84no—
330C8×C79—22no—
331C8×C79C2×#4114yes—
332C79⋊C8—22no—
333C79⋊C8—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—44no—
338C22×C79#54712yes—
339C22×C79C2×#13712yes—
340C22×C79#57612yes—
341C22×C79C23×D411yescharacteristic
342C2×D79—22no—
343C2×D79—22no—
344C2×D79—22no—
345C2×D79—44no—
346C2×D79—42no—
347C2×D79—42no—
348C2×D79—42no—
349C2×D79—84no—
350C4×C79—22no—
351C4×C79—42no—
352C4×C79—42no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79#54712yes—
356C4×C79C22×#4111yescharacteristic
357C4×C79C2×2−1+411yescharacteristic
358Dic79—22no—
359Dic79—22no—
360Dic79—42no—
361Dic79—42no—
362Dic79—42no—
363Dic79C2×#13714yes—
364C2×#3357—791nomaximal, Sylow
365C2×C79—42no—
366C2×C79#335714yescomplemented
367C2×C79C2×#54711yescharacteristic
368C2×C79C22×#13711yescharacteristic
369C2×C79C2×#57611yescharacteristic
370D79—42no—
371D79—82no—
372C2×#555—791no—
373C2×#554—791no—
374#3357—7916no—
375C2×#500—791no—
376C2×#485—791no—
377C2×#485—791no—
378C2×#480—791no—
379C2×#480—791no—
380C2×#477—791no—
381C2×#476—791no—
382C2×#468—791no—
383C2×#468—791no—
384C2×C4×SD16—791no—
385C2×#436—791no—
386C2×#428—791no—
387C2×#428D7911yescharacteristic, complemented
388C79C2×#335711yescharacteristic, complemented, Sylow
389C22×SD16—791no—
390C22×M16—791no—
391C22×M16C2×D7911yescharacteristic
392#555—798no—
393#555—1584no—
394#554—798no—
395#554—1584no—
396C2×C4⋊Q8—791no—
397C2×C4⋊Q8—791no—
398C2×#125—1581no—
399C2×#124—1581no—
400C2×#124—1581no—
401C2×C22⋊Q8—791no—
402C2×C22⋊Q8—791no—
403C2×C22⋊Q8—1581no—
404C2×C22⋊Q8—1581no—
405C2×#121—791no—
406C2×#121—791no—
407C2×#121—1581no—
408C2×C4×Q8—791no—
409C2×C4×D4—791no—
410C2×C4×D4—791no—
411C2×C4×D4—1581no—
412C2×#117—791no—
413C2×#117—1581no—
414C2×#117C2×D7911yescharacteristic
415C22×C4⋊C4—791no—
416C22×C4⋊C4C2×D7911yescharacteristic
417#500—798no—
418#485—798no—
419#485—798no—
420#480—798no—
421#480—798no—
422#477—798no—
423#476—798no—
424#468—798no—
425#468—798no—
426C4×SD16—798no—
427#436—798no—
428#428—798no—
429#428C2×D7918yescomplemented
430C2×#107—791no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107C2×D7911yescharacteristic
435C2×#107C2×D7911yescharacteristic
436C2×#106—791no—
437C2×#106C2×D7911yescharacteristic
438C2×#106C2×D7911yescharacteristic
439C2×C4⋊C8—791no—
440C2×#103—791no—
441C2×#103—791no—
442C2×#103—791no—
443C2×#102—791no—
444C2×#102—791no—
445C2×#102—791no—
446C2×C22⋊C8—791no—
447C2×C22⋊C8—791no—
448C2×C4×C8—791no—
449C22×Q8—791no—
450C22×Q8—1581no—
451C22×Q8—1581no—
452C22×D4—791no—
453C22×D4—791no—
454C22×D4—1581no—
455C22×D4—1581no—
456C23×C4—21no—
457C23×C4—791no—
458C23×C4—1581no—
459C23×C4—1581no—
460C23×C4C22×D7911yescharacteristic
461C2×SD16—794no—
462C2×SD16—1584no—
463C2×M16—24no—
464C2×M16—794no—
465C2×M16—1584no—
466C2×M16C22×D7914yes—
467C22×C8—791no—
468C22×C8—791no—
469C22×C8C22×D7911yescharacteristic
470C22×C8C22×D7911yescharacteristic
471C4⋊Q8—794no—
472C4⋊Q8—794no—
473C4⋊Q8—1582no—
474C4⋊Q8—1582no—
475#125—1588no—
476#124—1588no—
477#124—1588no—
478C22⋊Q8—794no—
479C22⋊Q8—794no—
480C22⋊Q8—1588no—
481C22⋊Q8—1588no—
482C22⋊Q8—1582no—
483C22⋊Q8—1582no—
484#121—794no—
485#121—794no—
486#121—1588no—
487#121—1582no—
488#121—1582no—
489C4×Q8—794no—
490C4×Q8—1582no—
491C4×D4—794no—
492C4×D4—794no—
493C4×D4—794no—
494C4×D4—1582no—
495C4×D4—1588no—
496#117—22no—
497#117—794no—
498#117—1588no—
499#117—1582no—
500#117C22×D7914yes—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—791no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—794no—
507C2×C4⋊C4—1582no—
508C2×C4⋊C4—1581no—
509C2×C4⋊C4—1581no—
510C2×C4⋊C4—1581no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1581no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4C22×D7911yescharacteristic
515C2×C4⋊C4C22×D7911yescharacteristic
516C2×C4⋊C4C22×D7914yes—
517C2×C4⋊C4C22×D7911yescharacteristic
518C2×C4⋊C4C22×D7911yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—791no—
521C2×C22⋊C4—791no—
522C2×C22⋊C4—1581no—
523C2×C22⋊C4—1581no—
524C2×C22⋊C4—1581no—
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C42—21no—
529C2×C42—791no—
530C2×C42—1581no—
531C2×C42—1581no—
532#107—794no—
533#107—794no—
534#107—794no—
535#107—794no—
536#107C22×D7914yes—
537#107C22×D7914yes—
538#106—794no—
539#106C22×D7914yes—
540#106C22×D7914yes—
541C4⋊C8—794no—
542#103—794no—
543#103—794no—
544#103—794no—
545#102—794no—
546#102—794no—
547#102—794no—
548C22⋊C8—794no—
549C22⋊C8—794no—
550C4×C8—794no—
551C24—791no—
552C24—1581no—
553C24D4×D7911yescharacteristic
554C2×Q8—792no—
555C2×Q8—6322no—
556C2×Q8—6322no—
557C2×Q8—1584no—
558C2×Q8—1584no—
559C2×Q8—1582no—
560C2×Q8—1582no—
561C2×Q8—1581no—
562C2×D4—794no—
563C2×D4—792no—
564C2×D4—6322no—
565C2×D4—6322no—
566C2×D4—1584no—
567C2×D4—1584no—
568C2×D4—1584no—
569C2×D4—1582no—
570C2×D4—1582no—
571C2×D4—1581no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—3164no—
581C22×C4—791no—
582C22×C4—791no—
583C22×C4—791no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—6322no—
587C22×C4—1584no—
588C22×C4—1584no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4D4×D7912yes—
595C22×C4D4×D7911yescharacteristic
596C22×C4C23×D7912yes—
597C22×C4C23×D7911yescharacteristic
598SD16—1588no—
599M16—28no—
600M16—1588no—
601C2×C8—22no—
602C2×C8—792no—
603C2×C8—792no—
604C2×C8—1582no—
605C2×C8—1582no—
606C2×C8#1192962414yes—
607C2×C8C23×D7912yes—
608C2×C8C23×D7912yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—794no—
615C4⋊C4—792no—
616C4⋊C4—792no—
617C4⋊C4—1584no—
618C4⋊C4—1584no—
619C4⋊C4—1584no—
620C4⋊C4—1584no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1581no—
624C4⋊C4—1581no—
625C4⋊C4C23×D7912yes—
626C4⋊C4C23×D7912yes—
627C4⋊C4C23×D7912yes—
628C4⋊C4C23×D7912yes—
629C22⋊C4—24no—
630C22⋊C4—794no—
631C22⋊C4—794no—
632C22⋊C4—1584no—
633C22⋊C4—1584no—
634C22⋊C4—1584no—
635C22⋊C4—1584no—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C42—24no—
639C42—792no—
640C42—792no—
641C42—1584no—
642C42—1584no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—3162no—
647C23—3162no—
648C23—3162no—
649C23—792no—
650C23—1582no—
651C23—1582no—
652C23—1582no—
653C23—1582no—
654C23C2×D4×D7912yes—
655C23C2×D4×D7911yescharacteristic
656Q8—3162no—
657Q8—6324no—
658Q8—6324no—
659Q8—1582no—
660Q8—1582no—
661D4—3162no—
662D4—6324no—
663D4—6324no—
664D4—1588no—
665D4—1582no—
666D4—1582no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—3168no—
681C2×C4—3162no—
682C2×C4—3162no—
683C2×C4—3162no—
684C2×C4—794no—
685C2×C4—792no—
686C2×C4—792no—
687C2×C4—792no—
688C2×C4—6324no—
689C2×C4—1582no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1584no—
696C2×C4—1582no—
697C2×C4C2×D4×D7912yes—
698C2×C4C2×D4×D7911yescharacteristic
699C2×C4C2×#1192962412yes—
700C2×C4#1457920912yes—
701C2×C4C24×D7911yescharacteristic
702C8—22no—
703C8—1582no—
704C8—1582no—
705C8C2×#1192962414yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—3164no—
711C22—3162no—
712C22—3162no—
713C22—3162no—
714C22—6324no—
715C22—1582no—
716C22—1582no—
717C22—1582no—
718C22#1909921412yes—
719C22#137×D7912yes—
720C22#1909936712yes—
721C22C22×D4×D7911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—3162no—
728C4—3162no—
729C4—3162no—
730C4—794no—
731C4—1582no—
732C4—1582no—
733C4#1909921412yes—
734C4C22×#1192962411yescharacteristic
735C4C2×#1457920911yescharacteristic
736C2—42no—
737C2—3162no—
738C2—6322no—
739C2#2377602214yesdirect product factor
740C2C2×#1909921411yescharacteristic
741C2C2×#137×D7911yescharacteristic
742C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#428×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099276C2
hypercenterC2×#428D79
hypocenterC79C2×#3357
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#19099268C2semidirect
3. #23776022C2direct (N × H)
4. C2×#19098967C2semidirect
5. C2×#19098907C2semidirect
6. C2×#19098904C2semidirect
7. C2×#19098878C2semidirect
8. C2×#19098876C2semidirect
9. C2×#19098857C2semidirect
10. C2×#19098852C2semidirect
11. C2×#19098810C2semidirect
12. C2×#19098809C2semidirect
13. C2×#19098650C2semidirect
14. C2×#19098639C2semidirect
15. C2×#19098602C2semidirect
16. C2×#428×C79C2semidirect
22. #19099268C22semidirect
42. #19098967C22semidirect
43. #19098907C22semidirect
44. #19098904C22semidirect
45. #19098878C22semidirect
46. #19098876C22semidirect
47. #19098857C22semidirect
48. #19098852C22semidirect
49. #19098810C22semidirect
50. #19098809C22semidirect
51. #19098650C22semidirect
52. #19098639C22semidirect
53. #19098602C22semidirect
72. #428×C79C22semidirect
366. C2×C79#3357semidirect
387. C2×#428D79semidirect
388. C79C2×#3357semidirect
429. #428C2×D79semidirect
739. C2#23776022direct (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×#190992682
#237760222
C2×#190989672
C2×#190989072
C2×#190989042
C2×#190988782
C2×#190988762
C2×#190988572
C2×#190988522
C2×#190988102
C2×#190988092
C2×#190986502
C2×#190986392
C2×#190986022
C2×#428×C792
C2×#335779