Finite Group Databasebeta

← C2×#22622521 #33964695

Subgroups — C2×#22622521 #33964695

Order 18688.

2146 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989301C211yesmaximal, characteristic, complemented
2C2×#17989237C211yesmaximal, characteristic, complemented
3#22622521C2116yesmaximal, direct product factor
4C2×#17988984C211yesmaximal, characteristic, complemented
5C2×#17988904C211yesmaximal, characteristic, complemented
6C2×#17988903C211yesmaximal, characteristic, complemented
7C2×#17988909C211yesmaximal, characteristic, complemented
8C2×#17988908C211yesmaximal, characteristic, complemented
9C2×#17988875C211yesmaximal, characteristic, complemented
10C2×#17988865C211yesmaximal, characteristic, complemented
11C2×#17988837C211yesmaximal, characteristic, complemented
12C2×D8×Dic73C211yesmaximal, characteristic, complemented
13C2×#17988663C211yesmaximal, characteristic, complemented
14C2×#17988629C211yesmaximal, characteristic, complemented
15C2×#17988626C211yesmaximal, characteristic, complemented
16C2×#469×C73C211yesmaximal, characteristic, complemented
17C22×#11924027—21no—
18C22×#11924011C2211yescharacteristic
19#17989301—24no—
20#17989301C2218yescomplemented
21#17989237—24no—
22#17989237C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556590C2211yescharacteristic
25C2×#14556578—21no—
26C2×#14556577—21no—
27C2×#14556573—21no—
28C2×#14556572—21no—
29C2×#14556568—21no—
30C2×#14556563—21no—
31C2×#14556562C2211yescharacteristic
32C2×#14556562C2211yescharacteristic
33C2×D4×Dic73C2211yescharacteristic
34C2×D4×Dic73C2211yescharacteristic
35C2×C4×C22⋊D73C2211yescharacteristic
36C2×#14556550C2211yescharacteristic
37C2×#14556549C2211yescharacteristic
38C2×#14556547—21no—
39C22×C4⋊Dic73C2211yescharacteristic
40C2×C4⋊C4×D73C2211yescharacteristic
41#17988984C2218yescomplemented
42#17988909C2218yescomplemented
43#17988908C2218yescomplemented
44#17988904C2218yescomplemented
45#17988903C2218yescomplemented
46#17988875C2218yescomplemented
47#17988865C2218yescomplemented
48#17988837C2218yescomplemented
49D8×Dic73C2218yescomplemented
50#17988663C2218yescomplemented
51#17988629C2218yescomplemented
52#17988626C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556525C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556522C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×D8×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×#121×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#469×C73C2218yescomplemented
74C2×#106×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C2×#11924027—28no—
78C2×#11924027—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×C22⋊D73—21no—
82C22×C22⋊D73—21no—
83C22×C22⋊D73D411yescharacteristic
84C23×Dic73—21no—
85C23×Dic73—21no—
86C23×Dic73—21no—
87C22×C4×D73—21no—
88C22×C4×D73C2311yescharacteristic
89C2×#11924011—24no—
90C2×#11924011C2314yes—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93#14556590—22no—
94#14556590—22no—
95#14556590C2314yes—
96#14556590C2314yes—
97#14556578—28no—
98#14556577—28no—
99#14556573—28no—
100#14556572—28no—
101#14556568—28no—
102#14556563—28no—
103#14556562—22no—
104#14556562—22no—
105#14556562C2314yes—
106#14556562C2314yes—
107D4×Dic73—22no—
108D4×Dic73—22no—
109D4×Dic73C2314yes—
110D4×Dic73C2314yes—
111C4×C22⋊D73D414yes—
112C4×C22⋊D73C2314yes—
113#14556550—22no—
114#14556550C2314yes—
115#14556549—22no—
116#14556549C2314yes—
117#14556547—28no—
118C2×C4⋊Dic73—22no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×C4⋊Dic73C2311yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2314yes—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007D411yescharacteristic
129C4⋊C4×D73—22no—
130C4⋊C4×D73C2314yes—
131C2×C22⋊Dic73—21no—
132C2×C22⋊Dic73—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73D411yescharacteristic
137C2×#11924005—21no—
138C2×#11924005D411yescharacteristic
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73C2311yescharacteristic
142#14556525C2314yes—
143#14556525C2314yes—
144#14556524C2314yes—
145#14556523C2314yes—
146#14556523C2314yes—
147#14556522C2314yes—
148#14556522C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556512C2314yes—
152#14556512C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155C22⋊#10596831C2314yes—
156#14556503C2314yes—
157C8×Dic73C2314yes—
158C22×D4×C73—21no—
159C22×D4×C73—21no—
160C22×D4×C73C2311yescharacteristic
161C22×D4×C73C2311yescharacteristic
162C23×C4×C73C2311yescharacteristic
163C2×D8×C73—24no—
164C2×D8×C73C2314yes—
165C2×M16×C73—24no—
166C2×M16×C73C2314yes—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169#121×C73—22no—
170#121×C73—22no—
171#121×C73C2314yes—
172#121×C73C2314yes—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177#106×C73C2314yes—
178#102×C73C2314yes—
179#102×C73C2314yes—
180C23×D73C2×D411yescharacteristic
181#11924027—432no—
182C2×Dic146—24no—
183C2×Dic146—24no—
184C2×Dic146—44no—
185C2×Dic146—82no—
186C2×C22⋊D73—24no—
187C2×C22⋊D73—24no—
188C2×C22⋊D73—24no—
189C2×C22⋊D73—44no—
190C2×C22⋊D73—82no—
191C2×C22⋊D73C2×D414yes—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—24no—
197C22×Dic73—24no—
198C22×Dic73—24no—
199C22×Dic73—44no—
200C22×Dic73—44no—
201C22×Dic73—44no—
202C22×Dic73C2×D411yescharacteristic
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C2×C4×D73—22no—
206C2×C4×D73—22no—
207C2×C4×D73—24no—
208C2×C4×D73—44no—
209C2×C4×D73C2×D412yes—
210C2×C4×D73C2412yes—
211#11924011—28no—
212C2×#10596831—22no—
213C2×#10596831—22no—
214C2×#10596831C2412yes—
215C2×#10596831C2412yes—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—24no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223C4⋊Dic73C2412yes—
224C4⋊Dic73C2412yes—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007C2×D414yes—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73—24no—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234C22⋊Dic73C2×D414yes—
235#11924005—24no—
236#11924005C2×D414yes—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2412yes—
241C24×C73—21no—
242C24×C73—21no—
243C24×C73C2×D411yescharacteristic
244C2×D4×C73—24no—
245C2×D4×C73—24no—
246C2×D4×C73—21no—
247C2×D4×C73—21no—
248C2×D4×C73—22no—
249C2×D4×C73—22no—
250C2×D4×C73—22no—
251C2×D4×C73—22no—
252C2×D4×C73—44no—
253C2×D4×C73—82no—
254C2×D4×C73C2412yes—
255C2×D4×C73C2412yes—
256C22×C4×C73—22no—
257C22×C4×C73—22no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D412yes—
262C22×C4×C73C2412yes—
263C22×C4×C73C2411yescharacteristic
264D8×C73—28no—
265M16×C73—28no—
266C2×C8×C73—22no—
267C2×C8×C73#4114yescomplemented
268C2×C8×C73C2412yes—
269C2×C8×C73C2412yes—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73C2412yes—
273C4⋊C4×C73C2412yes—
274C22⋊C4×C73—24no—
275C22⋊C4×C73—24no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—42no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73—42no—
287C23×C73C22×D412yes—
288C23×C73C22×D411yescharacteristic
289C22×D73—22no—
290C22×D73—22no—
291C22×D73—22no—
292C22×D73C22×D412yes—
293D4×C73—22no—
294D4×C73—22no—
295D4×C73—22no—
296D4×C73—22no—
297D4×C73—48no—
298D4×C73—42no—
299D4×C73—42no—
300D4×C73—84no—
301C2×C4×C73—22no—
302C2×C4×C73—24no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—42no—
308C2×C4×C73—42no—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D411yescharacteristic
311C2×C4×C73C2×#4112yes—
312C2×C4×C732−1+412yes—
313C2×C4×C73C2511yescharacteristic
314C22⋊D73—28no—
315C22⋊D73—48no—
316C22⋊D73—84no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—48no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—48no—
329C2×Dic73—48no—
330C2×Dic73AGL(1,ℤ/8)14yes—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333C2×Dic73C22×D412yes—
334C4×D73—24no—
335C4×D73—22no—
336C4×D73—22no—
337C4×D73—48no—
338Dic146—48no—
339Dic146—84no—
340C8×C73—22no—
341C8×C73C2×#4114yescomplemented
342#10596831—22no—
343#10596831—22no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—22no—
347C22×C73—44no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—42no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—84no—
355C22×C73—84no—
356C22×C73#54712yes—
357C22×C73C2×AGL(1,ℤ/8)12yes—
358C22×C73#57712yes—
359C22×C73C23×D411yescharacteristic
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—44no—
364C4×C73—22no—
365C4×C73—42no—
366C4×C73—42no—
367C4×C73#54712yes—
368C4×C73C22×#4111yescharacteristic
369C4×C73C2×2−1+411yescharacteristic
370Dic73—22no—
371Dic73—22no—
372Dic73—42no—
373Dic73—42no—
374Dic73—42no—
375Dic73—42no—
376Dic73C2×AGL(1,ℤ/8)14yes—
377C2×#3354—731nomaximal, Sylow
378C2×C73—42no—
379C2×C73—82no—
380C2×C73—82no—
381C2×C73#335414yescomplemented
382C2×C73C2×#54711yescharacteristic
383C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C73C2×#57711yescharacteristic
385D73—42no—
386C2×#555—731no—
387C2×#547—731no—
388#3354—7316no—
389C2×#498—731no—
390C2×#481—731no—
391C2×#481—731no—
392C2×#482—731no—
393C2×#482—731no—
394C2×#476—731no—
395C2×#474—731no—
396C2×#469—731no—
397C2×#469D7311yescharacteristic, complemented
398C2×C4×D8—731no—
399C2×#436—731no—
400C2×#428—731no—
401C2×#428—731no—
402C73C2×#335411yescharacteristic, complemented, Sylow
403C22×#41—1461no—
404C22×D8C2×D7311yescharacteristic
405C22×M16—731no—
406C22×M16C2×D7311yescharacteristic
407#555—738no—
408#555—1464no—
409#547—738no—
410#547—1464no—
411C2×C4⋊Q8—731no—
412C2×C4⋊Q8—731no—
413C2×#124—1461no—
414C2×#124—1461no—
415C2×#123—1461no—
416C2×#123—1461no—
417C2×C22⋊Q8—1461no—
418C2×#121—731no—
419C2×#121—731no—
420C2×#121—1461no—
421C2×#121C2×D7311yescharacteristic
422C2×#121C2×D7311yescharacteristic
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4—731no—
426C2×#117—731no—
427C2×#117—731no—
428C2×#117—1461no—
429C22×C4⋊C4—731no—
430C22×C4⋊C4—731no—
431#498—738no—
432#482—738no—
433#482—738no—
434#481—738no—
435#481—738no—
436#476—738no—
437#474—738no—
438#469—738no—
439#469C2×D7318yescomplemented
440C4×D8—738no—
441#436—738no—
442#428—738no—
443#428—738no—
444C2×#107—731no—
445C2×#107—731no—
446C2×#107—731no—
447C2×#106—731no—
448C2×#106—731no—
449C2×#106—731no—
450C2×#106—731no—
451C2×#106—731no—
452C2×#106C2×D7311yescharacteristic
453C2×C4⋊C8—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#102—731no—
457C2×#102—731no—
458C2×#102C2×D7311yescharacteristic
459C2×#102C2×D7311yescharacteristic
460C2×C22⋊C8—731no—
461C2×C22⋊C8—731no—
462C2×C4×C8—731no—
463C2×#41—2928no—
464C2×#41—1468no—
465C22×Q8—1461no—
466C22×Q8—1461no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—731no—
470C22×D4—1461no—
471C22×D4—1461no—
472C22×D4C22×D7311yescharacteristic
473C22×D4C22×D7311yescharacteristic
474C23×C4—731no—
475C23×C4—1461no—
476C23×C4—1461no—
477C23×C4—1461no—
478C23×C4—1461no—
479C23×C4C22×D7311yescharacteristic
480C2×D8—24no—
481C2×D8C22×D7314yes—
482C2×M16—24no—
483C2×M16—734no—
484C2×M16—1464no—
485C2×M16C22×D7314yes—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C4⋊Q8—734no—
491C4⋊Q8—734no—
492C4⋊Q8—1462no—
493C4⋊Q8—1462no—
494#124—1468no—
495#124—1468no—
496#123—1468no—
497#123—1468no—
498C22⋊Q8—1468no—
499#121—22no—
500#121—22no—
501#121—734no—
502#121—734no—
503#121—1462no—
504#121—1462no—
505#121—1468no—
506#121C22×D7314yes—
507#121C22×D7314yes—
508C4×D4—734no—
509C4×D4—734no—
510C4×D4—734no—
511C4×D4—734no—
512C4×D4—1462no—
513C4×D4—1462no—
514#117—734no—
515#117—734no—
516#117—1468no—
517#117—1462no—
518#117—1462no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—734no—
523C2×C4⋊C4—731no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—734no—
526C2×C4⋊C4—1462no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4—1461no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1462no—
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—731no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C22⋊C4—1461no—
542C2×C22⋊C4—1461no—
543C2×C22⋊C4—1461no—
544C2×C42—731no—
545C2×C42—1461no—
546C2×C42—1461no—
547#107—734no—
548#107—734no—
549#107—734no—
550#106—734no—
551#106—734no—
552#106—734no—
553#106—734no—
554#106—734no—
555#106C22×D7314yes—
556C4⋊C8—734no—
557#102—734no—
558#102—734no—
559#102—734no—
560#102—734no—
561#102C22×D7314yes—
562#102C22×D7314yes—
563C22⋊C8—734no—
564C22⋊C8—734no—
565C4×C8—734no—
566C24—21no—
567C24—21no—
568C24—731no—
569C24D4×D7311yescharacteristic
570#41—29232no—
571C2×Q8—2924no—
572C2×Q8—5842no—
573C2×Q8—1464no—
574C2×Q8—1464no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—44no—
584C2×D4—82no—
585C2×D4—2924no—
586C2×D4—5842no—
587C2×D4—734no—
588C2×D4—1464no—
589C2×D4—1464no—
590C2×D4—1464no—
591C2×D4C23×D7312yes—
592C2×D4C23×D7312yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—2924no—
598C22×C4—2924no—
599C22×C4—2924no—
600C22×C4—2924no—
601C22×C4—731no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—732no—
605C22×C4—732no—
606C22×C4—1464no—
607C22×C4—1464no—
608C22×C4—1464no—
609C22×C4—1464no—
610C22×C4—1461no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4D4×D7312yes—
617C22×C4D4×D7311yescharacteristic
618C22×C4C23×D7312yes—
619C22×C4C23×D7311yescharacteristic
620D8—28no—
621M16—28no—
622M16—1468no—
623C2×C8—22no—
624C2×C8—732no—
625C2×C8—732no—
626C2×C8—1462no—
627C2×C8—1462no—
628C2×C8#1192402714yescomplemented
629C2×C8C23×D7312yes—
630C2×C8C23×D7312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—734no—
634C4⋊C4—732no—
635C4⋊C4—732no—
636C4⋊C4—732no—
637C4⋊C4—732no—
638C4⋊C4—1464no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1461no—
642C4⋊C4—1461no—
643C4⋊C4—1464no—
644C4⋊C4—1461no—
645C4⋊C4—1461no—
646C4⋊C4C23×D7312yes—
647C4⋊C4C23×D7312yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—734no—
651C22⋊C4—734no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4—1464no—
656C22⋊C4—1464no—
657C22⋊C4—1464no—
658C42—732no—
659C42—732no—
660C42—1464no—
661C42—1464no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—732no—
674C23—1462no—
675C23—1462no—
676C23—1462no—
677C23C2×D4×D7312yes—
678C23C2×D4×D7311yescharacteristic
679Q8—2928no—
680Q8—5844no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—42no—
688D4—84no—
689D4—2928no—
690D4—5844no—
691D4—1468no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—2928no—
701C2×C4—2928no—
702C2×C4—2922no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—2922no—
706C2×C4—2928no—
707C2×C4—2928no—
708C2×C4—732no—
709C2×C4—734no—
710C2×C4—732no—
711C2×C4—732no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1464no—
721C2×C4C2×D4×D7312yes—
722C2×C4C2×D4×D7311yescharacteristic
723C2×C4C2×#1192402712yes—
724C2×C4#1455663812yes—
725C2×C4C24×D7311yescharacteristic
726C8—22no—
727C8—1462no—
728C8—1462no—
729C8C2×#1192402714yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—84no—
742C22—2924no—
743C22—1462no—
744C22—1462no—
745C22—1462no—
746C22#1798923712yes—
747C22AGL(1,ℤ/8)×D7312yes—
748C22#1798939712yes—
749C22C22×D4×D7311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—2922no—
754C4—2922no—
755C4—2922no—
756C4—2922no—
757C4—734no—
758C4—1462no—
759C4—1462no—
760C4#1798923712yes—
761C4C22×#1192402711yescharacteristic
762C4C2×#1455663811yescharacteristic
763C2—42no—
764C2—82no—
765C2—82no—
766C2—2922no—
767C2#2262252114yesdirect product factor
768C2C2×#1798923711yescharacteristic
769C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
770C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#469×C73C2
socleC23×C73C22×D4
hypercenterC2×#469D73
hypocenterC73C2×#3354
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#17989301C2semidirect
2. C2×#17989237C2semidirect
3. #22622521C2direct (N × H)
4. C2×#17988984C2semidirect
5. C2×#17988904C2semidirect
6. C2×#17988903C2semidirect
7. C2×#17988909C2semidirect
8. C2×#17988908C2semidirect
9. C2×#17988875C2semidirect
10. C2×#17988865C2semidirect
11. C2×#17988837C2semidirect
12. C2×D8×Dic73C2semidirect
13. C2×#17988663C2semidirect
14. C2×#17988629C2semidirect
15. C2×#17988626C2semidirect
16. C2×#469×C73C2semidirect
20. #17989301C22semidirect
22. #17989237C22semidirect
41. #17988984C22semidirect
42. #17988909C22semidirect
43. #17988908C22semidirect
44. #17988904C22semidirect
45. #17988903C22semidirect
46. #17988875C22semidirect
47. #17988865C22semidirect
48. #17988837C22semidirect
49. D8×Dic73C22semidirect
50. #17988663C22semidirect
51. #17988629C22semidirect
52. #17988626C22semidirect
73. #469×C73C22semidirect
267. C2×C8×C73#41semidirect
341. C8×C73C2×#41semidirect
381. C2×C73#3354semidirect
397. C2×#469D73semidirect
402. C73C2×#3354semidirect
439. #469C2×D73semidirect
628. C2×C8#11924027semidirect
729. C8C2×#11924027semidirect
767. C2#22622521direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893012
C2×#179892372
#226225212
C2×#179889842
C2×#179889042
C2×#179889032
C2×#179889092
C2×#179889082
C2×#179888752
C2×#179888652
C2×#179888372
C2×D8×Dic732
C2×#179886632
C2×#179886292
C2×#179886262
C2×#469×C732
C2×#335473