Finite Group Databasebeta

← C2×#22622537 #33964712

Subgroups — C2×#22622537 #33964712

Order 18688.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989285C211yesmaximal, characteristic, complemented
2C2×#17989284C211yesmaximal, characteristic, complemented
3#22622537C2116yesmaximal, direct product factor
4C2×#17988988C211yesmaximal, characteristic, complemented
5C2×#17988912C211yesmaximal, characteristic, complemented
6C2×#17988909C211yesmaximal, characteristic, complemented
7C2×#17988902C211yesmaximal, characteristic, complemented
8C2×#17988890C211yesmaximal, characteristic, complemented
9C2×#17988889C211yesmaximal, characteristic, complemented
10C2×#17988839C211yesmaximal, characteristic, complemented
11C2×#17988838C211yesmaximal, characteristic, complemented
12C2×#17988667C211yesmaximal, characteristic, complemented
13C2×#17988662C211yesmaximal, characteristic, complemented
14C2×#17988628C211yesmaximal, characteristic, complemented
15C2×#17988627C211yesmaximal, characteristic, complemented
16C2×#480×C73C211yesmaximal, characteristic, complemented
17C22×#11924013C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20#17989285—24no—
21#17989285C2218yescomplemented
22#17989284—24no—
23#17989284C2218yescomplemented
24C2×#14556586—21no—
25C2×#14556584—21no—
26C2×#14556582C2211yescharacteristic
27C2×#14556582C2211yescharacteristic
28C2×#14556576—21no—
29C2×#14556572—21no—
30C2×#14556566C2211yescharacteristic
31C2×#14556565—21no—
32C2×#14556565C2211yescharacteristic
33C2×#14556562—21no—
34C2×#14556562C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×C4×C22⋊D73—21no—
38C2×C4×C22⋊D73C2211yescharacteristic
39C2×#14556551—21no—
40C2×#14556550C2211yescharacteristic
41C2×#14556549C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988988C2218yescomplemented
44#17988912C2218yescomplemented
45#17988909C2218yescomplemented
46#17988902C2218yescomplemented
47#17988890C2218yescomplemented
48#17988889C2218yescomplemented
49#17988839C2218yescomplemented
50#17988838C2218yescomplemented
51#17988667C2218yescomplemented
52#17988662C2218yescomplemented
53#17988628C2218yescomplemented
54#17988627C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556522C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556522C2211yescharacteristic
62C2×#14556520C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556513C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×#121×C73C2211yescharacteristic
70C22×C4⋊C4×C73C2211yescharacteristic
71#480×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#107×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×D292—21no—
78C22×D292C2311yescharacteristic
79C22×C22⋊D73—21no—
80C22×C22⋊D73—21no—
81C22×C22⋊D73D411yescharacteristic
82C23×Dic73—21no—
83C22×C4×D73—21no—
84C22×C4×D73—21no—
85C22×C4×D73C2311yescharacteristic
86C2×#11924013—24no—
87C2×#11924013C2314yes—
88C2×#11924012—24no—
89C2×#11924012C2314yes—
90C2×#11924011—24no—
91C2×#11924011C2314yes—
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94#14556586—28no—
95#14556584—28no—
96#14556582—22no—
97#14556582—22no—
98#14556582C2314yes—
99#14556582C2314yes—
100#14556576—28no—
101#14556572—28no—
102#14556566—22no—
103#14556566C2314yes—
104#14556565—28no—
105#14556565—22no—
106#14556565C2314yes—
107#14556562—28no—
108#14556562—22no—
109#14556562C2314yes—
110D4×Dic73—22no—
111D4×Dic73C2314yes—
112#14556553—22no—
113#14556553C2314yes—
114C4×C22⋊D73—28no—
115C4×C22⋊D73D414yes—
116C4×C22⋊D73C2314yes—
117#14556551—28no—
118#14556550—22no—
119#14556550C2314yes—
120#14556549—22no—
121#14556549C2314yes—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007D411yescharacteristic
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73D411yescharacteristic
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73C2311yescharacteristic
145#14556525C2314yes—
146#14556524C2314yes—
147#14556524C2314yes—
148#14556523C2314yes—
149#14556522C2314yes—
150#14556522C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556513C2314yes—
154#14556513C2314yes—
155#14556512C2314yes—
156#14556511C2314yes—
157#14556503C2314yes—
158C8×Dic73C2314yes—
159C22×D4×C73—21no—
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C23×C4×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165#121×C73—22no—
166#121×C73C2314yes—
167C2×C4⋊C4×C73—22no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2314yes—
173C2×C22⋊C4×C73—21no—
174#107×C73C2314yes—
175#107×C73C2314yes—
176#102×C73C2314yes—
177#102×C73C2314yes—
178C22⋊C8×C73C2314yes—
179C23×D73—21no—
180C23×D73C2×D411yescharacteristic
181C2×D292—22no—
182C2×D292—22no—
183C2×D292—21no—
184C2×D292—24no—
185C2×D292—82no—
186C2×D292C2412yes—
187C2×C22⋊D73—24no—
188C2×C22⋊D73—24no—
189C2×C22⋊D73—42no—
190C2×C22⋊D73—44no—
191C2×C22⋊D73—44no—
192C2×C22⋊D73C2×D414yes—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—24no—
197C22×Dic73—82no—
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—24no—
204C2×C4×D73—24no—
205C2×C4×D73—82no—
206C2×C4×D73—82no—
207C2×C4×D73C2×D412yes—
208C2×C4×D73C2412yes—
209#11924013—28no—
210#11924012—28no—
211#11924011—28no—
212C2×#10596831—22no—
213C2×#10596831#4114yes—
214C2×#10596831C2412yes—
215C2×#10596831C2412yes—
216C4⋊Dic73—21no—
217C4⋊Dic73—21no—
218C4⋊Dic73—21no—
219C4⋊Dic73—24no—
220C4⋊Dic73—24no—
221C4⋊Dic73C2412yes—
222C4⋊Dic73C2412yes—
223C4⋊Dic73C2412yes—
224#11924007—24no—
225#11924007—24no—
226#11924007—24no—
227#11924007C2×D414yes—
228C22⋊Dic73—24no—
229C22⋊Dic73—24no—
230C22⋊Dic73—24no—
231C22⋊Dic73C2×D414yes—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005C2×D414yes—
237C4×Dic73—24no—
238C4×Dic73—24no—
239C4×Dic73C2×D412yes—
240C4×Dic73C2412yes—
241C24×C73—21no—
242C24×C73C2×D411yescharacteristic
243C2×D4×C73—24no—
244C2×D4×C73—21no—
245C2×D4×C73—22no—
246C2×D4×C73—22no—
247C2×D4×C73—82no—
248C2×D4×C73C2412yes—
249C22×C4×C73—22no—
250C22×C4×C73—22no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—24no—
255C22×C4×C73—82no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D412yes—
258C22×C4×C73C2412yes—
259C22×C4×C73C2411yescharacteristic
260C2×C8×C73—22no—
261C2×C8×C73—22no—
262C2×C8×C73C2412yes—
263C2×C8×C73C2412yes—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C4⋊C4×C73C2412yes—
271C22⋊C4×C73—24no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—42no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73C22×D412yes—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73C22×D412yes—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—42no—
292D4×C73—84no—
293C2×C4×C73—22no—
294C2×C4×C73—24no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—42no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73—84no—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4112yes—
307C2×C4×C732−1+412yes—
308C2×C4×C73C2511yescharacteristic
309C22⋊D73—44no—
310C22⋊D73—48no—
311C22⋊D73—48no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—84no—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C2×Dic73C22×D412yes—
325D292—22no—
326D292—22no—
327D292—42no—
328D292—84no—
329C4×D73—24no—
330C4×D73—22no—
331C4×D73—22no—
332C4×D73—84no—
333C4×D73—84no—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831C2×#4114yes—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—44no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—84no—
346C22×C73#54712yes—
347C22×C73#57512yes—
348C22×C73#57612yes—
349C22×C73C23×D411yescharacteristic
350C2×D73—22no—
351C2×D73—22no—
352C2×D73—22no—
353C2×D73—44no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—42no—
357C2×D73—84no—
358C4×C73—22no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73#54712yes—
363C4×C73C22×#4111yescharacteristic
364C4×C73C2×2−1+411yescharacteristic
365Dic73—22no—
366Dic73—22no—
367Dic73—22no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3355—731nomaximal, Sylow
372C2×C73—42no—
373C2×C73—82no—
374C2×C73#335514yescomplemented
375C2×C73C2×#54711yescharacteristic
376C2×C73C2×#57511yescharacteristic
377C2×C73C2×#57611yescharacteristic
378D73—42no—
379D73—82no—
380C2×#553—731no—
381C2×#553—731no—
382#3355—7316no—
383C2×#499—731no—
384C2×#482—731no—
385C2×#482—731no—
386C2×#480—731no—
387C2×#480D7311yescharacteristic, complemented
388C2×#478—731no—
389C2×#478—731no—
390C2×#469—731no—
391C2×#469—731no—
392C2×C4×D8—731no—
393C2×#436—731no—
394C2×#428—731no—
395C2×#428—731no—
396C73C2×#335511yescharacteristic, complemented, Sylow
397C22×D8—731no—
398C22×M16—731no—
399C22×M16—731no—
400#553—738no—
401#553—738no—
402#553—1464no—
403#553—1464no—
404C2×#126—1461no—
405C2×#126—1461no—
406C2×#125—731no—
407C2×#125—731no—
408C2×#123—1461no—
409C2×#123—1461no—
410C2×#121—731no—
411C2×#121—731no—
412C2×#121—731no—
413C2×#121—1461no—
414C2×#121—1461no—
415C2×#121C2×D7311yescharacteristic
416C2×C4×D4—731no—
417C2×C4×D4—731no—
418C2×C4×D4—731no—
419C2×C4×D4—1461no—
420C2×C4×D4—1461no—
421C2×#117—731no—
422C2×#117—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4C2×D7311yescharacteristic
425#499—738no—
426#482—738no—
427#482—738no—
428#480—738no—
429#480C2×D7318yescomplemented
430#478—738no—
431#478—738no—
432#469—738no—
433#469—738no—
434C4×D8—738no—
435#436—738no—
436#428—738no—
437#428—738no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#107C2×D7311yescharacteristic
442C2×#107C2×D7311yescharacteristic
443C2×#106—731no—
444C2×#106—731no—
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102C2×D7311yescharacteristic
453C2×#102C2×D7311yescharacteristic
454C2×C22⋊C8—731no—
455C2×C22⋊C8C2×D7311yescharacteristic
456C2×C4×C8—731no—
457C22×D4—21no—
458C22×D4—731no—
459C22×D4—731no—
460C22×D4—1461no—
461C22×D4—1461no—
462C22×D4—1461no—
463C22×D4C22×D7311yescharacteristic
464C23×C4—21no—
465C23×C4—731no—
466C23×C4—1461no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4C22×D7311yescharacteristic
470C2×D8—734no—
471C2×D8—1464no—
472C2×M16—734no—
473C2×M16—734no—
474C2×M16—1464no—
475C2×M16—1464no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8C22×D7311yescharacteristic
479C22×C8C22×D7311yescharacteristic
480#126—1468no—
481#126—1468no—
482#125—734no—
483#125—734no—
484#125—1462no—
485#125—1462no—
486#123—1468no—
487#123—1468no—
488#121—22no—
489#121—734no—
490#121—734no—
491#121—734no—
492#121—1462no—
493#121—1468no—
494#121—1462no—
495#121—1468no—
496#121—1462no—
497#121C22×D7314yes—
498C4×D4—734no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1462no—
503C4×D4—1462no—
504C4×D4—1468no—
505C4×D4—1468no—
506#117—734no—
507#117—734no—
508#117—1462no—
509#117—1462no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—734no—
517C2×C4⋊C4—1462no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4C22×D7311yescharacteristic
524C2×C4⋊C4C22×D7311yescharacteristic
525C2×C4⋊C4C22×D7311yescharacteristic
526C2×C4⋊C4C22×D7314yes—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—731no—
529C2×C22⋊C4—731no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C42—731no—
538C2×C42—1461no—
539C2×C42—1461no—
540#107—734no—
541#107—734no—
542#107—734no—
543#107C22×D7314yes—
544#107C22×D7314yes—
545#106—734no—
546#106—734no—
547#106—734no—
548#106—734no—
549C4⋊C8—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102C22×D7314yes—
555#102C22×D7314yes—
556C22⋊C8—734no—
557C22⋊C8C22×D7314yes—
558C4×C8—734no—
559C24—21no—
560C24—731no—
561C24—1461no—
562C24D4×D7311yescharacteristic
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—82no—
568C2×D4—2924no—
569C2×D4—2924no—
570C2×D4—2922no—
571C2×D4—5842no—
572C2×D4—734no—
573C2×D4—732no—
574C2×D4—1464no—
575C2×D4—1464no—
576C2×D4—1464no—
577C2×D4—1461no—
578C2×D4—1462no—
579C2×D4—1462no—
580C2×D4C23×D7312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—5842no—
589C22×C4—5842no—
590C22×C4—5842no—
591C22×C4—731no—
592C22×C4—731no—
593C22×C4—731no—
594C22×C4—732no—
595C22×C4—732no—
596C22×C4—1464no—
597C22×C4—1464no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1464no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4D4×D7312yes—
605C22×C4D4×D7311yescharacteristic
606C22×C4C23×D7312yes—
607C22×C4C23×D7311yescharacteristic
608D8—1468no—
609M16—1468no—
610M16—1468no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—734no—
614C2×C8—732no—
615C2×C8—732no—
616C2×C8—1462no—
617C2×C8C23×D7312yes—
618C2×C8C23×D7312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—734no—
624C4⋊C4—732no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1461no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C4⋊C4C23×D7312yes—
636C4⋊C4C23×D7312yes—
637C4⋊C4C23×D7312yes—
638C22⋊C4—24no—
639C22⋊C4—734no—
640C22⋊C4—734no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C42—732no—
649C42—732no—
650C42—1464no—
651C42—1464no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—2922no—
660C23—2922no—
661C23—2922no—
662C23—732no—
663C23—1462no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23C2×D4×D7312yes—
668C23C2×D4×D7311yescharacteristic
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673D4—2928no—
674D4—2928no—
675D4—2924no—
676D4—2922no—
677D4—5844no—
678D4—1462no—
679D4—1462no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—2922no—
692C2×C4—2922no—
693C2×C4—2922no—
694C2×C4—5844no—
695C2×C4—5844no—
696C2×C4—5844no—
697C2×C4—732no—
698C2×C4—732no—
699C2×C4—732no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1464no—
709C2×C4C2×D4×D7312yes—
710C2×C4C2×D4×D7311yescharacteristic
711C2×C4#41×D7312yes—
712C2×C4#1455663812yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—22no—
716C8—734no—
717C8—1462no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2924no—
727C22—2922no—
728C22—2922no—
729C22—2922no—
730C22—5844no—
731C22—1462no—
732C22—1462no—
733C22—1462no—
734C22#1798923512yes—
735C22#1798938612yes—
736C22#1798938812yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—2922no—
743C4—2922no—
744C4—2922no—
745C4—1462no—
746C4—1462no—
747C4—1462no—
748C4#1798923512yes—
749C4C2×#41×D7311yescharacteristic
750C4C2×#1455663811yescharacteristic
751C2—42no—
752C2—82no—
753C2—2922no—
754C2—5842no—
755C2#2262253714yesdirect product factor
756C2C2×#1798923511yescharacteristic
757C2C2×#1798938611yescharacteristic
758C2C2×#1798938811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#480×C73C2
socleC23×C73C22×D4
hypercenterC2×#480D73
hypocenterC73C2×#3355
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#17989285C2semidirect
2. C2×#17989284C2semidirect
3. #22622537C2direct (N × H)
4. C2×#17988988C2semidirect
5. C2×#17988912C2semidirect
6. C2×#17988909C2semidirect
7. C2×#17988902C2semidirect
8. C2×#17988890C2semidirect
9. C2×#17988889C2semidirect
10. C2×#17988839C2semidirect
11. C2×#17988838C2semidirect
12. C2×#17988667C2semidirect
13. C2×#17988662C2semidirect
14. C2×#17988628C2semidirect
15. C2×#17988627C2semidirect
16. C2×#480×C73C2semidirect
21. #17989285C22semidirect
23. #17989284C22semidirect
43. #17988988C22semidirect
44. #17988912C22semidirect
45. #17988909C22semidirect
46. #17988902C22semidirect
47. #17988890C22semidirect
48. #17988889C22semidirect
49. #17988839C22semidirect
50. #17988838C22semidirect
51. #17988667C22semidirect
52. #17988662C22semidirect
53. #17988628C22semidirect
54. #17988627C22semidirect
71. #480×C73C22semidirect
374. C2×C73#3355semidirect
387. C2×#480D73semidirect
396. C73C2×#3355semidirect
429. #480C2×D73semidirect
755. C2#22622537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892852
C2×#179892842
#226225372
C2×#179889882
C2×#179889122
C2×#179889092
C2×#179889022
C2×#179888902
C2×#179888892
C2×#179888392
C2×#179888382
C2×#179886672
C2×#179886622
C2×#179886282
C2×#179886272
C2×#480×C732
C2×#335573