Finite Group Databasebeta

← C2×#22622121 #33962738

Subgroups — C2×#22622121 #33962738

Order 18688.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989301C211yesmaximal, characteristic, complemented
2C2×#17989244C211yesmaximal, characteristic, complemented
3#22622121C2116yesmaximal, direct product factor
4C2×#17988945C211yesmaximal, characteristic, complemented
5C2×#17988929C211yesmaximal, characteristic, complemented
6C2×#17988909C211yesmaximal, characteristic, complemented
7C2×#17988870C211yesmaximal, characteristic, complemented
8C2×#17988837C211yesmaximal, characteristic, complemented
9C2×#17988814C211yesmaximal, characteristic, complemented
10C2×#17988800C211yesmaximal, characteristic, complemented
11C2×#17988724C211yesmaximal, characteristic, complemented
12C2×#17988688C211yesmaximal, characteristic, complemented
13C2×#17988655C211yesmaximal, characteristic, complemented
14C2×#17988594C211yesmaximal, characteristic, complemented
15C2×#17988583C211yesmaximal, characteristic, complemented
16C2×#449×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C23×#10596831C2211yescharacteristic
21#17989301—24no—
22#17989301C2218yescomplemented
23#17989244—24no—
24#17989244C2218yescomplemented
25C2×#14556590C2211yescharacteristic
26C2×#14556578—21no—
27C2×#14556578—21no—
28C2×#14556578C2211yescharacteristic
29C2×#14556577—21no—
30C2×#14556570—21no—
31C2×#14556570C2211yescharacteristic
32C2×#14556563—21no—
33C2×#14556562—21no—
34C2×#14556562C2211yescharacteristic
35C2×#14556562C2211yescharacteristic
36C2×Q8×Dic73C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×C4×C22⋊D73—21no—
39C2×C4×C22⋊D73C2211yescharacteristic
40C2×#14556550C2211yescharacteristic
41C2×#14556549C2211yescharacteristic
42C2×#14556547—21no—
43#17988945C2218yescomplemented
44#17988929C2218yescomplemented
45#17988909C2218yescomplemented
46#17988870C2218yescomplemented
47#17988837C2218yescomplemented
48#17988814C2218yescomplemented
49#17988800C2218yescomplemented
50#17988724C2218yescomplemented
51#17988688C2218yescomplemented
52#17988655C2218yescomplemented
53C2×#14556525C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57#17988594C2218yescomplemented
58#17988583C2218yescomplemented
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×#41×C73C2211yescharacteristic
70C22×SD16×C73C2211yescharacteristic
71C22×D8×C73C2211yescharacteristic
72C2×#121×C73C2211yescharacteristic
73#449×C73C2218yescomplemented
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C2×Q8×D73—22no—
81C2×Q8×D73—24no—
82C2×Q8×D73—42no—
83C2×Q8×D73C2314yes—
84C22×C22⋊D73—21no—
85C22×C22⋊D73—21no—
86C22×C22⋊D73D411yescharacteristic
87C23×Dic73—21no—
88C22×C4×D73—21no—
89C22×C4×D73C2311yescharacteristic
90C2×#11924016—42no—
91C2×#11924016C2314yes—
92C2×#11924011—42no—
93C2×#11924011C2314yes—
94C22×#10596831—42no—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2314yes—
98#14556590—22no—
99#14556590C2314yes—
100#14556578—28no—
101#14556578—28no—
102#14556578—22no—
103#14556578C2314yes—
104#14556577—28no—
105#14556570—28no—
106#14556570—22no—
107#14556570C2314yes—
108#14556563—28no—
109#14556562—28no—
110#14556562—22no—
111#14556562—22no—
112#14556562C2314yes—
113#14556562C2314yes—
114Q8×Dic73—22no—
115Q8×Dic73C2314yes—
116D4×Dic73—22no—
117D4×Dic73C2314yes—
118C4×C22⋊D73—28no—
119C4×C22⋊D73D414yes—
120C4×C22⋊D73C2314yes—
121#14556550—22no—
122#14556550C2314yes—
123#14556549—22no—
124#14556549C2314yes—
125#14556547—28no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×C22⋊Dic73—21no—
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73D411yescharacteristic
141C2×#11924005—21no—
142C2×#11924005D411yescharacteristic
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556525C2314yes—
148#14556523C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556516C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556512C2314yes—
157#14556512C2314yes—
158#14556512C2314yes—
159#14556503C2314yes—
160#14556501C2314yes—
161C2×#41×C73—22no—
162C2×#41×C73—24no—
163C2×#41×C73—42no—
164C2×#41×C73C2314yes—
165C22×Q8×C73C2311yescharacteristic
166C22×D4×C73—21no—
167C22×D4×C73—21no—
168C22×D4×C73C2311yescharacteristic
169C22×D4×C73C2311yescharacteristic
170C23×C4×C73—21no—
171C23×C4×C73C2311yescharacteristic
172C2×SD16×C73—24no—
173C2×SD16×C73C2314yes—
174C2×D8×C73—42no—
175C2×D8×C73C2314yes—
176C22×C8×C73C2311yescharacteristic
177C22×C8×C73C2311yescharacteristic
178#121×C73—22no—
179#121×C73C2314yes—
180C2×C4⋊C4×C73C2311yescharacteristic
181C2×C22⋊C4×C73—21no—
182#103×C73C2314yes—
183#102×C73C2314yes—
184C22⋊C8×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—21no—
189C2×Dic146—24no—
190C2×Dic146—24no—
191C2×Dic146—44no—
192C2×Dic146—82no—
193C2×Dic146C2412yes—
194Q8×D73—28no—
195Q8×D73—44no—
196Q8×D73—48no—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—42no—
200C2×C22⋊D73—44no—
201C2×C22⋊D73—82no—
202C2×C22⋊D73C2×D414yes—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—24no—
208C22×Dic73—44no—
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C2×C4×D73—22no—
213C2×C4×D73—22no—
214C2×C4×D73—24no—
215C2×C4×D73—44no—
216C2×C4×D73C2×D412yes—
217C2×C4×D73C2412yes—
218#11924016—44no—
219#11924011—44no—
220C2×#10596831—22no—
221C2×#10596831—22no—
222C2×#10596831—44no—
223C2×#10596831C2412yes—
224C2×#10596831C2412yes—
225C4⋊Dic73—21no—
226C4⋊Dic73—21no—
227C4⋊Dic73—21no—
228C4⋊Dic73—24no—
229C4⋊Dic73C2412yes—
230C4⋊Dic73C2412yes—
231C4⋊Dic73C2412yes—
232#11924007—24no—
233#11924007—24no—
234#11924007C2×D414yes—
235C22⋊Dic73—24no—
236C22⋊Dic73—24no—
237C22⋊Dic73—24no—
238C22⋊Dic73—24no—
239C22⋊Dic73—24no—
240C22⋊Dic73—24no—
241C22⋊Dic73—24no—
242C22⋊Dic73C2×D414yes—
243#11924005—24no—
244#11924005C2×D414yes—
245C4×Dic73—24no—
246C4×Dic73—24no—
247C4×Dic73—24no—
248C4×Dic73C2×D412yes—
249C4×Dic73C2412yes—
250C24×C73—21no—
251C24×C73—21no—
252C24×C73C2×D411yescharacteristic
253#41×C73—28no—
254#41×C73—44no—
255#41×C73—48no—
256C2×Q8×C73—21no—
257C2×Q8×C73—22no—
258C2×Q8×C73#4114yes—
259C2×Q8×C73C2412yes—
260C2×D4×C73—24no—
261C2×D4×C73—24no—
262C2×D4×C73—21no—
263C2×D4×C73—21no—
264C2×D4×C73—22no—
265C2×D4×C73—22no—
266C2×D4×C73—22no—
267C2×D4×C73—22no—
268C2×D4×C73—44no—
269C2×D4×C73—82no—
270C2×D4×C73C2412yes—
271C2×D4×C73C2412yes—
272C22×C4×C73—21no—
273C22×C4×C73—22no—
274C22×C4×C73—22no—
275C22×C4×C73—21no—
276C22×C4×C73—24no—
277C22×C4×C73—44no—
278C22×C4×C73C2×D411yescharacteristic
279C22×C4×C73C2×D412yes—
280C22×C4×C73C2412yes—
281C22×C4×C73C2411yescharacteristic
282SD16×C73—28no—
283D8×C73—44no—
284C2×C8×C73—22no—
285C2×C8×C73—22no—
286C2×C8×C73C2412yes—
287C2×C8×C73C2412yes—
288C4⋊C4×C73—21no—
289C4⋊C4×C73C2412yes—
290C22⋊C4×C73—24no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—42no—
297C23×C73—42no—
298C23×C73—42no—
299C23×C73—42no—
300C23×C73—42no—
301C23×C73—42no—
302C23×C73C22×D412yes—
303C23×C73C22×D411yescharacteristic
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—22no—
307C22×D73C22×D412yes—
308Q8×C73—24no—
309Q8×C73—22no—
310Q8×C73C2×#4114yes—
311D4×C73—22no—
312D4×C73—22no—
313D4×C73—22no—
314D4×C73—22no—
315D4×C73—48no—
316D4×C73—42no—
317D4×C73—42no—
318D4×C73—84no—
319C2×C4×C73—22no—
320C2×C4×C73—24no—
321C2×C4×C73—22no—
322C2×C4×C73—24no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—48no—
327C2×C4×C73—42no—
328C2×C4×C73C22×D412yes—
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C2×#4112yes—
331C2×C4×C73H(5,𝔽2)12yes—
332C2×C4×C73C2511yescharacteristic
333C22⋊D73—44no—
334C22⋊D73—48no—
335C22⋊D73—84no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—22no—
343C2×Dic73—48no—
344C2×Dic73—42no—
345C2×Dic73—42no—
346C2×Dic73—42no—
347C2×Dic73—42no—
348C2×Dic73C22×D412yes—
349C2×Dic73C22×D412yes—
350C2×Dic73C22×D412yes—
351C4×D73—24no—
352C4×D73—22no—
353C4×D73—22no—
354C4×D73—48no—
355Dic146—22no—
356Dic146—22no—
357Dic146—48no—
358Dic146—42no—
359Dic146—84no—
360C8×C73—22no—
361C8×C73—22no—
362#10596831—22no—
363#10596831—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—44no—
368C22×C73—42no—
369C22×C73—42no—
370C22×C73—42no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—84no—
375C22×C73—84no—
376C22×C73#54612yes—
377C22×C73#57512yes—
378C22×C73#57712yes—
379C22×C73C23×D411yescharacteristic
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—22no—
383C2×D73—44no—
384C4×C73—24no—
385C4×C73—22no—
386C4×C73—42no—
387C4×C73#54612yes—
388C4×C73C22×#4111yescharacteristic
389C4×C73C2×H(5,𝔽2)11yescharacteristic
390Dic73—22no—
391Dic73—22no—
392Dic73—22no—
393Dic73—42no—
394Dic73—42no—
395Dic73—42no—
396Dic73—42no—
397C2×#3321—731nomaximal, Sylow
398C2×C73—42no—
399C2×C73—82no—
400C2×C73—82no—
401C2×C73#332114yescomplemented
402C2×C73C2×#54611yescharacteristic
403C2×C73C2×#57511yescharacteristic
404C2×C73C2×#57711yescharacteristic
405D73—42no—
406C2×#555—731no—
407C2×#548—731no—
408#3321—7316no—
409C2×#489—731no—
410C2×#485—731no—
411C2×#482—731no—
412C2×#475—731no—
413C2×#469—731no—
414C2×#465—731no—
415C2×#463—731no—
416C2×#449D7311yescharacteristic, complemented
417C2×#448—731no—
418C2×#440—731no—
419C2×#435—731no—
420C2×#419—731no—
421C2×#416—731no—
422C73C2×#332111yescharacteristic, complemented, Sylow
423C22×#41C2×D7311yescharacteristic
424C23×Q8—731no—
425C22×SD16—731no—
426C22×SD16C2×D7311yescharacteristic
427C22×D8C2×D7311yescharacteristic
428C22×M16—731no—
429C23×C8—731no—
430#555—738no—
431#555—1464no—
432#548—738no—
433#548—1464no—
434C2×C4⋊Q8—731no—
435C2×#124—731no—
436C2×#124—1461no—
437C2×#124—1461no—
438C2×#124—1461no—
439C2×C22⋊Q8—731no—
440C2×C22⋊Q8—1461no—
441C2×#121—731no—
442C2×#121—731no—
443C2×#121—1461no—
444C2×#121—1461no—
445C2×#121C2×D7311yescharacteristic
446C2×C4×Q8—731no—
447C2×C4×D4—731no—
448C2×C4×D4—731no—
449C2×C4×D4—1461no—
450C2×#117—731no—
451C2×#117—731no—
452C2×#117—1461no—
453#489—738no—
454#485—738no—
455#482—738no—
456#475—738no—
457#469—738no—
458#465—738no—
459#463—738no—
460#449C2×D7318yescomplemented
461#448—738no—
462#440—738no—
463#435—738no—
464C2×#107—731no—
465C2×#106—731no—
466C2×#106—731no—
467C2×C4⋊C8—731no—
468#419—738no—
469#416—738no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#103—731no—
473C2×#103—731no—
474C2×#103—731no—
475C2×#103C2×D7311yescharacteristic
476C2×#102—731no—
477C2×#102—731no—
478C2×#102—731no—
479C2×#102C2×D7311yescharacteristic
480C2×C22⋊C8—731no—
481C2×C22⋊C8C2×D7311yescharacteristic
482C2×#97—731no—
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D7314yes—
487C22×Q8—2922no—
488C22×Q8—734no—
489C22×Q8—731no—
490C22×Q8—1461no—
491C22×Q8—1461no—
492C22×Q8—1464no—
493C22×Q8—1462no—
494C22×Q8C22×D7311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—731no—
498C22×D4—1461no—
499C22×D4—1461no—
500C22×D4C22×D7311yescharacteristic
501C22×D4C22×D7311yescharacteristic
502C23×C4—21no—
503C23×C4—731no—
504C23×C4—1461no—
505C23×C4—1461no—
506C23×C4C22×D7311yescharacteristic
507C2×SD16—24no—
508C2×SD16—2922no—
509C2×SD16—734no—
510C2×SD16C22×D7314yes—
511C2×D8—42no—
512C2×D8C22×D7314yes—
513C2×M16—2922no—
514C2×M16—734no—
515C22×C8—2922no—
516C22×C8—734no—
517C22×C8—731no—
518C22×C8—731no—
519C22×C8C22×D7311yescharacteristic
520C22×C8C22×D7311yescharacteristic
521C4⋊Q8—734no—
522C4⋊Q8—1462no—
523#124—734no—
524#124—1462no—
525#124—1468no—
526#124—1468no—
527#124—1468no—
528C22⋊Q8—734no—
529C22⋊Q8—1468no—
530C22⋊Q8—1462no—
531#121—22no—
532#121—734no—
533#121—734no—
534#121—1462no—
535#121—1462no—
536#121—1468no—
537#121—1468no—
538#121C22×D7314yes—
539C4×Q8—734no—
540C4×Q8—1462no—
541C4×D4—734no—
542C4×D4—734no—
543C4×D4—734no—
544C4×D4—1462no—
545C4×D4—1468no—
546#117—734no—
547#117—734no—
548#117—1468no—
549#117—1462no—
550#117—1462no—
551C2×C4⋊C4—731no—
552C2×C4⋊C4—731no—
553C2×C4⋊C4—731no—
554C2×C4⋊C4—731no—
555C2×C4⋊C4—1461no—
556C2×C4⋊C4—1461no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4C22×D7311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—731no—
561C2×C22⋊C4—731no—
562C2×C22⋊C4—1461no—
563C2×C22⋊C4—1461no—
564C2×C22⋊C4—1461no—
565C2×C22⋊C4—1461no—
566C2×C22⋊C4—1461no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4—1461no—
569C2×C22⋊C4—1461no—
570C2×C42—731no—
571C2×C42—1461no—
572C2×C42—1461no—
573C2×C42—1461no—
574#107—734no—
575#106—734no—
576#106—734no—
577C4⋊C8—734no—
578#103—734no—
579#103—734no—
580#103—734no—
581#103—734no—
582#103—734no—
583#103C22×D7314yes—
584#102—734no—
585#102—734no—
586#102—734no—
587#102C22×D7314yes—
588C22⋊C8—734no—
589C22⋊C8C22×D7314yes—
590#97—734no—
591C24—21no—
592C24—21no—
593C24—731no—
594C24D4×D7311yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—2924no—
601C2×Q8—2928no—
602C2×Q8—2924no—
603C2×Q8—5842no—
604C2×Q8—732no—
605C2×Q8—1464no—
606C2×Q8—1464no—
607C2×Q8—1468no—
608C2×Q8—1462no—
609C2×Q8—1462no—
610C2×Q8—1461no—
611C2×Q8#1192402714yes—
612C2×Q8C23×D7312yes—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—82no—
623C2×D4—2924no—
624C2×D4—2922no—
625C2×D4—5842no—
626C2×D4—734no—
627C2×D4—1464no—
628C2×D4—1464no—
629C2×D4C23×D7312yes—
630C2×D4C23×D7312yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—24no—
636C22×C4—44no—
637C22×C4—2924no—
638C22×C4—2924no—
639C22×C4—731no—
640C22×C4—731no—
641C22×C4—731no—
642C22×C4—732no—
643C22×C4—732no—
644C22×C4—1464no—
645C22×C4—1464no—
646C22×C4—1461no—
647C22×C4—1461no—
648C22×C4—1461no—
649C22×C4—1461no—
650C22×C4—1462no—
651C22×C4—1462no—
652C22×C4D4×D7312yes—
653C22×C4D4×D7311yescharacteristic
654C22×C4C23×D7312yes—
655C22×C4C23×D7311yescharacteristic
656SD16—28no—
657SD16—2924no—
658D8—44no—
659M16—2924no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—2924no—
663C2×C8—732no—
664C2×C8—732no—
665C2×C8—1462no—
666C2×C8—1462no—
667C2×C8C23×D7312yes—
668C2×C8C23×D7312yes—
669C4⋊C4—21no—
670C4⋊C4—734no—
671C4⋊C4—732no—
672C4⋊C4—732no—
673C4⋊C4—732no—
674C4⋊C4—1464no—
675C4⋊C4—1464no—
676C4⋊C4—1464no—
677C4⋊C4—1461no—
678C4⋊C4—1461no—
679C4⋊C4—1461no—
680C4⋊C4C23×D7312yes—
681C22⋊C4—24no—
682C22⋊C4—734no—
683C22⋊C4—734no—
684C22⋊C4—1464no—
685C22⋊C4—1464no—
686C22⋊C4—1464no—
687C22⋊C4—1464no—
688C22⋊C4—1464no—
689C22⋊C4—1464no—
690C22⋊C4—1464no—
691C22⋊C4—1464no—
692C42—732no—
693C42—732no—
694C42—1464no—
695C42—1464no—
696C42—1464no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—732no—
709C23—1462no—
710C23—1462no—
711C23—1462no—
712C23C2×D4×D7312yes—
713C23C2×D4×D7311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—2928no—
717Q8—2922no—
718Q8—5844no—
719Q8—1462no—
720Q8—1462no—
721Q8C2×#1192402714yes—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—42no—
728D4—42no—
729D4—84no—
730D4—2928no—
731D4—2924no—
732D4—5844no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—2928no—
743C2×C4—2922no—
744C2×C4—2922no—
745C2×C4—2922no—
746C2×C4—2922no—
747C2×C4—2928no—
748C2×C4—732no—
749C2×C4—732no—
750C2×C4—732no—
751C2×C4—1462no—
752C2×C4—1462no—
753C2×C4—1462no—
754C2×C4—1462no—
755C2×C4—1462no—
756C2×C4—1462no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1462no—
760C2×C4—1464no—
761C2×C4C2×D4×D7312yes—
762C2×C4C2×D4×D7311yescharacteristic
763C2×C4C2×#1192402712yes—
764C2×C4#1455663612yes—
765C2×C4C24×D7311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1462no—
769C8—1462no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—84no—
782C22—2924no—
783C22—1462no—
784C22—1462no—
785C22—1462no—
786C22#1798922412yes—
787C22#1798938412yes—
788C22#1798939712yes—
789C22C22×D4×D7311yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—2922no—
794C4—2922no—
795C4—2922no—
796C4—2922no—
797C4—1462no—
798C4—1462no—
799C4—1462no—
800C4#1798922412yes—
801C4C22×#1192402711yescharacteristic
802C4C2×#1455663611yescharacteristic
803C2—42no—
804C2—82no—
805C2—82no—
806C2—2922no—
807C2#2262212114yesdirect product factor
808C2C2×#1798922411yescharacteristic
809C2C2×#1798938411yescharacteristic
810C2C2×#1798939711yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#449×C73C2
socleC23×C73C22×D4
hypercenterC2×#449D73
hypocenterC73C2×#3321
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#17989301C2semidirect
2. C2×#17989244C2semidirect
3. #22622121C2direct (N × H)
4. C2×#17988945C2semidirect
5. C2×#17988929C2semidirect
6. C2×#17988909C2semidirect
7. C2×#17988870C2semidirect
8. C2×#17988837C2semidirect
9. C2×#17988814C2semidirect
10. C2×#17988800C2semidirect
11. C2×#17988724C2semidirect
12. C2×#17988688C2semidirect
13. C2×#17988655C2semidirect
14. C2×#17988594C2semidirect
15. C2×#17988583C2semidirect
16. C2×#449×C73C2semidirect
22. #17989301C22semidirect
24. #17989244C22semidirect
43. #17988945C22semidirect
44. #17988929C22semidirect
45. #17988909C22semidirect
46. #17988870C22semidirect
47. #17988837C22semidirect
48. #17988814C22semidirect
49. #17988800C22semidirect
50. #17988724C22semidirect
51. #17988688C22semidirect
52. #17988655C22semidirect
57. #17988594C22semidirect
58. #17988583C22semidirect
73. #449×C73C22semidirect
401. C2×C73#3321semidirect
416. C2×#449D73semidirect
422. C73C2×#3321semidirect
460. #449C2×D73semidirect
807. C2#22622121direct (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×#179892442
#226221212
C2×#179889452
C2×#179889292
C2×#179889092
C2×#179888702
C2×#179888372
C2×#179888142
C2×#179888002
C2×#179887242
C2×#179886882
C2×#179886552
C2×#179885942
C2×#179885832
C2×#449×C732
C2×#332173