Finite Group Databasebeta

← C2×#22621829 #33962403

Subgroups — C2×#22621829 #33962403

Order 18688.

2210 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×#17989285C211yesmaximal, characteristic, complemented
2C2×#17989248C211yesmaximal, characteristic, complemented
3#22621829C2116yesmaximal, direct product factor
4C2×#17988943C211yesmaximal, characteristic, complemented
5C2×#17988905C211yesmaximal, characteristic, complemented
6C2×#17988927C211yesmaximal, characteristic, complemented
7C2×#17988896C211yesmaximal, characteristic, complemented
8C2×#17988823C211yesmaximal, characteristic, complemented
9C2×#17988819C211yesmaximal, characteristic, complemented
10C2×#17988805C211yesmaximal, characteristic, complemented
11C2×#17988735C211yesmaximal, characteristic, complemented
12C2×#17988726C211yesmaximal, characteristic, complemented
13C2×#17988672C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D73C211yesmaximal, characteristic, complemented
15C2×#17988582C211yesmaximal, characteristic, complemented
16C22×#103×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C22×D584C2211yescharacteristic
21C22×C8×D73C2211yescharacteristic
22#17989285—24no—
23#17989285C2218yescomplemented
24#17989248—24no—
25#17989248C2218yescomplemented
26C2×#14556586—21no—
27C2×#14556582C2211yescharacteristic
28C2×#14556580—21no—
29C2×#14556580C2211yescharacteristic
30C2×#14556576—21no—
31C2×#14556567—21no—
32C2×#14556567C2211yescharacteristic
33C2×#14556566C2211yescharacteristic
34C2×#14556565—21no—
35C2×#14556565—21no—
36C2×#14556565C2211yescharacteristic
37C2×#14556565C2211yescharacteristic
38C2×Q8×Dic73C2211yescharacteristic
39C2×#14556553C2211yescharacteristic
40C2×C4×C22⋊D73—21no—
41C2×C4×C22⋊D73—21no—
42C2×C4×C22⋊D73C2211yescharacteristic
43C2×#14556549C2211yescharacteristic
44#17988943C2218yescomplemented
45#17988927C2218yescomplemented
46#17988905C2218yescomplemented
47#17988896C2218yescomplemented
48#17988823C2218yescomplemented
49#17988819C2218yescomplemented
50#17988805C2218yescomplemented
51#17988735C2218yescomplemented
52#17988726C2218yescomplemented
53#17988672C2218yescomplemented
54C8×C22⋊D73C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59#17988582C2218yescomplemented
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C23×Q8×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72C2×#103×C73C2211yescharacteristic
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2218yescomplemented
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—42no—
80C2×#11924029C2314yes—
81C22×D292—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73D411yescharacteristic
88C22×C4×D73—21no—
89C22×C4×D73—21no—
90C22×C4×D73C2311yescharacteristic
91C2×#11924015—24no—
92C2×#11924015—42no—
93C2×#11924015C2314yes—
94C2×#11924015C2314yes—
95C2×D584—42no—
96C2×D584C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99C2×C8×D73—42no—
100C2×C8×D73C2314yes—
101#14556586—28no—
102#14556582—22no—
103#14556582C2314yes—
104#14556580—28no—
105#14556580—22no—
106#14556580C2314yes—
107#14556576—28no—
108#14556567—22no—
109#14556567—28no—
110#14556567C2314yes—
111#14556566—22no—
112#14556566C2314yes—
113#14556565—28no—
114#14556565—28no—
115#14556565—22no—
116#14556565—22no—
117#14556565C2314yes—
118#14556565C2314yes—
119Q8×Dic73—22no—
120Q8×Dic73C2314yes—
121#14556553—22no—
122#14556553C2314yes—
123C4×C22⋊D73—28no—
124C4×C22⋊D73—28no—
125C4×C22⋊D73D414yes—
126C4×C22⋊D73C2314yes—
127#14556549—22no—
128#14556549C2314yes—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73—21no—
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2311yescharacteristic
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007D411yescharacteristic
136C2×C22⋊Dic73D411yescharacteristic
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556525C2314yes—
150#14556522C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556513C2314yes—
156#14556513C2314yes—
157#14556511C2314yes—
158#14556511C2314yes—
159C22⋊#10596831C2314yes—
160#14556503C2314yes—
161C8×Dic73C2314yes—
162C22×Q8×C73—22no—
163C22×Q8×C73—21no—
164C22×Q8×C73—24no—
165C22×Q8×C73—42no—
166C22×Q8×C73C2311yescharacteristic
167C22×Q8×C73C2314yes—
168C22×Q8×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73—21no—
171C23×C4×C73C2311yescharacteristic
172C22×C8×C73—42no—
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175C22×C8×C73C2314yes—
176C2×C4⋊C4×C73—22no—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C4⋊C4×C73C2314yes—
181#103×C73C2314yes—
182#103×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73—21no—
186C23×D73—21no—
187C23×D73C2×D411yescharacteristic
188#11924029—28no—
189#11924029—44no—
190#11924029—48no—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—24no—
196C2×D292—21no—
197C2×D292—21no—
198C2×D292—24no—
199C2×D292—44no—
200C2×D292—82no—
201C2×D292C2412yes—
202C2×D292C2412yes—
203C2×C22⋊D73—24no—
204C2×C22⋊D73—24no—
205C2×C22⋊D73—24no—
206C2×C22⋊D73—44no—
207C2×C22⋊D73—44no—
208C2×C22⋊D73C2×D414yes—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73C2×D411yescharacteristic
212C22×Dic73C2×D411yescharacteristic
213C22×Dic73C2×D411yescharacteristic
214C2×C4×D73—22no—
215C2×C4×D73—22no—
216C2×C4×D73—24no—
217C2×C4×D73—24no—
218C2×C4×D73—44no—
219C2×C4×D73—82no—
220C2×C4×D73C2×D412yes—
221C2×C4×D73C2412yes—
222#11924015—28no—
223#11924015—44no—
224D584—44no—
225C2×#10596831—22no—
226C2×#10596831—22no—
227C2×#10596831C2412yes—
228C2×#10596831C2412yes—
229C8×D73—44no—
230C4⋊Dic73—21no—
231C4⋊Dic73—21no—
232C4⋊Dic73—24no—
233C4⋊Dic73—24no—
234C4⋊Dic73C2412yes—
235C4⋊Dic73C2412yes—
236#11924007—24no—
237#11924007—24no—
238#11924007C2×D414yes—
239C22⋊Dic73C2×D414yes—
240#11924005—24no—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005—24no—
246#11924005—24no—
247#11924005—24no—
248#11924005C2×D414yes—
249C4×Dic73—24no—
250C4×Dic73—24no—
251C4×Dic73C2×D412yes—
252C4×Dic73C2412yes—
253C24×C73C2×D411yescharacteristic
254C2×Q8×C73—21no—
255C2×Q8×C73—24no—
256C2×Q8×C73—21no—
257C2×Q8×C73—22no—
258C2×Q8×C73—28no—
259C2×Q8×C73—22no—
260C2×Q8×C73—22no—
261C2×Q8×C73—44no—
262C2×Q8×C73—44no—
263C2×Q8×C73—48no—
264C2×Q8×C73#4114yes—
265C2×Q8×C73C2412yes—
266C2×Q8×C73C2412yes—
267C22×C4×C73—21no—
268C22×C4×C73—22no—
269C22×C4×C73—22no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—24no—
274C22×C4×C73—24no—
275C22×C4×C73—44no—
276C22×C4×C73—82no—
277C22×C4×C73C2×D411yescharacteristic
278C22×C4×C73C2×D412yes—
279C22×C4×C73C2412yes—
280C22×C4×C73C2411yescharacteristic
281C2×C8×C73—22no—
282C2×C8×C73—22no—
283C2×C8×C73—44no—
284C2×C8×C73C2412yes—
285C2×C8×C73C2412yes—
286C4⋊C4×C73—21no—
287C4⋊C4×C73—21no—
288C4⋊C4×C73—24no—
289C4⋊C4×C73C2412yes—
290C4⋊C4×C73C2412yes—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73#13514yes—
294C23×C73C22×D412yes—
295C23×C73C22×D411yescharacteristic
296C22×D73—22no—
297C22×D73—22no—
298C22×D73—22no—
299C22×D73—22no—
300C22×D73—22no—
301C22×D73—42no—
302C22×D73—42no—
303C22×D73—42no—
304C22×D73—42no—
305C22×D73—42no—
306C22×D73—42no—
307C22×D73C22×D412yes—
308Q8×C73—24no—
309Q8×C73—22no—
310Q8×C73—22no—
311Q8×C73—22no—
312Q8×C73—48no—
313Q8×C73—42no—
314Q8×C73C2×#4114yes—
315C2×C4×C73—22no—
316C2×C4×C73—24no—
317C2×C4×C73—22no—
318C2×C4×C73—24no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—48no—
325C2×C4×C73—42no—
326C2×C4×C73—42no—
327C2×C4×C73—42no—
328C2×C4×C73—84no—
329C2×C4×C73C22×D412yes—
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C2×#4112yes—
332C2×C4×C73H(5,𝔽2)12yes—
333C2×C4×C73C2511yescharacteristic
334C22⋊D73—28no—
335C22⋊D73—48no—
336C22⋊D73—48no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—42no—
343C2×Dic73—42no—
344C2×Dic73C22×D412yes—
345C2×Dic73C22×D412yes—
346C2×Dic73C22×D412yes—
347D292—22no—
348D292—22no—
349D292—22no—
350D292—22no—
351D292—48no—
352D292—42no—
353D292—42no—
354D292—84no—
355C4×D73—24no—
356C4×D73—22no—
357C4×D73—22no—
358C4×D73—48no—
359C4×D73—84no—
360C8×C73—22no—
361C8×C73—22no—
362#10596831—22no—
363#10596831—22no—
364C22×C73—22no—
365C22×C73—28no—
366C22×C73—22no—
367C22×C73#54612yes—
368C22×C73C2×#13514yes—
369C22×C73C2×#13512yes—
370C22×C73#57712yes—
371C22×C73C23×D411yescharacteristic
372C2×D73—22no—
373C2×D73—22no—
374C2×D73—22no—
375C2×D73—44no—
376C2×D73—42no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C2×D73—84no—
383C2×D73—84no—
384C4×C73—24no—
385C4×C73—22no—
386C4×C73—42no—
387C4×C73—42no—
388C4×C73—42no—
389C4×C73#54612yes—
390C4×C73C22×#4111yescharacteristic
391C4×C73C2×H(5,𝔽2)11yescharacteristic
392Dic73—22no—
393Dic73—22no—
394Dic73—22no—
395Dic73—42no—
396Dic73—42no—
397C2×#3301—731nomaximal, Sylow
398C2×C73—24no—
399C2×C73#330114yescomplemented
400C2×C73C2×#54611yescharacteristic
401C2×C73C22×#13511yescharacteristic
402C2×C73C2×#57711yescharacteristic
403D73—42no—
404D73—82no—
405D73—82no—
406C2×#553—731no—
407C2×#548—731no—
408#3301—7316no—
409C2×#488—731no—
410C2×#481—731no—
411C2×#485—731no—
412C2×#479—731no—
413C2×#466—731no—
414C2×#465—731no—
415C2×#463—731no—
416C2×#449—731no—
417C2×#448—731no—
418C2×C4×SD16—731no—
419C2×C8×D4—731no—
420C2×#416—731no—
421C22×#103D7311yescharacteristic, complemented
422C73C2×#330111yescharacteristic, complemented, Sylow
423C22×#41—731no—
424C23×Q8C2×D7311yescharacteristic
425C22×SD16—731no—
426C22×SD16—731no—
427C22×D8—731no—
428C23×C8—731no—
429C23×C8C2×D7311yescharacteristic
430#553—738no—
431#553—1464no—
432#548—738no—
433#548—1464no—
434C2×#126—1461no—
435C2×#125—731no—
436C2×#124—731no—
437C2×#124—1461no—
438C2×#123—1461no—
439C2×C22⋊Q8—731no—
440C2×C22⋊Q8—1461no—
441C2×#121—731no—
442C2×#121—731no—
443C2×#121—731no—
444C2×#121—1461no—
445C2×#121—1461no—
446C2×C4×Q8—731no—
447C2×C4×D4—731no—
448C2×C4×D4—731no—
449C2×C4×D4—1461no—
450C2×C4×D4—1461no—
451C2×#117—731no—
452C22×C4⋊C4C2×D7311yescharacteristic
453#488—738no—
454#485—738no—
455#481—738no—
456#479—738no—
457#466—738no—
458#465—738no—
459#463—738no—
460#449—738no—
461#448—738no—
462C4×SD16—738no—
463C8×D4—738no—
464C2×#107—731no—
465C2×#106—731no—
466C2×#106—731no—
467C2×C4⋊C8—731no—
468#416—738no—
469C2×#103—731no—
470C2×#103—731no—
471C2×#103C2×D7311yescharacteristic
472C2×#103C2×D7311yescharacteristic
473C2×#103C2×D7311yescharacteristic
474C2×#103C2×D7311yescharacteristic
475C2×#103C2×D7318yescomplemented
476C2×#102—731no—
477C2×#102—731no—
478C2×#102—731no—
479C2×#102—731no—
480C2×C22⋊C8—731no—
481C2×C22⋊C8—731no—
482C2×C4×C8—731no—
483C2×#41—2922no—
484C2×#41—734no—
485C2×#41—1464no—
486C2×#41—1462no—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8C22×D7311yescharacteristic
492C22×Q8C22×D7314yes—
493C22×Q8C22×D7311yescharacteristic
494C22×D4—731no—
495C22×D4—731no—
496C22×D4—731no—
497C22×D4—1461no—
498C22×D4—1461no—
499C22×D4—1461no—
500C22×D4—1461no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—731no—
504C23×C4—1461no—
505C23×C4—1461no—
506C23×C4C22×D7311yescharacteristic
507C2×SD16—2922no—
508C2×SD16—734no—
509C2×SD16—734no—
510C2×SD16—1464no—
511C2×D8—2922no—
512C2×D8—734no—
513C22×C8—42no—
514C22×C8—2922no—
515C22×C8—734no—
516C22×C8—731no—
517C22×C8—731no—
518C22×C8C22×D7311yescharacteristic
519C22×C8C22×D7311yescharacteristic
520C22×C8C22×D7314yes—
521#126—1468no—
522#125—734no—
523#125—1462no—
524#124—734no—
525#124—1462no—
526#124—1468no—
527#123—1468no—
528C22⋊Q8—734no—
529C22⋊Q8—1468no—
530C22⋊Q8—1462no—
531#121—734no—
532#121—734no—
533#121—734no—
534#121—1462no—
535#121—1468no—
536#121—1468no—
537#121—1462no—
538#121—1462no—
539C4×Q8—734no—
540C4×Q8—1462no—
541C4×D4—734no—
542C4×D4—734no—
543C4×D4—734no—
544C4×D4—1462no—
545C4×D4—1468no—
546C4×D4—1468no—
547#117—734no—
548#117—1462no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—731no—
552C2×C4⋊C4—731no—
553C2×C4⋊C4—731no—
554C2×C4⋊C4—1461no—
555C2×C4⋊C4—1461no—
556C2×C4⋊C4—1461no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4C22×D7311yescharacteristic
559C2×C4⋊C4C22×D7311yescharacteristic
560C2×C4⋊C4C22×D7314yes—
561C2×C22⋊C4—731no—
562C2×C22⋊C4—731no—
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×C22⋊C4—1461no—
571C2×C42—731no—
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#103C22×D7314yes—
581#103C22×D7314yes—
582#103C22×D7314yes—
583#103C22×D7314yes—
584#102—734no—
585#102—734no—
586#102—734no—
587#102—734no—
588C22⋊C8—734no—
589C22⋊C8—734no—
590C4×C8—734no—
591C24—731no—
592C24—1461no—
593C24—1461no—
594C24D4×D7311yescharacteristic
595#41—2928no—
596#41—2924no—
597#41—1468no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8#1192402814yes—
609C2×Q8C23×D7312yes—
610C2×Q8C23×D7312yes—
611C2×D4—2924no—
612C2×D4—2924no—
613C2×D4—2924no—
614C2×D4—5842no—
615C2×D4—734no—
616C2×D4—732no—
617C2×D4—732no—
618C2×D4—1464no—
619C2×D4—1464no—
620C2×D4—1464no—
621C2×D4—1464no—
622C2×D4—1464no—
623C2×D4—1461no—
624C2×D4—1461no—
625C2×D4—1462no—
626C2×D4—1462no—
627C2×D4—1462no—
628C2×D4—1462no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—82no—
639C22×C4—2924no—
640C22×C4—5842no—
641C22×C4—731no—
642C22×C4—731no—
643C22×C4—731no—
644C22×C4—732no—
645C22×C4—732no—
646C22×C4—1464no—
647C22×C4—1464no—
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—2924no—
657SD16—1468no—
658D8—2924no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—44no—
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—21no—
671C4⋊C4—24no—
672C4⋊C4—734no—
673C4⋊C4—732no—
674C4⋊C4—732no—
675C4⋊C4—1464no—
676C4⋊C4—1464no—
677C4⋊C4—1464no—
678C4⋊C4—1464no—
679C4⋊C4—1461no—
680C4⋊C4—1461no—
681C4⋊C4C23×D7312yes—
682C4⋊C4C23×D7312yes—
683C22⋊C4—734no—
684C22⋊C4—734no—
685C22⋊C4—1464no—
686C22⋊C4—1464no—
687C22⋊C4—1464no—
688C22⋊C4—1464no—
689C22⋊C4—1464no—
690C22⋊C4—1464no—
691C22⋊C4—1464no—
692C22⋊C4—1464no—
693C42—732no—
694C42—732no—
695C42—1464no—
696C42—1464no—
697C23—22no—
698C23—22no—
699C23—2922no—
700C23—2922no—
701C23—2922no—
702C23—2922no—
703C23—2922no—
704C23—2922no—
705C23—732no—
706C23—1462no—
707C23—1462no—
708C23—1462no—
709C23—1462no—
710C23—1462no—
711C23#1455661414yes—
712C23C2×D4×D7312yes—
713C23C2×D4×D7311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8C2×#1192402814yes—
721D4—2928no—
722D4—2928no—
723D4—2928no—
724D4—2922no—
725D4—2922no—
726D4—5844no—
727D4—1468no—
728D4—1462no—
729D4—1462no—
730D4—1462no—
731D4—1462no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—2928no—
747C2×C4—2922no—
748C2×C4—2922no—
749C2×C4—5844no—
750C2×C4—732no—
751C2×C4—732no—
752C2×C4—732no—
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×#1192402812yes—
764C2×C4#1455663612yes—
765C2×C4C24×D7311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1462no—
769C8—1462no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—2924no—
774C22—2922no—
775C22—2922no—
776C22—2922no—
777C22—2922no—
778C22—2922no—
779C22—2922no—
780C22—5844no—
781C22—5844no—
782C22—1462no—
783C22—1462no—
784C22—1462no—
785C22#1798922712yes—
786C22C2×#1455661414yes—
787C22C2×#1455661412yes—
788C22#1798939312yes—
789C22C22×D4×D7311yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—2922no—
796C4—2922no—
797C4—1462no—
798C4—1462no—
799C4—1462no—
800C4#1798922712yes—
801C4C22×#1192402811yescharacteristic
802C4C2×#1455663611yescharacteristic
803C2—24no—
804C2—2922no—
805C2—5842no—
806C2—5842no—
807C2#2262182914yesdirect product factor
808C2C2×#1798922711yescharacteristic
809C2C22×#1455661411yescharacteristic
810C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC22×#103×C73C2
socleC23×C73C22×D4
hypercenterC22×#103D73
hypocenterC73C2×#3301
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#17989285C2semidirect
2. C2×#17989248C2semidirect
3. #22621829C2direct (N × H)
4. C2×#17988943C2semidirect
5. C2×#17988905C2semidirect
6. C2×#17988927C2semidirect
7. C2×#17988896C2semidirect
8. C2×#17988823C2semidirect
9. C2×#17988819C2semidirect
10. C2×#17988805C2semidirect
11. C2×#17988735C2semidirect
12. C2×#17988726C2semidirect
13. C2×#17988672C2semidirect
14. C2×C8×C22⋊D73C2semidirect
15. C2×#17988582C2semidirect
16. C22×#103×C73C2semidirect
23. #17989285C22semidirect
25. #17989248C22semidirect
44. #17988943C22semidirect
45. #17988927C22semidirect
46. #17988905C22semidirect
47. #17988896C22semidirect
48. #17988823C22semidirect
49. #17988819C22semidirect
50. #17988805C22semidirect
51. #17988735C22semidirect
52. #17988726C22semidirect
53. #17988672C22semidirect
54. C8×C22⋊D73C22semidirect
59. #17988582C22semidirect
76. C2×#103×C73C22semidirect
399. C2×C73#3301semidirect
421. C22×#103D73semidirect
422. C73C2×#3301semidirect
475. C2×#103C2×D73semidirect
807. C2#22621829direct (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×#179892482
#226218292
C2×#179889432
C2×#179889052
C2×#179889272
C2×#179888962
C2×#179888232
C2×#179888192
C2×#179888052
C2×#179887352
C2×#179887262
C2×#179886722
C2×C8×C22⋊D732
C2×#179885822
C22×#103×C732
C2×#330173