Finite Group Databasebeta

← C2×#22621495 #33961023

Subgroups — C2×#22621495 #33961023

Order 18688.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D73C211yesmaximal, characteristic, complemented
2C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
3C2×#17989244C211yesmaximal, characteristic
4#22621495C2116yesmaximal, direct product factor
5C2×#17988978C211yesmaximal, characteristic, complemented
6C2×#17988845C211yesmaximal, characteristic, complemented
7C2×#17988813C211yesmaximal, characteristic, complemented
8C2×#17988807C211yesmaximal, characteristic, complemented
9C2×#17988795C211yesmaximal, characteristic, complemented
10C2×#17988749C211yesmaximal, characteristic, complemented
11C2×#17988743C211yesmaximal, characteristic, complemented
12C2×#17988741C211yesmaximal, characteristic, complemented
13C2×#17988724C211yesmaximal, characteristic, complemented
14C2×#17988694C211yesmaximal, characteristic, complemented
15C2×#17988656C211yesmaximal, characteristic, complemented
16C22×#137×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×Dic292C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924018C2211yescharacteristic
22C22×#11924018C2211yescharacteristic
23C2×Q16×D73—28no—
24C2×Q16×D73C2218yescomplemented
25C22×#11924016C2211yescharacteristic
26C22×C8×D73C2211yescharacteristic
27Q8×C22⋊D73—24no—
28Q8×C22⋊D73C2218yescomplemented
29#17989244—24no—
30#17989244C2218yes—
31C2×#14556589—21no—
32C2×#14556589C2211yescharacteristic
33C2×#14556578—21no—
34C2×#14556578C2211yescharacteristic
35C2×#14556570—21no—
36C2×#14556570—21no—
37C2×#14556570C2211yescharacteristic
38C2×#14556570C2211yescharacteristic
39C2×#14556567—21no—
40C2×#14556567C2211yescharacteristic
41C2×#14556562—21no—
42C2×#14556562C2211yescharacteristic
43C2×Q8×Dic73C2211yescharacteristic
44C2×Q8×Dic73C2211yescharacteristic
45C2×C4×C22⋊D73—21no—
46C2×C4×C22⋊D73—21no—
47C2×C4×C22⋊D73C2211yescharacteristic
48#17988978C2218yescomplemented
49#17988845C2218yescomplemented
50#17988813C2218yescomplemented
51#17988807C2218yescomplemented
52#17988795C2218yescomplemented
53#17988749C2218yescomplemented
54#17988743C2218yescomplemented
55#17988741C2218yescomplemented
56#17988724C2218yescomplemented
57#17988694C2218yescomplemented
58#17988656C2218yescomplemented
59C2×#14556523C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556515C2211yescharacteristic
65C2×#14556515C2211yescharacteristic
66C2×#14556512C2211yescharacteristic
67C2×C22⋊#10596831C2211yescharacteristic
68C2×#14556503C2211yescharacteristic
69C2×#14556501C2211yescharacteristic
70C22×#41×C73C2211yescharacteristic
71C23×Q8×C73C2211yescharacteristic
72C2×#137×C73—28no—
73C2×#137×C73C2218yescomplemented
74C22×Q16×C73C2211yescharacteristic
75C22×Q16×C73C2211yescharacteristic
76C22×SD16×C73C2211yescharacteristic
77C22×SD16×C73C2211yescharacteristic
78C22×M16×C73C2211yescharacteristic
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146C2311yescharacteristic
82C22×Dic146C2311yescharacteristic
83C2×Q8×D73—22no—
84C2×Q8×D73—22no—
85C2×Q8×D73—24no—
86C2×Q8×D73—24no—
87C2×Q8×D73—42no—
88C2×Q8×D73—42no—
89C2×Q8×D73C2314yes—
90C2×Q8×D73C2314yes—
91C22×C22⋊D73—21no—
92C22×C22⋊D73D411yescharacteristic
93C22×C4×D73—21no—
94C22×C4×D73—21no—
95C22×C4×D73C2311yescharacteristic
96C2×Dic292—24no—
97C2×Dic292C2314yes—
98C2×#11924018—24no—
99C2×#11924018—24no—
100C2×#11924018—42no—
101C2×#11924018C2314yes—
102C2×#11924018C2314yes—
103C2×#11924018C2314yes—
104Q16×D73—232no—
105C2×#11924016—42no—
106C2×#11924016C2314yes—
107C22×#10596831C2311yescharacteristic
108C22×#10596831C2311yescharacteristic
109C2×C8×D73—24no—
110C2×C8×D73C2314yes—
111#14556589—28no—
112#14556589—22no—
113#14556589C2314yes—
114#14556578—28no—
115#14556578—22no—
116#14556578C2314yes—
117#14556570—28no—
118#14556570—28no—
119#14556570—22no—
120#14556570—22no—
121#14556570C2314yes—
122#14556570C2314yes—
123#14556567—22no—
124#14556567—28no—
125#14556567C2314yes—
126#14556562—28no—
127#14556562—22no—
128#14556562C2314yes—
129Q8×Dic73—22no—
130Q8×Dic73—22no—
131Q8×Dic73C2314yes—
132Q8×Dic73C2314yes—
133C4×C22⋊D73—28no—
134C4×C22⋊D73—28no—
135C4×C22⋊D73D414yes—
136C4×C22⋊D73C2314yes—
137C2×C4⋊Dic73—21no—
138C2×C4⋊Dic73—21no—
139C2×C4⋊Dic73C2311yescharacteristic
140C2×C4⋊Dic73C2311yescharacteristic
141C2×#11924007—21no—
142C2×#11924007—21no—
143C2×#11924007—21no—
144C2×#11924007—21no—
145C2×#11924007—21no—
146C2×#11924007D411yescharacteristic
147C2×C22⋊Dic73—21no—
148C2×C22⋊Dic73—21no—
149C2×C22⋊Dic73—21no—
150C2×C22⋊Dic73—21no—
151C2×C22⋊Dic73—21no—
152C2×C22⋊Dic73D411yescharacteristic
153C2×#11924005—21no—
154C2×#11924005D411yescharacteristic
155C2×C4×Dic73—21no—
156C2×C4×Dic73—21no—
157C2×C4×Dic73C2311yescharacteristic
158#14556523C2314yes—
159#14556520C2314yes—
160#14556516C2314yes—
161#14556516C2314yes—
162#14556515C2314yes—
163#14556515C2314yes—
164#14556515C2314yes—
165#14556512C2314yes—
166C22⋊#10596831C2314yes—
167#14556503C2314yes—
168#14556501C2314yes—
169C2×#41×C73—22no—
170C2×#41×C73—24no—
171C2×#41×C73—42no—
172C2×#41×C73C2314yes—
173C22×Q8×C73—21no—
174C22×Q8×C73—22no—
175C22×Q8×C73—24no—
176C22×Q8×C73—42no—
177C22×Q8×C73C2311yescharacteristic
178C22×Q8×C73C2314yes—
179C22×Q8×C73C2311yescharacteristic
180C22×Q8×C73C2311yescharacteristic
181C22×D4×C73—21no—
182C22×D4×C73C2311yescharacteristic
183C23×C4×C73—21no—
184C23×C4×C73—21no—
185C23×C4×C73C2311yescharacteristic
186#137×C73—232no—
187C2×Q16×C73—24no—
188C2×Q16×C73D418yescomplemented
189C2×Q16×C73C2314yes—
190C2×Q16×C73C2314yes—
191C2×SD16×C73—24no—
192C2×SD16×C73—24no—
193C2×SD16×C73C2314yes—
194C2×SD16×C73C2314yes—
195C2×M16×C73—24no—
196C2×M16×C73C2314yes—
197C22×C8×C73C2311yescharacteristic
198C22×C8×C73C2311yescharacteristic
199C23×D73C2×D411yescharacteristic
200C2×Dic146—22no—
201C2×Dic146—22no—
202C2×Dic146—22no—
203C2×Dic146—22no—
204C2×Dic146—21no—
205C2×Dic146—21no—
206C2×Dic146—24no—
207C2×Dic146—24no—
208C2×Dic146—44no—
209C2×Dic146—44no—
210C2×Dic146C2412yes—
211C2×Dic146C2412yes—
212Q8×D73—28no—
213Q8×D73—28no—
214Q8×D73—44no—
215Q8×D73—44no—
216Q8×D73—48no—
217Q8×D73—48no—
218C2×C22⋊D73—24no—
219C2×C22⋊D73—24no—
220C2×C22⋊D73—44no—
221C2×C22⋊D73C2×D414yes—
222C22×Dic73—21no—
223C22×Dic73—21no—
224C22×Dic73—21no—
225C22×Dic73—21no—
226C22×Dic73C2×D411yescharacteristic
227C22×Dic73C2×D411yescharacteristic
228C22×Dic73C2×D411yescharacteristic
229C2×C4×D73—22no—
230C2×C4×D73—22no—
231C2×C4×D73—24no—
232C2×C4×D73—24no—
233C2×C4×D73—44no—
234C2×C4×D73—44no—
235C2×C4×D73C2×D412yes—
236C2×C4×D73C2412yes—
237Dic292—28no—
238#11924018—28no—
239#11924018—28no—
240#11924018—44no—
241#11924016—44no—
242C2×#10596831—22no—
243C2×#10596831—22no—
244C2×#10596831C2412yes—
245C2×#10596831C2412yes—
246C8×D73—28no—
247C4⋊Dic73—21no—
248C4⋊Dic73—21no—
249C4⋊Dic73—24no—
250C4⋊Dic73—24no—
251C4⋊Dic73C2412yes—
252C4⋊Dic73C2412yes—
253#11924007—24no—
254#11924007—24no—
255#11924007—24no—
256#11924007—24no—
257#11924007—24no—
258#11924007C2×D414yes—
259C22⋊Dic73—24no—
260C22⋊Dic73—24no—
261C22⋊Dic73—24no—
262C22⋊Dic73—24no—
263C22⋊Dic73—24no—
264C22⋊Dic73C2×D414yes—
265#11924005—24no—
266#11924005C2×D414yes—
267C4×Dic73—24no—
268C4×Dic73—24no—
269C4×Dic73C2×D412yes—
270C4×Dic73C2412yes—
271C24×C73—21no—
272C24×C73C2×D411yescharacteristic
273#41×C73—28no—
274#41×C73—44no—
275#41×C73—48no—
276C2×Q8×C73—21no—
277C2×Q8×C73—21no—
278C2×Q8×C73—24no—
279C2×Q8×C73—21no—
280C2×Q8×C73—22no—
281C2×Q8×C73—22no—
282C2×Q8×C73—28no—
283C2×Q8×C73—22no—
284C2×Q8×C73—22no—
285C2×Q8×C73—44no—
286C2×Q8×C73—44no—
287C2×Q8×C73—48no—
288C2×Q8×C73C2×D414yes—
289C2×Q8×C73C2×D414yes—
290C2×Q8×C73C2412yes—
291C2×Q8×C73C2412yes—
292C2×Q8×C73C2412yes—
293C2×D4×C73—24no—
294C2×D4×C73—22no—
295C2×D4×C73—21no—
296C2×D4×C73—22no—
297C2×D4×C73—44no—
298C2×D4×C73C2412yes—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—22no—
302C22×C4×C73—22no—
303C22×C4×C73—21no—
304C22×C4×C73—24no—
305C22×C4×C73—24no—
306C22×C4×C73—44no—
307C22×C4×C73—44no—
308C22×C4×C73C2×D411yescharacteristic
309C22×C4×C73C2×D412yes—
310C22×C4×C73C2412yes—
311C22×C4×C73C2411yescharacteristic
312Q16×C73—28no—
313Q16×C73C2×D4116yescomplemented
314SD16×C73—28no—
315SD16×C73—28no—
316M16×C73—28no—
317C2×C8×C73—22no—
318C2×C8×C73C2×D414yes—
319C2×C8×C73C2412yes—
320C2×C8×C73C2412yes—
321C23×C73—22no—
322C23×C73—22no—
323C23×C73—22no—
324C23×C73—22no—
325C23×C73—42no—
326C23×C73—42no—
327C23×C73—42no—
328C23×C73C22×D412yes—
329C23×C73C22×D411yescharacteristic
330C22×D73—22no—
331C22×D73—22no—
332C22×D73#13714yescomplemented
333C22×D73C22×D412yes—
334Q8×C73—24no—
335Q8×C73—24no—
336Q8×C73—22no—
337Q8×C73—22no—
338Q8×C73—22no—
339Q8×C73—22no—
340Q8×C73—48no—
341Q8×C73—42no—
342Q8×C73C22×D414yes—
343Q8×C73C22×D414yes—
344D4×C73—22no—
345D4×C73—22no—
346D4×C73—48no—
347D4×C73—42no—
348C2×C4×C73—22no—
349C2×C4×C73—24no—
350C2×C4×C73—24no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—24no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—48no—
358C2×C4×C73—48no—
359C2×C4×C73—42no—
360C2×C4×C73C22×D412yes—
361C2×C4×C73C22×D411yescharacteristic
362C2×C4×C73C22×D412yes—
363C2×C4×C73H(5,𝔽2)12yes—
364C2×C4×C73C2511yescharacteristic
365C22⋊D73—28no—
366C22⋊D73—48no—
367C2×Dic73—22no—
368C2×Dic73—22no—
369C2×Dic73—22no—
370C2×Dic73—22no—
371C2×Dic73—22no—
372C2×Dic73—22no—
373C2×Dic73—22no—
374C2×Dic73—42no—
375C2×Dic73—42no—
376C2×Dic73—42no—
377C2×Dic73—42no—
378C2×Dic73C22×D412yes—
379C2×Dic73C22×D412yes—
380C2×Dic73C22×D412yes—
381C4×D73—24no—
382C4×D73—22no—
383C4×D73—22no—
384C4×D73—48no—
385C4×D73—48no—
386Dic146—22no—
387Dic146—22no—
388Dic146—22no—
389Dic146—22no—
390Dic146—48no—
391Dic146—48no—
392Dic146—42no—
393Dic146—42no—
394C8×C73—22no—
395C8×C73C22×D414yes—
396#10596831—22no—
397#10596831—22no—
398C22×C73—22no—
399C22×C73—22no—
400C22×C73—22no—
401C22×C73—44no—
402C22×C73—42no—
403C22×C73—42no—
404C22×C73—42no—
405C22×C73—84no—
406C22×C73D4212yes—
407C22×C73C2×#13712yes—
408C22×C73#57812yes—
409C22×C73C23×D411yescharacteristic
410C2×D73—22no—
411C2×D73—28no—
412C2×D73—22no—
413C2×D73C2×#13714yescomplemented
414C4×C73—24no—
415C4×C73—24no—
416C4×C73—22no—
417C4×C73—42no—
418C4×C73D4212yes—
419C4×C73C23×D411yescharacteristic
420C4×C73C2×H(5,𝔽2)11yescharacteristic
421Dic73—22no—
422Dic73—22no—
423Dic73—22no—
424Dic73—42no—
425Dic73—42no—
426Dic73—42no—
427Dic73—42no—
428C2×#3270—731nomaximal, Sylow
429C2×C73—42no—
430C2×C73—82no—
431C2×C73#327014yescomplemented
432C2×C73C2×D4211yescharacteristic
433C2×C73C22×#13711yescharacteristic
434C2×C73C2×#57811yescharacteristic
435D73—24no—
436C22×#137D7311yescharacteristic, complemented
437C23×Q16—731no—
438C2×D4×Q8—731no—
439C2×#548—731no—
440#3270—7316no—
441C2×#497—731no—
442C2×#470—731no—
443C2×#465—731no—
444C2×#464—731no—
445C2×#462—731no—
446C2×#452—731no—
447C2×#451—731no—
448C2×#451—731no—
449C2×#448—731no—
450C2×#441—731no—
451C2×#435—731no—
452C73C2×#327011yescharacteristic, complemented, Sylow
453C22×#41C2×D7311yescharacteristic
454C23×Q8—731no—
455C23×Q8—731no—
456C23×Q8C2×D7311yescharacteristic
457C2×#137—28no—
458C2×#137C2×D7318yescomplemented
459C22×Q16—731no—
460C22×Q16—731no—
461C22×Q16—731no—
462C22×Q16—738no—
463C22×Q16—731no—
464C22×Q16—1468no—
465C22×Q16C2×D7311yescharacteristic
466C22×Q16C2×D7311yescharacteristic
467C22×SD16—731no—
468C22×SD16C2×D7311yescharacteristic
469C22×SD16C2×D7311yescharacteristic
470C22×M16C2×D7311yescharacteristic
471C23×C8—731no—
472D4×Q8—738no—
473D4×Q8—1464no—
474#548—738no—
475#548—1464no—
476C2×C4⋊Q8—731no—
477C2×C4⋊Q8—1461no—
478C2×#124—731no—
479C2×#124—1461no—
480C2×C22⋊Q8—731no—
481C2×C22⋊Q8—731no—
482C2×C22⋊Q8—731no—
483C2×C22⋊Q8—1461no—
484C2×C22⋊Q8—1461no—
485C2×C22⋊Q8—1461no—
486C2×#121—731no—
487C2×#121—1461no—
488C2×C4×Q8—731no—
489C2×C4×Q8—731no—
490C2×C4×D4—731no—
491C2×C4×D4—1461no—
492C2×C4×D4—1461no—
493#497—738no—
494#470—738no—
495#465—738no—
496#464—738no—
497#462—738no—
498#452—738no—
499#451—738no—
500#451—738no—
501#448—738no—
502#441—738no—
503#435—738no—
504C2×#106—731no—
505C2×C4⋊C8—731no—
506C2×#103—731no—
507C2×#103—731no—
508C2×#103—731no—
509C2×#103—731no—
510C2×#103—731no—
511C2×#102—731no—
512C2×C22⋊C8—731no—
513C2×C22⋊C8—731no—
514C2×#97—731no—
515C2×#41—22no—
516C2×#41—24no—
517C2×#41—42no—
518C2×#41C22×D7314yes—
519C22×Q8—21no—
520C22×Q8—22no—
521C22×Q8—24no—
522C22×Q8—42no—
523C22×Q8—2922no—
524C22×Q8—2922no—
525C22×Q8—734no—
526C22×Q8—734no—
527C22×Q8—731no—
528C22×Q8—731no—
529C22×Q8—1461no—
530C22×Q8—1461no—
531C22×Q8—1464no—
532C22×Q8—1464no—
533C22×Q8—1462no—
534C22×Q8—1462no—
535C22×Q8C22×D7311yescharacteristic
536C22×Q8C22×D7314yes—
537C22×Q8C22×D7311yescharacteristic
538C22×Q8C22×D7311yescharacteristic
539C22×D4—21no—
540C22×D4—731no—
541C22×D4—1461no—
542C22×D4C22×D7311yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—731no—
546C23×C4—1461no—
547C23×C4—1461no—
548C23×C4C22×D7311yescharacteristic
549#137—232no—
550C2×Q16—24no—
551C2×Q16—2922no—
552C2×Q16—734no—
553C2×Q16—734no—
554C2×Q16—734no—
555C2×Q16—734no—
556C2×Q16—1464no—
557C2×Q16—1464no—
558C2×Q16—14632no—
559C2×Q16—1464no—
560C2×Q16C22⋊D7318yescomplemented
561C2×Q16C22×D7314yes—
562C2×Q16C22×D7314yes—
563C2×SD16—24no—
564C2×SD16—24no—
565C2×SD16—2922no—
566C2×SD16—734no—
567C2×SD16C22×D7314yes—
568C2×SD16C22×D7314yes—
569C2×M16—24no—
570C2×M16C22×D7314yes—
571C22×C8—731no—
572C22×C8—731no—
573C22×C8—734no—
574C22×C8—1464no—
575C22×C8C22×D7311yescharacteristic
576C22×C8C22×D7311yescharacteristic
577C4⋊Q8—734no—
578C4⋊Q8—1462no—
579C4⋊Q8—1468no—
580#124—734no—
581#124—1462no—
582#124—1468no—
583C22⋊Q8—734no—
584C22⋊Q8—734no—
585C22⋊Q8—734no—
586C22⋊Q8—1468no—
587C22⋊Q8—1468no—
588C22⋊Q8—1468no—
589C22⋊Q8—1462no—
590C22⋊Q8—1462no—
591C22⋊Q8—1462no—
592#121—734no—
593#121—1462no—
594#121—1468no—
595C4×Q8—734no—
596C4×Q8—734no—
597C4×Q8—1462no—
598C4×Q8—1462no—
599C4×D4—734no—
600C4×D4—734no—
601C4×D4—1468no—
602C4×D4—1468no—
603C2×C4⋊C4—731no—
604C2×C4⋊C4—731no—
605C2×C4⋊C4—731no—
606C2×C4⋊C4—1461no—
607C2×C4⋊C4—1461no—
608C2×C4⋊C4—1461no—
609C2×C4⋊C4—1461no—
610C2×C4⋊C4—1461no—
611C2×C4⋊C4—1461no—
612C2×C4⋊C4—1461no—
613C2×C22⋊C4—731no—
614C2×C22⋊C4—731no—
615C2×C22⋊C4—1461no—
616C2×C22⋊C4—1461no—
617C2×C22⋊C4—1461no—
618C2×C22⋊C4—1461no—
619C2×C22⋊C4—1461no—
620C2×C22⋊C4—1461no—
621C2×C42—731no—
622C2×C42—1461no—
623C2×C42—1461no—
624#106—734no—
625C4⋊C8—734no—
626#103—734no—
627#103—734no—
628#103—734no—
629#103—734no—
630#103—734no—
631#102—734no—
632C22⋊C8—734no—
633C22⋊C8—734no—
634#97—734no—
635C24—21no—
636C24—731no—
637C24D4×D7311yescharacteristic
638#41—28no—
639#41—44no—
640#41—48no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—24no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—28no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—48no—
653C2×Q8—2924no—
654C2×Q8—2924no—
655C2×Q8—2928no—
656C2×Q8—2928no—
657C2×Q8—2924no—
658C2×Q8—2924no—
659C2×Q8—732no—
660C2×Q8—732no—
661C2×Q8—1464no—
662C2×Q8—1464no—
663C2×Q8—1468no—
664C2×Q8—1468no—
665C2×Q8—1462no—
666C2×Q8—1462no—
667C2×Q8—1462no—
668C2×Q8—1462no—
669C2×Q8—1461no—
670C2×Q8—1461no—
671C2×Q8C2×C22⋊D7314yes—
672C2×Q8C2×C22⋊D7314yes—
673C2×Q8C23×D7312yes—
674C2×Q8C23×D7312yes—
675C2×Q8C23×D7312yes—
676C2×D4—24no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—44no—
681C2×D4—2924no—
682C2×D4—734no—
683C2×D4—1464no—
684C2×D4—1464no—
685C2×D4C23×D7312yes—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—2924no—
696C22×C4—2924no—
697C22×C4—731no—
698C22×C4—731no—
699C22×C4—731no—
700C22×C4—732no—
701C22×C4—732no—
702C22×C4—1464no—
703C22×C4—1464no—
704C22×C4—1461no—
705C22×C4—1461no—
706C22×C4—1461no—
707C22×C4—1461no—
708C22×C4—1462no—
709C22×C4—1462no—
710C22×C4D4×D7312yes—
711C22×C4D4×D7311yescharacteristic
712C22×C4C23×D7312yes—
713C22×C4C23×D7311yescharacteristic
714Q16—28no—
715Q16—2924no—
716Q16—1468no—
717Q16—1468no—
718Q16—1468no—
719Q16C2×C22⋊D73116yescomplemented
720SD16—28no—
721SD16—28no—
722SD16—2924no—
723M16—28no—
724C2×C8—22no—
725C2×C8—732no—
726C2×C8—732no—
727C2×C8—1462no—
728C2×C8—1462no—
729C2×C8—1468no—
730C2×C8C2×C22⋊D7314yes—
731C2×C8C23×D7312yes—
732C2×C8C23×D7312yes—
733C4⋊C4—734no—
734C4⋊C4—732no—
735C4⋊C4—732no—
736C4⋊C4—1464no—
737C4⋊C4—1464no—
738C4⋊C4—1464no—
739C4⋊C4—1464no—
740C4⋊C4—1464no—
741C4⋊C4—1464no—
742C4⋊C4—1464no—
743C4⋊C4—1461no—
744C4⋊C4—1461no—
745C22⋊C4—734no—
746C22⋊C4—734no—
747C22⋊C4—1464no—
748C22⋊C4—1464no—
749C22⋊C4—1464no—
750C22⋊C4—1464no—
751C22⋊C4—1464no—
752C22⋊C4—1464no—
753C42—732no—
754C42—732no—
755C42—1464no—
756C42—1464no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—734no—
765C23—732no—
766C23—1462no—
767C23—1462no—
768C23C2×D4×D7312yes—
769C23C2×D4×D7311yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—24no—
773Q8—24no—
774Q8—22no—
775Q8—22no—
776Q8—48no—
777Q8—42no—
778Q8—2928no—
779Q8—2928no—
780Q8—2922no—
781Q8—2922no—
782Q8—1462no—
783Q8—1462no—
784Q8—1462no—
785Q8—1462no—
786Q8C22×C22⋊D7314yes—
787Q8C22×C22⋊D7314yes—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—2928no—
793D4—1468no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—48no—
804C2×C4—48no—
805C2×C4—42no—
806C2×C4—2928no—
807C2×C4—2928no—
808C2×C4—2922no—
809C2×C4—2922no—
810C2×C4—2922no—
811C2×C4—2922no—
812C2×C4—732no—
813C2×C4—732no—
814C2×C4—732no—
815C2×C4—1462no—
816C2×C4—1462no—
817C2×C4—1462no—
818C2×C4—1462no—
819C2×C4—1462no—
820C2×C4—1462no—
821C2×C4—1462no—
822C2×C4—1462no—
823C2×C4—1462no—
824C2×C4—1464no—
825C2×C4C2×D4×D7312yes—
826C2×C4C2×D4×D7311yescharacteristic
827C2×C4C22×C22⋊D7312yes—
828C2×C4#1455663612yes—
829C2×C4C24×D7311yescharacteristic
830C8—22no—
831C8—1462no—
832C8—1462no—
833C8C22×C22⋊D7314yes—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—44no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—84no—
842C22—734no—
843C22—1468no—
844C22—1462no—
845C22—1462no—
846C22D4×C22⋊D7312yes—
847C22#137×D7312yes—
848C22#1798940312yes—
849C22C22×D4×D7311yescharacteristic
850C4—22no—
851C4—24no—
852C4—24no—
853C4—42no—
854C4—2922no—
855C4—2922no—
856C4—2922no—
857C4—2922no—
858C4—1462no—
859C4—1462no—
860C4—1462no—
861C4D4×C22⋊D7312yes—
862C4C23×C22⋊D7311yescharacteristic
863C4C2×#1455663611yescharacteristic
864C2—42no—
865C2—82no—
866C2—1464no—
867C2#2262149514yesdirect product factor
868C2C2×D4×C22⋊D7311yescharacteristic
869C2C2×#137×D7311yescharacteristic
870C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC22×#137×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989244C2
hypercenterC22×#137D73
hypocenterC73C2×#3270
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D73C2semidirect
2. C2×Q8×C22⋊D73C2semidirect
4. #22621495C2direct (N × H)
5. C2×#17988978C2semidirect
6. C2×#17988845C2semidirect
7. C2×#17988813C2semidirect
8. C2×#17988807C2semidirect
9. C2×#17988795C2semidirect
10. C2×#17988749C2semidirect
11. C2×#17988743C2semidirect
12. C2×#17988741C2semidirect
13. C2×#17988724C2semidirect
14. C2×#17988694C2semidirect
15. C2×#17988656C2semidirect
16. C22×#137×C73C2semidirect
24. C2×Q16×D73C22semidirect
28. Q8×C22⋊D73C22semidirect
48. #17988978C22semidirect
49. #17988845C22semidirect
50. #17988813C22semidirect
51. #17988807C22semidirect
52. #17988795C22semidirect
53. #17988749C22semidirect
54. #17988743C22semidirect
55. #17988741C22semidirect
56. #17988724C22semidirect
57. #17988694C22semidirect
58. #17988656C22semidirect
73. C2×#137×C73C22semidirect
188. C2×Q16×C73D4semidirect
313. Q16×C73C2×D4semidirect
332. C22×D73#137semidirect
413. C2×D73C2×#137semidirect
431. C2×C73#3270semidirect
436. C22×#137D73semidirect
452. C73C2×#3270semidirect
458. C2×#137C2×D73semidirect
560. C2×Q16C22⋊D73semidirect
719. Q16C2×C22⋊D73semidirect
867. C2#22621495direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q16×D732
C2×Q8×C22⋊D732
C2×#179892442
#226214952
C2×#179889782
C2×#179888452
C2×#179888132
C2×#179888072
C2×#179887952
C2×#179887492
C2×#179887432
C2×#179887412
C2×#179887242
C2×#179886942
C2×#179886562
C22×#137×C732
C2×#327073