Finite Group Databasebeta

← C2×#22621497 #33961025

Subgroups — C2×#22621497 #33961025

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×#14556621C211yesmaximal, characteristic, complemented
2C23×#11924018C211yesmaximal, characteristic, complemented
3C2×D4×Dic146C211yesmaximal, characteristic, complemented
4#22621497C2116yesmaximal, direct product factor
5C2×#17988982C211yesmaximal, characteristic, complemented
6C2×#17988843C211yesmaximal, characteristic, complemented
7C2×#17988814C211yesmaximal, characteristic, complemented
8C2×#17988806C211yesmaximal, characteristic, complemented
9C2×#17988797C211yesmaximal, characteristic, complemented
10C2×#17988749C211yesmaximal, characteristic, complemented
11C2×#17988743C211yesmaximal, characteristic, complemented
12C2×#17988742C211yesmaximal, characteristic, complemented
13C2×#17988725C211yesmaximal, characteristic, complemented
14C2×#17988692C211yesmaximal, characteristic, complemented
15C2×#17988659C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic
17C23×Dic146C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C2×#14556621—28no—
20C2×#14556621C2218yescomplemented
21C22×#11924018—28no—
22C22×#11924018C2211yescharacteristic
23C22×#11924018C2211yescharacteristic
24C22×#11924018C2211yescharacteristic
25C22×#11924018C2211yescharacteristic
26C22×#11924018C2211yescharacteristic
27C22×#11924018C2211yescharacteristic
28C22×#11924018C2218yescomplemented
29C22×#11924016C2211yescharacteristic
30C22×#11924016C2211yescharacteristic
31C22×#11924016C2211yescharacteristic
32C22×#11924012C2211yescharacteristic
33C23×#10596831C2211yescharacteristic
34D4×Dic146—24no—
35D4×Dic146C2218yescomplemented
36C2×#14556591C2211yescharacteristic
37C2×#14556590—21no—
38C2×#14556570C2211yescharacteristic
39C2×#14556570C2211yescharacteristic
40C2×#14556568—21no—
41C2×#14556568—21no—
42C2×C4×Dic146C2211yescharacteristic
43C2×D4×Dic73—21no—
44#17988982C2218yescomplemented
45#17988843C2218yescomplemented
46#17988814C2218yescomplemented
47#17988806C2218yescomplemented
48#17988797C2218yescomplemented
49#17988749C2218yescomplemented
50#17988743C2218yescomplemented
51#17988742C2218yescomplemented
52#17988725C2218yescomplemented
53#17988692C2218yescomplemented
54#17988659C2218yescomplemented
55C2×#14556522C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556515C2211yescharacteristic
58C2×#14556515C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556512C2211yescharacteristic
63C2×C22⋊#10596831C2211yescharacteristic
64C2×C22⋊#10596831C2211yescharacteristic
65C2×#14556502C2211yescharacteristic
66C22×#41×C73C2211yescharacteristic
67C23×Q8×C73C2211yescharacteristic
68#548×C73—24no—
69#548×C73C2218yes—
70C2×#124×C73—21no—
71C2×#124×C73C2211yescharacteristic
72C2×C22⋊Q8×C73—21no—
73C2×C22⋊Q8×C73C2211yescharacteristic
74C2×#121×C73—21no—
75C2×#121×C73C2211yescharacteristic
76C2×C4×Q8×C73C2211yescharacteristic
77C2×C4×D4×C73—21no—
78C2×C4×D4×C73C2211yescharacteristic
79C22×Dic146—24no—
80C22×Dic146—24no—
81C22×Dic146—21no—
82C22×Dic146—21no—
83C22×Dic146—22no—
84C22×Dic146—22no—
85C22×Dic146—42no—
86C22×Dic146—42no—
87C22×Dic146C2311yescharacteristic
88C22×Dic146C2311yescharacteristic
89C22×Dic146C2314yes—
90C22×Dic146C2314yes—
91C22×Dic146C2311yescharacteristic
92C23×Dic73—21no—
93C23×Dic73—21no—
94#14556621—232no—
95C2×#11924018—24no—
96C2×#11924018—232no—
97C2×#11924018—24no—
98C2×#11924018—24no—
99C2×#11924018—24no—
100C2×#11924018—42no—
101C2×#11924018D418yescomplemented
102C2×#11924018C2314yes—
103C2×#11924018C2314yes—
104C2×#11924018C2314yes—
105C2×#11924018C2314yes—
106C2×#11924018C2314yes—
107C2×#11924018C2314yes—
108C2×#11924016—24no—
109C2×#11924016—24no—
110C2×#11924016—42no—
111C2×#11924016C2314yes—
112C2×#11924016C2314yes—
113C2×#11924016C2314yes—
114C2×#11924012—24no—
115C2×#11924012C2314yes—
116C22×#10596831—24no—
117C22×#10596831C2311yescharacteristic
118C22×#10596831C2311yescharacteristic
119C22×#10596831C2314yes—
120C22×#10596831C2311yescharacteristic
121C22×#10596831C2311yescharacteristic
122#14556591—22no—
123#14556591C2314yes—
124#14556590—28no—
125#14556570—22no—
126#14556570—22no—
127#14556570C2314yes—
128#14556570C2314yes—
129#14556568—28no—
130#14556568—28no—
131C4×Dic146—22no—
132C4×Dic146C2314yes—
133D4×Dic73—28no—
134C2×C4⋊Dic73—21no—
135C2×C4⋊Dic73—21no—
136C2×C4⋊Dic73C2311yescharacteristic
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×C22⋊Dic73—21no—
141C2×C22⋊Dic73—21no—
142C2×C4×Dic73—21no—
143#14556522C2314yes—
144C4⋊#10596831C2314yes—
145#14556515C2314yes—
146#14556515C2314yes—
147#14556514C2314yes—
148#14556514C2314yes—
149#14556514C2314yes—
150#14556512C2314yes—
151C22⋊#10596831C2314yes—
152C22⋊#10596831C2314yes—
153#14556502C2314yes—
154C2×#41×C73—22no—
155C2×#41×C73—24no—
156C2×#41×C73—42no—
157C2×#41×C73C2314yes—
158C22×Q8×C73—21no—
159C22×Q8×C73—22no—
160C22×Q8×C73—24no—
161C22×Q8×C73—42no—
162C22×Q8×C73C2311yescharacteristic
163C22×Q8×C73C2314yes—
164C22×Q8×C73C2311yescharacteristic
165C22×D4×C73—21no—
166C22×D4×C73—21no—
167C22×D4×C73D411yescharacteristic
168C22×D4×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73—21no—
171C23×C4×C73C2311yescharacteristic
172C23×C4×C73C2311yescharacteristic
173#124×C73—28no—
174#124×C73—22no—
175#124×C73C2314yes—
176C22⋊Q8×C73—22no—
177C22⋊Q8×C73—28no—
178C22⋊Q8×C73C2314yes—
179#121×C73—28no—
180#121×C73—22no—
181#121×C73C2314yes—
182C4×Q8×C73—22no—
183C4×Q8×C73C2314yes—
184C4×D4×C73—28no—
185C4×D4×C73D414yes—
186C4×D4×C73C2314yes—
187C2×C4⋊C4×C73—21no—
188C2×C4⋊C4×C73—21no—
189C2×C4⋊C4×C73D411yescharacteristic
190C2×C4⋊C4×C73C2311yescharacteristic
191C2×C22⋊C4×C73—21no—
192C2×C22⋊C4×C73—21no—
193C2×C22⋊C4×C73—21no—
194C2×C22⋊C4×C73—21no—
195C2×C22⋊C4×C73D411yescharacteristic
196C2×C22⋊C4×C73D411yescharacteristic
197C2×C42×C73—21no—
198C2×C42×C73C2311yescharacteristic
199C2×Dic146—21no—
200C2×Dic146—22no—
201C2×Dic146—22no—
202C2×Dic146—22no—
203C2×Dic146—22no—
204C2×Dic146—22no—
205C2×Dic146—28no—
206C2×Dic146—28no—
207C2×Dic146—24no—
208C2×Dic146—24no—
209C2×Dic146—21no—
210C2×Dic146—21no—
211C2×Dic146—44no—
212C2×Dic146—44no—
213C2×Dic146—48no—
214C2×Dic146—48no—
215C2×Dic146—44no—
216C2×Dic146—44no—
217C2×Dic146C2×D414yes—
218C2×Dic146C2412yes—
219C2×Dic146C2412yes—
220C2×Dic146C2412yes—
221C22×Dic73—21no—
222C22×Dic73—21no—
223C22×Dic73—21no—
224C22×Dic73—21no—
225C22×Dic73—24no—
226C22×Dic73—24no—
227C22×Dic73—44no—
228C22×Dic73—44no—
229#11924018—28no—
230#11924018—28no—
231#11924018—28no—
232#11924018—28no—
233#11924018—44no—
234#11924018C2×D4116yescomplemented
235#11924016—28no—
236#11924016—28no—
237#11924016—44no—
238#11924012—28no—
239C2×#10596831—22no—
240C2×#10596831—22no—
241C2×#10596831—22no—
242C2×#10596831—28no—
243C2×#10596831C2×D414yes—
244C2×#10596831C2412yes—
245C2×#10596831C2412yes—
246C2×#10596831C2412yes—
247C2×#10596831C2412yes—
248C4⋊Dic73—24no—
249C4⋊Dic73—24no—
250C4⋊Dic73—21no—
251C4⋊Dic73C2412yes—
252#11924007—24no—
253#11924007—24no—
254#11924007—24no—
255C22⋊Dic73—24no—
256C22⋊Dic73—24no—
257C4×Dic73—24no—
258C24×C73—21no—
259C24×C73C2×D411yescharacteristic
260C24×C73C2×D411yescharacteristic
261#41×C73—28no—
262#41×C73—44no—
263#41×C73—48no—
264C2×Q8×C73—21no—
265C2×Q8×C73—24no—
266C2×Q8×C73—21no—
267C2×Q8×C73—22no—
268C2×Q8×C73—28no—
269C2×Q8×C73—22no—
270C2×Q8×C73—22no—
271C2×Q8×C73—44no—
272C2×Q8×C73—44no—
273C2×Q8×C73—48no—
274C2×Q8×C73C2×D414yes—
275C2×Q8×C73C2412yes—
276C2×Q8×C73C2412yes—
277C2×D4×C73—24no—
278C2×D4×C73—24no—
279C2×D4×C73—24no—
280C2×D4×C73—22no—
281C2×D4×C73—21no—
282C2×D4×C73—22no—
283C2×D4×C73—44no—
284C2×D4×C73—44no—
285C2×D4×C73C2×D414yes—
286C2×D4×C73C2412yes—
287C22×C4×C73—21no—
288C22×C4×C73—22no—
289C22×C4×C73—22no—
290C22×C4×C73—22no—
291C22×C4×C73—22no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—24no—
295C22×C4×C73—24no—
296C22×C4×C73—44no—
297C22×C4×C73—44no—
298C22×C4×C73C2×D411yescharacteristic
299C22×C4×C73C2×D411yescharacteristic
300C22×C4×C73C2×D411yescharacteristic
301C22×C4×C73C2×D411yescharacteristic
302C22×C4×C73C2×D412yes—
303C22×C4×C73C2×D412yes—
304C22×C4×C73C2412yes—
305C22×C4×C73C2412yes—
306C22×C4×C73C2411yescharacteristic
307C4⋊C4×C73—24no—
308C4⋊C4×C73—24no—
309C4⋊C4×C73—21no—
310C4⋊C4×C73C2×D414yes—
311C4⋊C4×C73C2412yes—
312C22⋊C4×C73—24no—
313C22⋊C4×C73—24no—
314C22⋊C4×C73—24no—
315C22⋊C4×C73—24no—
316C22⋊C4×C73C2×D414yes—
317C22⋊C4×C73C2×D414yes—
318C42×C73—24no—
319C42×C73C2×D412yes—
320C42×C73C2412yes—
321C23×C73—22no—
322C23×C73—22no—
323C23×C73—22no—
324C23×C73—22no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—42no—
328C23×C73—42no—
329C23×C73—42no—
330C23×C73#13714yescomplemented
331C23×C73C22×D412yes—
332C23×C73C22×D412yes—
333C23×C73C22×D411yescharacteristic
334Q8×C73—24no—
335Q8×C73—22no—
336Q8×C73—22no—
337Q8×C73—22no—
338Q8×C73—48no—
339Q8×C73—42no—
340Q8×C73C22×D414yes—
341D4×C73—28no—
342D4×C73—22no—
343D4×C73—22no—
344D4×C73—48no—
345D4×C73—48no—
346D4×C73—42no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—24no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—24no—
354C2×C4×C73—24no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—48no—
362C2×C4×C73—48no—
363C2×C4×C73—42no—
364C2×C4×C73—42no—
365C2×C4×C73C22×D412yes—
366C2×C4×C73C22×D412yes—
367C2×C4×C73C22×D412yes—
368C2×C4×C73C22×D412yes—
369C2×C4×C73C22×D412yes—
370C2×C4×C73C22×D411yescharacteristic
371C2×C4×C73H(5,𝔽2)12yes—
372C2×C4×C73C2511yescharacteristic
373C2×Dic73—24no—
374C2×Dic73—22no—
375C2×Dic73—22no—
376C2×Dic73—22no—
377C2×Dic73—22no—
378C2×Dic73—48no—
379C2×Dic73—48no—
380C2×Dic73—42no—
381C2×Dic73—42no—
382C2×Dic73—42no—
383Dic146—24no—
384Dic146—22no—
385Dic146—22no—
386Dic146—22no—
387Dic146—22no—
388Dic146—22no—
389Dic146—48no—
390Dic146—48no—
391Dic146—42no—
392Dic146—42no—
393Dic146C22×D414yes—
394#10596831—22no—
395#10596831—22no—
396#10596831—22no—
397#10596831C22×D414yes—
398C22×C73—22no—
399C22×C73—28no—
400C22×C73—22no—
401C22×C73—22no—
402C22×C73—22no—
403C22×C73—22no—
404C22×C73—44no—
405C22×C73—42no—
406C22×C73—42no—
407C22×C73—42no—
408C22×C73—84no—
409C22×C73D4212yes—
410C22×C73C2×#13712yes—
411C22×C73C2×#13714yescomplemented
412C22×C73#57812yes—
413C22×C73C23×D411yescharacteristic
414C4×C73—22no—
415C4×C73—22no—
416C4×C73—24no—
417C4×C73—22no—
418C4×C73—22no—
419C4×C73—42no—
420C4×C73—42no—
421C4×C73D4212yes—
422C4×C73C23×D411yescharacteristic
423C4×C73C2×H(5,𝔽2)11yescharacteristic
424Dic73—24no—
425Dic73—42no—
426Dic73—42no—
427Dic73—42no—
428C2×#3270—731nomaximal, Sylow
429C2×C73—24no—
430C2×C73—42no—
431C2×C73—82no—
432C2×C73#327014yescomplemented
433C2×C73C2×D4211yescharacteristic
434C2×C73C22×#13711yescharacteristic
435C2×C73C2×#57811yescharacteristic
436C22×#137—731no—
437C23×Q16—731no—
438C2×D4×Q8—731no—
439C2×#548D7311yescharacteristic
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—738no—
458C2×#137—1468no—
459C22×Q16—731no—
460C22×Q16—731no—
461C22×Q16—731no—
462C22×Q16—731no—
463C22×Q16—731no—
464C22×Q16—731no—
465C22×Q16—738no—
466C22×Q16—1468no—
467C22×SD16—731no—
468C22×SD16—731no—
469C22×SD16—731no—
470C22×M16—731no—
471C23×C8—731no—
472D4×Q8—738no—
473D4×Q8—1464no—
474#548—24no—
475#548C2×D7318yes—
476C2×C4⋊Q8—731no—
477C2×C4⋊Q8—1461no—
478C2×#124—21no—
479C2×#124C2×D7311yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8—731no—
482C2×C22⋊Q8—731no—
483C2×C22⋊Q8—1461no—
484C2×C22⋊Q8—1461no—
485C2×C22⋊Q8C2×D7311yescharacteristic
486C2×#121—21no—
487C2×#121C2×D7311yescharacteristic
488C2×C4×Q8—731no—
489C2×C4×Q8C2×D7311yescharacteristic
490C2×C4×D4—21no—
491C2×C4×D4—1461no—
492C2×C4×D4C2×D7311yescharacteristic
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—731no—
530C22×Q8—1464no—
531C22×Q8—1464no—
532C22×Q8—1461no—
533C22×Q8—1461no—
534C22×Q8—1462no—
535C22×Q8—1462no—
536C22×Q8C22×D7311yescharacteristic
537C22×Q8C22×D7314yes—
538C22×Q8C22×D7311yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C22⋊D7311yescharacteristic
542C22×D4C22×D7311yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—1461no—
546C23×C4—1461no—
547C23×C4C22×D7311yescharacteristic
548C23×C4C22×D7311yescharacteristic
549#137—14632no—
550C2×Q16—2922no—
551C2×Q16—734no—
552C2×Q16—738no—
553C2×Q16—734no—
554C2×Q16—734no—
555C2×Q16—734no—
556C2×Q16—734no—
557C2×Q16—734no—
558C2×Q16—1464no—
559C2×Q16—14632no—
560C2×Q16—1464no—
561C2×Q16—1464no—
562C2×Q16—1464no—
563C2×SD16—2922no—
564C2×SD16—734no—
565C2×SD16—734no—
566C2×SD16—734no—
567C2×SD16—1464no—
568C2×SD16—1464no—
569C2×M16—734no—
570C2×M16—1464no—
571C22×C8—731no—
572C22×C8—731no—
573C22×C8—734no—
574C22×C8—731no—
575C22×C8—731no—
576C22×C8—1464no—
577C4⋊Q8—734no—
578C4⋊Q8—1468no—
579C4⋊Q8—1462no—
580#124—28no—
581#124—22no—
582#124C22×D7314yes—
583C22⋊Q8—22no—
584C22⋊Q8—28no—
585C22⋊Q8—734no—
586C22⋊Q8—734no—
587C22⋊Q8—1462no—
588C22⋊Q8—1462no—
589C22⋊Q8—1468no—
590C22⋊Q8—1468no—
591C22⋊Q8C22×D7314yes—
592#121—28no—
593#121—22no—
594#121C22×D7314yes—
595C4×Q8—22no—
596C4×Q8—734no—
597C4×Q8—1462no—
598C4×Q8C22×D7314yes—
599C4×D4—28no—
600C4×D4—1468no—
601C4×D4C22⋊D7314yes—
602C4×D4C22×D7314yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
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⋊C4C22⋊D7311yescharacteristic
612C2×C4⋊C4C22×D7311yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—1461no—
618C2×C22⋊C4—1461no—
619C2×C22⋊C4C22⋊D7311yescharacteristic
620C2×C22⋊C4C22⋊D7311yescharacteristic
621C2×C42—21no—
622C2×C42—1461no—
623C2×C42C22×D7311yescharacteristic
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—
636C24C2×C22⋊D7311yescharacteristic
637C24C2×C22⋊D7311yescharacteristic
638#41—28no—
639#41—44no—
640#41—48no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—28no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—44no—
649C2×Q8—44no—
650C2×Q8—48no—
651C2×Q8—2928no—
652C2×Q8—2928no—
653C2×Q8—2924no—
654C2×Q8—2924no—
655C2×Q8—2924no—
656C2×Q8—2924no—
657C2×Q8—734no—
658C2×Q8—732no—
659C2×Q8—732no—
660C2×Q8—732no—
661C2×Q8—1468no—
662C2×Q8—1468no—
663C2×Q8—1462no—
664C2×Q8—1462no—
665C2×Q8—1462no—
666C2×Q8—1462no—
667C2×Q8—1461no—
668C2×Q8—1461no—
669C2×Q8—1464no—
670C2×Q8—1464no—
671C2×Q8—1461no—
672C2×Q8—1462no—
673C2×Q8D4×D7314yes—
674C2×Q8C23×D7312yes—
675C2×Q8C23×D7312yes—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4C2×C22⋊D7314yes—
685C2×D4C23×D7312yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—24no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—2924no—
698C22×C4—2924no—
699C22×C4—1464no—
700C22×C4—1464no—
701C22×C4—1461no—
702C22×C4—1461no—
703C22×C4—1461no—
704C22×C4—1461no—
705C22×C4C2×C22⋊D7312yes—
706C22×C4C2×C22⋊D7312yes—
707C22×C4C2×C22⋊D7311yescharacteristic
708C22×C4C2×C22⋊D7311yescharacteristic
709C22×C4C2×C22⋊D7311yescharacteristic
710C22×C4C2×C22⋊D7311yescharacteristic
711C22×C4C23×D7312yes—
712C22×C4C23×D7312yes—
713C22×C4C23×D7311yescharacteristic
714Q16—2924no—
715Q16—7316no—
716Q16—1468no—
717Q16—1468no—
718Q16—1468no—
719Q16—1468no—
720SD16—2924no—
721SD16—1468no—
722SD16—1468no—
723M16—1468no—
724C2×C8—734no—
725C2×C8—732no—
726C2×C8—732no—
727C2×C8—732no—
728C2×C8—732no—
729C2×C8—1468no—
730C2×C8—1462no—
731C2×C8—1462no—
732C2×C8—1462no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—732no—
737C4⋊C4—1464no—
738C4⋊C4—1464no—
739C4⋊C4—1464no—
740C4⋊C4—1461no—
741C4⋊C4—1464no—
742C4⋊C4—1464no—
743C4⋊C4C2×C22⋊D7314yes—
744C4⋊C4C23×D7312yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—1464no—
750C22⋊C4—1464no—
751C22⋊C4C2×C22⋊D7314yes—
752C22⋊C4C2×C22⋊D7314yes—
753C42—24no—
754C42—1464no—
755C42C2×C22⋊D7312yes—
756C42C23×D7312yes—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23#1455662114yescomplemented
767C23C22×C22⋊D7312yes—
768C23C22×C22⋊D7312yes—
769C23C22×C22⋊D7311yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—48no—
775Q8—42no—
776Q8—2928no—
777Q8—2928no—
778Q8—2922no—
779Q8—2922no—
780Q8—734no—
781Q8—1462no—
782Q8—1462no—
783Q8—1462no—
784Q8—1462no—
785Q8—1462no—
786Q8—1464no—
787Q8C2×D4×D7314yes—
788D4—28no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—42no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—2922no—
813C2×C4—2922no—
814C2×C4—2922no—
815C2×C4—2928no—
816C2×C4—2928no—
817C2×C4—1462no—
818C2×C4—1462no—
819C2×C4—1462no—
820C2×C4—1462no—
821C2×C4—1464no—
822C2×C4C2×D4×D7312yes—
823C2×C4C22×C22⋊D7312yes—
824C2×C4C22×C22⋊D7312yes—
825C2×C4C22×C22⋊D7312yes—
826C2×C4C22×C22⋊D7312yes—
827C2×C4C22×C22⋊D7311yescharacteristic
828C2×C4#1455663612yes—
829C2×C4C24×D7311yescharacteristic
830C8—734no—
831C8—1462no—
832C8—1462no—
833C8—1462no—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—84no—
845C22D4×C22⋊D7312yes—
846C22C2×#1455662112yes—
847C22C2×#1455662114yescomplemented
848C22#1798940212yes—
849C22C23×C22⋊D7311yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—2922no—
858C4—2922no—
859C4—2922no—
860C4—1464no—
861C4D4×C22⋊D7312yes—
862C4C22×D4×D7311yescharacteristic
863C4C2×#1455663611yescharacteristic
864C2—24no—
865C2—42no—
866C2—82no—
867C2#2262149714yesdirect product factor
868C2C2×D4×C22⋊D7311yescharacteristic
869C2C22×#1455662111yescharacteristic
870C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
Fitting, prime radicalC2×#548×C73C2
socleC23×C73C22×D4
hypercenterC2×#548D73
hypocenterC73C2×#3270
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556621C2semidirect
2. C23×#11924018C2semidirect
3. C2×D4×Dic146C2semidirect
4. #22621497C2direct (N × H)
5. C2×#17988982C2semidirect
6. C2×#17988843C2semidirect
7. C2×#17988814C2semidirect
8. C2×#17988806C2semidirect
9. C2×#17988797C2semidirect
10. C2×#17988749C2semidirect
11. C2×#17988743C2semidirect
12. C2×#17988742C2semidirect
13. C2×#17988725C2semidirect
14. C2×#17988692C2semidirect
15. C2×#17988659C2semidirect
20. C2×#14556621C22semidirect
28. C22×#11924018C22semidirect
35. D4×Dic146C22semidirect
44. #17988982C22semidirect
45. #17988843C22semidirect
46. #17988814C22semidirect
47. #17988806C22semidirect
48. #17988797C22semidirect
49. #17988749C22semidirect
50. #17988743C22semidirect
51. #17988742C22semidirect
52. #17988725C22semidirect
53. #17988692C22semidirect
54. #17988659C22semidirect
101. C2×#11924018D4semidirect
234. #11924018C2×D4semidirect
330. C23×C73#137semidirect
411. C22×C73C2×#137semidirect
432. C2×C73#3270semidirect
452. C73C2×#3270semidirect
766. C23#14556621semidirect
847. C22C2×#14556621semidirect
867. C2#22621497direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145566212
C23×#119240182
C2×D4×Dic1462
#226214972
C2×#179889822
C2×#179888432
C2×#179888142
C2×#179888062
C2×#179887972
C2×#179887492
C2×#179887432
C2×#179887422
C2×#179887252
C2×#179886922
C2×#179886592
C2×#548×C732
C2×#327073