Finite Group Databasebeta

← C2×#11737582 #14222094

Subgroups — C2×#11737582 #14222094

Order 1792.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90489C211yesmaximal, characteristic
2C2×#90316C211yesmaximal, characteristic, complemented
3C2×C7×#450C211yesmaximal, characteristic
4C2×#89990C211yesmaximal, characteristic
5C2×#89934C211yesmaximal, characteristic, complemented
6C2×#89934C211yesmaximal, characteristic, complemented
7C2×#89936C211yesmaximal, characteristic, complemented
8C2×SD16×Dic7C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10#11737582C2116yesmaximal, direct product factor
11C2×#89535C211yesmaximal, characteristic, complemented
12C2×#89538C211yesmaximal, characteristic, complemented
13C2×#89529C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89495C211yesmaximal, characteristic, complemented
16C2×#89492C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Dic7—21no—
22C22×C22⋊Dic7—21no—
23C2×Q8×Dic7C2211yescharacteristic, complemented
24C2×#6507C2211yescharacteristic, complemented
25#90489—24no—
26#90489C2218yes—
27C2×D4×Dic7—21no—
28C2×D4×Dic7—21no—
29C2×D4×Dic7C2211yescharacteristic
30C2×D4×Dic7C2211yescharacteristic
31C2×D4×Dic7C2211yescharacteristic
32C2×D4×Dic7C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C22×#1142C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38#90316—24no—
39#90316C2218yescomplemented
40C2×#6453—21no—
41C2×#6453C2211yescharacteristic, complemented
42C2×#6452—21no—
43C2×#6450C2211yescharacteristic, complemented
44C2×#6442—21no—
45C2×#6442—21no—
46C7×#450C2218yes—
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×#6409C2211yescharacteristic, complemented
51C2×#6409C2211yescharacteristic, complemented
52#89990C2218yes—
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89936C2218yescomplemented
57#89934C2218yescomplemented
58#89934C2218yescomplemented
59SD16×Dic7C2218yescomplemented
60C2×#6392C2211yescharacteristic, complemented
61C2×#6391C2211yescharacteristic, complemented
62C2×#6390C2211yescharacteristic, complemented
63C2×#6390C2211yescharacteristic, complemented
64C2×#6389C2211yescharacteristic, complemented
65C2×Dic7⋊C8C2211yescharacteristic, complemented
66C2×Dic7⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic7C2211yescharacteristic, complemented
68#89817C2218yescomplemented
69C2×#6382C2211yescharacteristic, complemented
70C2×#6381C2211yescharacteristic, complemented
71#89538C2218yescomplemented
72#89535C2218yescomplemented
73#89530C2218yescomplemented
74#89529C2218yescomplemented
75#89495C2218yescomplemented
76#89492C2218yescomplemented
77C2×#3123—71nomaximal, Sylow
78C25×C7—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—24no—
81C22×C7×D4—24no—
82C22×C7×D4—21no—
83C22×C7×D4—22no—
84C22×C7×D4C2314yes—
85C22×C7×D4C2311yescharacteristic
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×Dic7—21no—
89C23×Dic7—21no—
90C23×Dic7—21no—
91C23×Dic7—21no—
92C22×Dic14C2311yescharacteristic
93C2×C7×SD16—24no—
94C2×C7×SD16—24no—
95C2×C7×SD16C2314yes—
96C2×C7×SD16C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C7×C22⋊Q8—22no—
100C7×C22⋊Q8C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—28no—
111C2×C22⋊Dic7—28no—
112C2×C22⋊Dic7D411yescharacteristic
113C2×C22⋊Dic7D411yescharacteristic
114Q8×Dic7—22no—
115Q8×Dic7C2314yescomplemented
116#6507—22no—
117#6507C2314yescomplemented
118D4×Dic7—28no—
119D4×Dic7—28no—
120D4×Dic7—22no—
121D4×Dic7—22no—
122D4×Dic7—22no—
123D4×Dic7—22no—
124D4×Dic7C2314yes—
125D4×Dic7C2314yes—
126D4×Dic7C2314yes—
127D4×Dic7C2314yes—
128C2×#1142—24no—
129C2×#1142—24no—
130C2×#1142C2314yes—
131C2×#1142C2314yes—
132#6489—22no—
133#6489D414yes—
134#6489C2314yes—
135#6489C2314yes—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7D411yescharacteristic
139C2×C4⋊Dic7D411yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2311yescharacteristic
143#6487—22no—
144#6487C2314yes—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157#6453—28no—
158#6453—22no—
159#6453C2314yescomplemented
160#6452—28no—
161#6450—22no—
162#6450C2314yescomplemented
163#6442—28no—
164#6442—28no—
165C7×#102C2314yes—
166C7×#102C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yescomplemented
169#6409C2314yescomplemented
170#6406C2314yes—
171#6406C2314yes—
172C22⋊(C7⋊C8)C2314yes—
173#6392C2314yescomplemented
174#6391C2314yescomplemented
175#6390C2314yescomplemented
176#6390C2314yescomplemented
177#6389C2314yescomplemented
178Dic7⋊C8C2314yescomplemented
179Dic7⋊C8C2314yescomplemented
180C8×Dic7C2314yescomplemented
181#6382C2314yescomplemented
182#6381C2314yescomplemented
183C2×#541—71no—
184C2×#518—71no—
185#3123—716no—
186C2×#485—71no—
187C2×#485—71no—
188C2×#478—71no—
189C2×#478—71no—
190C2×#461—71no—
191C2×#461—71no—
192C2×#450—71no—
193C2×#450D711yescharacteristic
194C2×#440—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—28no—
200C24×C7—21no—
201C24×C7—21no—
202C24×C7—24no—
203C24×C7—82no—
204C24×C7—82no—
205C24×C7C2×D411yescharacteristic
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8C2412yes—
210C2×C7×D4—28no—
211C2×C7×D4—216no—
212C2×C7×D4—28no—
213C2×C7×D4—28no—
214C2×C7×D4—24no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—22no—
218C2×C7×D4—22no—
219C2×C7×D4#4114yes—
220C2×C7×D4#4114yes—
221C2×C7×D4C2412yes—
222C2×C7×D4C2412yes—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2411yescharacteristic
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—24no—
236C22×Dic7—24no—
237C22×Dic7—24no—
238C22×Dic7—24no—
239C22×Dic7—82no—
240C22×Dic7—82no—
241C22×Dic7—82no—
242C22×Dic7—82no—
243C22×Dic7C2×D411yescharacteristic
244C22×Dic7C2×D411yescharacteristic
245C22×Dic7C2×D411yescharacteristic
246C22×Dic7C2×D411yescharacteristic
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—21no—
250C2×Dic14C2412yes—
251C7×SD16—28no—
252C7×SD16—28no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267C22⋊Dic7C2×D414yes—
268C22⋊Dic7C2×D414yes—
269#1142—28no—
270#1142—28no—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—21no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7C2×D414yes—
277C4⋊Dic7C2×D414yes—
278C4⋊Dic7C2412yes—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2×D412yes—
291C4×Dic7C2412yes—
292C4×Dic7C2412yes—
293C2×C7⋊C8—22no—
294C2×C7⋊C8—22no—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297C23×D4C2×D711yescharacteristic
298C22×SD16—71no—
299C22×SD16—71no—
300C22×SD16C2×D711yescharacteristic
301C22×SD16C2×D711yescharacteristic
302#541—78no—
303#541—144no—
304C2×C4⋊Q8—71no—
305C2×#126—141no—
306C2×#126—141no—
307C2×#125—71no—
308C2×#125—141no—
309C2×#125—141no—
310C2×C22⋊Q8—71no—
311C2×C22⋊Q8C2×D711yescharacteristic
312#518—78no—
313#518—144no—
314C2×C4×Q8—71no—
315C2×C4×Q8—71no—
316C2×C4×D4—71no—
317C2×C4×D4—71no—
318C2×C4×D4—71no—
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×C4×D4—141no—
322C2×#117—71no—
323C2×#117—71no—
324C22×C22⋊C4—141no—
325C22×C22⋊C4—141no—
326#485—78no—
327#485—78no—
328#478—78no—
329#478—78no—
330#461—78no—
331#461—78no—
332#450—78no—
333#450C2×D718yes—
334#440—78no—
335#440—78no—
336C4×SD16—78no—
337C4×SD16—78no—
338#433—78no—
339C2×#107—71no—
340C2×#107—71no—
341C2×#106—71no—
342C2×#106—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102C2×D711yescharacteristic
352C2×#102C2×D711yescharacteristic
353C2×C22⋊C8—71no—
354C2×C22⋊C8C2×D711yescharacteristic
355C2×#97—71no—
356C2×C4×C8—71no—
357C23×C7—216no—
358C23×C7—22no—
359C23×C7—24no—
360C23×C7—24no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7—84no—
370C23×C7—84no—
371C23×C7—816no—
372C23×C7C22×D412yes—
373C23×C7C22×D411yescharacteristic
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—42no—
377C7×D4—216no—
378C7×D4—24no—
379C7×D4—24no—
380C7×D4—22no—
381C7×D4—22no—
382C7×D4C2×#4114yes—
383C7×D4C2×#4114yes—
384C2×C4×C7—22no—
385C2×C4×C7—24no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C7C2×#4112yes—
396C2×C4×C7C2511yescharacteristic
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—42no—
408C2×Dic7—42no—
409C2×Dic7—84no—
410C2×Dic7—84no—
411C2×Dic7—84no—
412C2×Dic7—84no—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415C2×Dic7C22×D412yes—
416C2×Dic7C22×D412yes—
417Dic14—22no—
418Dic14—22no—
419Dic14—42no—
420C7×C8—22no—
421C7×C8—22no—
422C7⋊C8—22no—
423C7⋊C8—22no—
424C25—21no—
425C22×Q8—71no—
426C22×Q8C22×D711yescharacteristic
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—21no—
430C22×D4—22no—
431C22×D4C22×D714yes—
432C22×D4C22×D711yescharacteristic
433C22×D4C22×D711yescharacteristic
434C23×C4—141no—
435C23×C4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C23×C4C22×D711yescharacteristic
439C2×SD16—24no—
440C2×SD16—24no—
441C2×SD16—74no—
442C2×SD16—74no—
443C2×SD16—144no—
444C2×SD16—144no—
445C2×SD16C22×D714yes—
446C2×SD16C22×D714yes—
447C22×C8—71no—
448C22×C8—71no—
449C22×C8C22×D711yescharacteristic
450C22×C8C22×D711yescharacteristic
451C4⋊Q8—74no—
452C4⋊Q8—142no—
453#126—148no—
454#126—148no—
455#125—74no—
456#125—142no—
457#125—148no—
458#125—148no—
459C22⋊Q8—22no—
460C22⋊Q8—74no—
461C22⋊Q8—142no—
462C22⋊Q8C22×D714yes—
463C4×Q8—74no—
464C4×Q8—74no—
465C4×Q8—142no—
466C4×Q8—142no—
467C4×D4—74no—
468C4×D4—74no—
469C4×D4—74no—
470C4×D4—74no—
471C4×D4—142no—
472C4×D4—142no—
473C4×D4—142no—
474C4×D4—142no—
475C4×D4—148no—
476C4×D4—148no—
477#117—74no—
478#117—74no—
479#117—74no—
480#117—142no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—71no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4C22×D711yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—71no—
497C2×C22⋊C4—71no—
498C2×C22⋊C4—148no—
499C2×C22⋊C4—148no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C42—71no—
507C2×C42—71no—
508C2×C42—141no—
509C2×C42—141no—
510C2×C42—141no—
511#107—74no—
512#107—74no—
513#106—74no—
514#106—74no—
515C4⋊C8—74no—
516C4⋊C8—74no—
517#103—74no—
518#103—74no—
519#103—74no—
520#103—74no—
521#102—74no—
522#102—74no—
523#102C22×D714yes—
524#102C22×D714yes—
525C22⋊C8—74no—
526C22⋊C8C22×D714yes—
527#97—74no—
528C4×C8—74no—
529C22×C7—22no—
530C22×C7—24no—
531C22×C7—24no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—44no—
535C22×C7—48no—
536C22×C7—48no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—816no—
542C22×C7#52512yes—
543C22×C7#57712yes—
544C22×C7#57712yes—
545C22×C7C23×D411yescharacteristic
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7#52512yes—
550C4×C7C22×#4111yescharacteristic
551C4×C7C22×#4111yescharacteristic
552Dic7—22no—
553Dic7—22no—
554Dic7—22no—
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560C24—28no—
561C24—21no—
562C24—21no—
563C24—24no—
564C24—82no—
565C24—82no—
566C24D4×D711yescharacteristic
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—72no—
571C2×Q8—141no—
572C2×Q8—142no—
573C2×Q8—142no—
574C2×Q8C23×D712yes—
575C2×D4—28no—
576C2×D4—216no—
577C2×D4—28no—
578C2×D4—28no—
579C2×D4—24no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4#115914yes—
585C2×D4#115914yes—
586C2×D4C23×D712yes—
587C2×D4C23×D712yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—71no—
593C22×C4—71no—
594C22×C4—71no—
595C22×C4—71no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—141no—
604C22×C4—562no—
605C22×C4—562no—
606C22×C4—562no—
607C22×C4—562no—
608C22×C4D4×D712yes—
609C22×C4D4×D711yescharacteristic
610C22×C4C23×D712yes—
611C22×C4C23×D711yescharacteristic
612SD16—28no—
613SD16—28no—
614SD16—148no—
615SD16—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—74no—
627C4⋊C4—74no—
628C4⋊C4—72no—
629C4⋊C4—72no—
630C4⋊C4—72no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—141no—
639C4⋊C4—141no—
640C4⋊C4—141no—
641C4⋊C4C23×D712yes—
642C22⋊C4—24no—
643C22⋊C4—74no—
644C22⋊C4—74no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C22⋊C4—144no—
650C22⋊C4—144no—
651C42—72no—
652C42—72no—
653C42—72no—
654C42—72no—
655C42—144no—
656C42—144no—
657C42—144no—
658C2×C7—42no—
659C2×C7—44no—
660C2×C7—44no—
661C2×C7#312314yescomplemented
662C2×C7C2×#52511yescharacteristic
663C2×C7C2×#57711yescharacteristic
664C2×C7C2×#57711yescharacteristic
665C23—216no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—84no—
678C23—84no—
679C23—816no—
680C23C2×D4×D712yes—
681C23C2×D4×D711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—142no—
686Q8—142no—
687Q8—282no—
688D4—216no—
689D4—24no—
690D4—24no—
691D4—22no—
692D4—22no—
693D4C2×#115914yes—
694D4C2×#115914yes—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—72no—
704C2×C4—72no—
705C2×C4—72no—
706C2×C4—72no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4—564no—
720C2×C4—564no—
721C2×C4—564no—
722C2×C4—564no—
723C2×C4C2×D4×D712yes—
724C2×C4C2×D4×D711yescharacteristic
725C2×C4C2×#115912yes—
726C2×C4C2×#115912yes—
727C2×C4C24×D711yescharacteristic
728C8—22no—
729C8—22no—
730C8—142no—
731C8—142no—
732C7C2×#312311yescharacteristic, complemented, Sylow
733C22—22no—
734C22—24no—
735C22—24no—
736C22—22no—
737C22—22no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—48no—
742C22—48no—
743C22—42no—
744C22—42no—
745C22—816no—
746C22#9027712yes—
747C22#9045312yes—
748C22#9046612yes—
749C22C22×D4×D711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—142no—
754C4—142no—
755C4—142no—
756C4—142no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4—282no—
761C4#9027712yes—
762C4C22×#115911yescharacteristic
763C4C22×#115911yescharacteristic
764C2—42no—
765C2—44no—
766C2—44no—
767C2#1173758214yesdirect product factor
768C2C2×#9027711yescharacteristic
769C2C2×#9045311yescharacteristic
770C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#450C2
socleC23×C7C22×D4
prime radicalC23×C7×D4C22
hypercenterC2×#450D7
hypocenterC7C2×#3123
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. C2×#90316C2semidirect
5. C2×#89934C2semidirect
6. C2×#89934C2semidirect
7. C2×#89936C2semidirect
8. C2×SD16×Dic7C2semidirect
9. C2×#89817C2semidirect
10. #11737582C2direct (N × H)
11. C2×#89535C2semidirect
12. C2×#89538C2semidirect
13. C2×#89529C2semidirect
14. C2×#89530C2semidirect
15. C2×#89495C2semidirect
16. C2×#89492C2semidirect
23. C2×Q8×Dic7C22semidirect
24. C2×#6507C22semidirect
39. #90316C22semidirect
41. C2×#6453C22semidirect
43. C2×#6450C22semidirect
50. C2×#6409C22semidirect
51. C2×#6409C22semidirect
56. #89936C22semidirect
57. #89934C22semidirect
58. #89934C22semidirect
59. SD16×Dic7C22semidirect
60. C2×#6392C22semidirect
61. C2×#6391C22semidirect
62. C2×#6390C22semidirect
63. C2×#6390C22semidirect
64. C2×#6389C22semidirect
65. C2×Dic7⋊C8C22semidirect
66. C2×Dic7⋊C8C22semidirect
67. C2×C8×Dic7C22semidirect
68. #89817C22semidirect
69. C2×#6382C22semidirect
70. C2×#6381C22semidirect
71. #89538C22semidirect
72. #89535C22semidirect
73. #89530C22semidirect
74. #89529C22semidirect
75. #89495C22semidirect
76. #89492C22semidirect
115. Q8×Dic7C23semidirect
117. #6507C23semidirect
159. #6453C23semidirect
162. #6450C23semidirect
168. #6409C23semidirect
169. #6409C23semidirect
173. #6392C23semidirect
174. #6391C23semidirect
175. #6390C23semidirect
176. #6390C23semidirect
177. #6389C23semidirect
178. Dic7⋊C8C23semidirect
179. Dic7⋊C8C23semidirect
180. C8×Dic7C23semidirect
181. #6382C23semidirect
182. #6381C23semidirect
661. C2×C7#3123semidirect
732. C7C2×#3123semidirect
767. C2#11737582direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904892
C2×#903162
C2×C7×#4502
C2×#899902
C2×#899342
C2×#899362
C2×SD16×Dic72
C2×#898172
#117375822
C2×#895352
C2×#895382
C2×#895292
C2×#895302
C2×#894952
C2×#894922
C2×#31237