Finite Group Databasebeta

← C2×#11738275 #14232370

Subgroups — C2×#11738275 #14232370

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90326C211yesmaximal, characteristic, complemented
2C2×#90305C211yesmaximal, characteristic
3C2×C7×#468C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×#89936C211yesmaximal, characteristic, complemented
6C2×#89899C211yesmaximal, characteristic, complemented
7C2×#89893C211yesmaximal, characteristic, complemented
8C2×#89817C211yesmaximal, characteristic, complemented
9C2×#89805C211yesmaximal, characteristic, complemented
10#11738275C2116yesmaximal, direct product factor
11C2×D7×#107C211yesmaximal, characteristic, complemented
12C2×#89648C211yesmaximal, characteristic, complemented
13C2×#89581C211yesmaximal, characteristic, complemented
14C2×#89571C211yesmaximal, characteristic, complemented
15C2×#89549C211yesmaximal, characteristic, complemented
16C2×#89531C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#121C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6501—21no—
24C2×#6501C2211yescharacteristic
25C2×#6498—21no—
26C2×D4×Dic7C2211yescharacteristic
27C2×C4×C22⋊D7C2211yescharacteristic
28C2×#6489C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90326—24no—
32#90326C2218yescomplemented
33#90305—24no—
34#90305C2218yes—
35C2×#6460—21no—
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6453C2211yescharacteristic
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×(C22⋊D7)⋊C4—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×#6442—21no—
44C2×#6441—21no—
45C7×#468C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89943C2218yescomplemented
55#89936C2218yescomplemented
56#89899C2218yescomplemented
57#89893C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6389C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65#89817C2218yescomplemented
66#89805C2218yescomplemented
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71D7×#107C2218yescomplemented
72#89648C2218yescomplemented
73#89581C2218yescomplemented
74#89571C2218yescomplemented
75#89549C2218yescomplemented
76#89531C2218yescomplemented
77C2×#3346—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7D411yescharacteristic
84C23×Dic7—21no—
85C23×Dic7—21no—
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7C2311yescharacteristic
89C22×Dic14—21no—
90C2×C7×SD16—24no—
91C2×C7×SD16C2314yes—
92C2×C7×M16—24no—
93C2×C7×M16C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×C22⋊Q8—22no—
97C7×C22⋊Q8C2314yes—
98C7×#121—22no—
99C7×#121C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7D411yescharacteristic
109#6509—22no—
110#6509C2314yes—
111Q8×Dic7—22no—
112Q8×Dic7C2314yes—
113#6501—28no—
114#6501—22no—
115#6501C2314yes—
116#6498—28no—
117D4×Dic7—22no—
118D4×Dic7C2314yes—
119C4×C22⋊D7D414yes—
120C4×C22⋊D7C2314yes—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4D411yescharacteristic
123#6489—22no—
124#6489C2314yes—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—22no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2314yes—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4D411yescharacteristic
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×C8×D7—24no—
146C2×C8×D7C2314yes—
147#6460—28no—
148D7×C4⋊C4—22no—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151D7×C4⋊C4C2314yes—
152#6453—22no—
153#6453C2314yes—
154#6452—28no—
155#6451—22no—
156#6451C2314yes—
157(C22⋊D7)⋊C4—28no—
158(C22⋊D7)⋊C4—28no—
159#6442—28no—
160#6441—28no—
161C7×#107C2314yes—
162C7×#103C2314yes—
163C7×#102C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6406C2314yes—
167#6406C2314yes—
168C22⋊(C7⋊C8)C2314yes—
169(C2×D7)⋊C8C2314yes—
170#6392C2314yes—
171#6392C2314yes—
172#6391C2314yes—
173#6391C2314yes—
174#6389C2314yes—
175Dic7⋊C8C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#554—71no—
181C2×#553—71no—
182#3346—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#481—71no—
186C2×#485—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#474—71no—
190C2×#468D711yescharacteristic, complemented
191C2×#465—71no—
192C2×#440—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#107—71no—
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C23×D7C2×D411yescharacteristic
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C2×C7×D4—24no—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—82no—
208C2×C7×D4C2412yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2411yescharacteristic
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7C2×D414yes—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—24no—
227C22×Dic7—24no—
228C22×Dic7—82no—
229C22×Dic7—82no—
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C2×C4×D7—22no—
234C2×C4×D7—22no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—82no—
238C2×C4×D7—82no—
239C2×C4×D7C2×D412yes—
240C2×C4×D7C2412yes—
241C2×Dic14—24no—
242C2×Dic14—82no—
243C7×SD16—28no—
244C7×M16—28no—
245C2×C7×C8—22no—
246C2×C7×C8#4114yes—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C22⋊Dic7—24no—
257C22⋊Dic7—24no—
258C22⋊Dic7—24no—
259C22⋊Dic7C2×D414yes—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4C2×D414yes—
262C4⋊Dic7—21no—
263C4⋊Dic7—24no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—24no—
268C4⋊Dic7—24no—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D412yes—
282C4×Dic7C2412yes—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287C8×D7—28no—
288C22×SD16C2×D711yescharacteristic
289C22×M16C2×D711yescharacteristic
290C23×C8—71no—
291#554—78no—
292#554—144no—
293#553—78no—
294#553—144no—
295C2×C4⋊Q8—71no—
296C2×#126—141no—
297C2×#125—71no—
298C2×#125—141no—
299C2×#123—141no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—141no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8C2×D711yescharacteristic
304C2×#121—71no—
305C2×#121—141no—
306C2×#121C2×D711yescharacteristic
307C2×C4×Q8—71no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—141no—
311C2×C4×D4—141no—
312C2×#117—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4—71no—
315C22×C4⋊C4—71no—
316#501—78no—
317#485—78no—
318#484—78no—
319#481—78no—
320#480—78no—
321#479—78no—
322#474—78no—
323#468C2×D718yescomplemented
324#465—78no—
325#440—78no—
326#435—78no—
327#428—78no—
328C2×#107—71no—
329C2×#107—71no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—78no—
334C2×#107C2×D711yescharacteristic
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×C4⋊C8—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103C2×D711yescharacteristic
342C2×#102—71no—
343C2×#102—71no—
344C2×#102C2×D711yescharacteristic
345C2×C22⋊C8—71no—
346C2×C22⋊C8—71no—
347C2×#97—71no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7C22×D412yes—
356C23×C7C22×D411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7#13714yes—
360C22×D7C22×D412yes—
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—42no—
364C7×D4—22no—
365C7×D4—22no—
366C7×D4—42no—
367C7×D4—84no—
368C2×C4×C7—22no—
369C2×C4×C7—24no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D411yescharacteristic
380C2×C4×C7C2×#4112yes—
381C2×C4×C72−1+412yes—
382C2×C4×C7C2511yescharacteristic
383C22⋊D7—28no—
384C22⋊D7—48no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—84no—
397C2×Dic7—84no—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C4×D7—24no—
402C4×D7—22no—
403C4×D7—22no—
404C4×D7—84no—
405C4×D7—84no—
406Dic14—84no—
407C7×C8—22no—
408C7×C8C2×#4114yes—
409C7⋊C8—22no—
410C7⋊C8—22no—
411C22×Q8—141no—
412C22×Q8C22×D711yescharacteristic
413C22×D4—21no—
414C22×D4—71no—
415C22×D4—141no—
416C22×D4C22×D711yescharacteristic
417C23×C4—71no—
418C23×C4—141no—
419C23×C4—141no—
420C23×C4—141no—
421C23×C4—141no—
422C23×C4C22×D711yescharacteristic
423C2×SD16—24no—
424C2×SD16C22×D714yes—
425C2×M16—24no—
426C2×M16C22×D714yes—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8—74no—
430C22×C8—144no—
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D711yescharacteristic
433C4⋊Q8—74no—
434C4⋊Q8—142no—
435#126—148no—
436#125—74no—
437#125—142no—
438#125—148no—
439#123—148no—
440C22⋊Q8—22no—
441C22⋊Q8—74no—
442C22⋊Q8—148no—
443C22⋊Q8—148no—
444C22⋊Q8—142no—
445C22⋊Q8C22×D714yes—
446#121—22no—
447#121—74no—
448#121—142no—
449#121—148no—
450#121C22×D714yes—
451C4×Q8—74no—
452C4×Q8—142no—
453C4×D4—74no—
454C4×D4—74no—
455C4×D4—74no—
456C4×D4—142no—
457C4×D4—148no—
458C4×D4—148no—
459#117—74no—
460#117—142no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—71no—
463C2×C4⋊C4—71no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—142no—
471C2×C4⋊C4—142no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—142no—
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—71no—
486C2×C22⋊C4—71no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C42—71no—
492C2×C42—141no—
493C2×C42—141no—
494#107—74no—
495#107—74no—
496#107—74no—
497#107—74no—
498#107—74no—
499#107C22×D714yes—
500#106—74no—
501#106—74no—
502#106—74no—
503C4⋊C8—74no—
504#103—74no—
505#103—74no—
506#103C22×D714yes—
507#102—74no—
508#102—74no—
509#102C22×D714yes—
510C22⋊C8—74no—
511C22⋊C8—74no—
512#97—74no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—22no—
516C22×C7—44no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—84no—
521C22×C7#54712yes—
522C22×C7C2×#13712yes—
523C22×C7#57612yes—
524C22×C7C23×D411yescharacteristic
525C2×D7—28no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7C2×#13714yes—
529C4×C7—22no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7#54712yes—
534C4×C7C22×#4111yescharacteristic
535C4×C7C2×2−1+411yescharacteristic
536Dic7—22no—
537Dic7—22no—
538Dic7—22no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—21no—
544C24—71no—
545C24D4×D711yescharacteristic
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—144no—
550C2×Q8—562no—
551C2×Q8C23×D712yes—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—74no—
557C2×D4—82no—
558C2×D4—144no—
559C2×D4—144no—
560C2×D4—284no—
561C2×D4C23×D712yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—71no—
568C22×C4—71no—
569C22×C4—71no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—144no—
573C22×C4—144no—
574C22×C4—144no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—144no—
582C22×C4—562no—
583C22×C4—562no—
584C22×C4—562no—
585C22×C4—562no—
586C22×C4D4×D712yes—
587C22×C4D4×D711yescharacteristic
588C22×C4C23×D712yes—
589C22×C4C23×D711yescharacteristic
590SD16—28no—
591M16—28no—
592C2×C8—22no—
593C2×C8—72no—
594C2×C8—72no—
595C2×C8—142no—
596C2×C8—142no—
597C2×C8—148no—
598C2×C8#115914yes—
599C2×C8C23×D712yes—
600C2×C8C23×D712yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—74no—
605C4⋊C4—72no—
606C4⋊C4—72no—
607C4⋊C4—72no—
608C4⋊C4—72no—
609C4⋊C4—144no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—141no—
617C4⋊C4—141no—
618C4⋊C4—144no—
619C4⋊C4—141no—
620C4⋊C4—141no—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—74no—
626C22⋊C4—74no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—72no—
632C42—72no—
633C42—144no—
634C42—144no—
635C2×C7—42no—
636C2×C7—82no—
637C2×C7#334614yescomplemented
638C2×C7C2×#54711yescharacteristic
639C2×C7C22×#13711yescharacteristic
640C2×C7C2×#57611yescharacteristic
641D7—24no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—74no—
650C23—72no—
651C23—142no—
652C23—142no—
653C23C2×D4×D712yes—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—564no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—84no—
663D4—148no—
664D4—288no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—72no—
676C2×C4—72no—
677C2×C4—72no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—144no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—564no—
693C2×C4—564no—
694C2×C4—564no—
695C2×C4—564no—
696C2×C4C2×D4×D712yes—
697C2×C4C2×D4×D711yescharacteristic
698C2×C4C2×#115912yes—
699C2×C4#655412yes—
700C2×C4C24×D711yescharacteristic
701C8—22no—
702C8—142no—
703C8—142no—
704C8C2×#115914yes—
705C7C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—74no—
714C22—84no—
715C22—142no—
716C22—142no—
717C22—148no—
718C22#9030212yes—
719C22#9046512yes—
720C22D7×#13712yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—142no—
727C4—142no—
728C4—142no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4#9030212yes—
734C4C22×#115911yescharacteristic
735C4C2×#655411yescharacteristic
736C2—42no—
737C2—82no—
738C2—144no—
739C2#1173827514yesdirect product factor
740C2C2×#9030211yescharacteristic
741C2C2×#9046511yescharacteristic
742C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#468C2
socleC23×C7C22×D4
prime radicalC2×#90305C2
hypercenterC2×#468D7
hypocenterC7C2×#3346
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#90326C2semidirect
3. C2×C7×#468C2semidirect
4. C2×#89943C2semidirect
5. C2×#89936C2semidirect
6. C2×#89899C2semidirect
7. C2×#89893C2semidirect
8. C2×#89817C2semidirect
9. C2×#89805C2semidirect
10. #11738275C2direct (N × H)
11. C2×D7×#107C2semidirect
12. C2×#89648C2semidirect
13. C2×#89581C2semidirect
14. C2×#89571C2semidirect
15. C2×#89549C2semidirect
16. C2×#89531C2semidirect
32. #90326C22semidirect
45. C7×#468C22semidirect
54. #89943C22semidirect
55. #89936C22semidirect
56. #89899C22semidirect
57. #89893C22semidirect
65. #89817C22semidirect
66. #89805C22semidirect
71. D7×#107C22semidirect
72. #89648C22semidirect
73. #89581C22semidirect
74. #89571C22semidirect
75. #89549C22semidirect
76. #89531C22semidirect
190. C2×#468D7semidirect
323. #468C2×D7semidirect
637. C2×C7#3346semidirect
705. C7C2×#3346semidirect
739. C2#11738275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903262
C2×#903052
C2×C7×#4682
C2×#899432
C2×#899362
C2×#898992
C2×#898932
C2×#898172
C2×#898052
#117382752
C2×D7×#1072
C2×#896482
C2×#895812
C2×#895712
C2×#895492
C2×#895312
C2×#33467