Finite Group Databasebeta

← C2×#11730919 #13513424

Subgroups — C2×#11730919 #13513424

Order 1792.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6441C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
3C2×#89982C211yesmaximal, characteristic
4C22×C7⋊#95C211yesmaximal, characteristic
5C2×#89722C211yesmaximal, characteristic
6C2×C22⋊C4×Dic7C211yesmaximal, characteristic
7C2×C22⋊C4×Dic7C211yesmaximal, characteristic
8C2×#89701C211yesmaximal, characteristic, complemented
9C2×#89705C211yesmaximal, characteristic, complemented
10C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11730919C2116yesmaximal, direct product factor
13C2×#89418C211yesmaximal, characteristic, complemented
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89427C211yesmaximal, characteristic, complemented
16C2×#89426C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C23×Dic14C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C2×#6441C4116yescomplemented
39C2×#6441C2218yes—
40C4×C7×C22⋊C4C2218yes—
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43#89982C2218yes—
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2218yes—
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89722C2218yes—
58C22⋊C4×Dic7C2218yes—
59C22⋊C4×Dic7C2218yes—
60C4×C4⋊Dic7C2218yescomplemented
61#89705C2218yescomplemented
62C4×Dic7⋊C4C2218yescomplemented
63#89701C2218yescomplemented
64#89427C2218yescomplemented
65#89427C2218yescomplemented
66#89426C2218yescomplemented
67#89418C2218yescomplemented
68C2×#2368—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C23×C4×C7—24no—
71C23×C4×C7—24no—
72C23×C4×C7—42no—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2314yes—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7—24no—
81C23×Dic7—24no—
82C23×Dic7—42no—
83C23×Dic7—42no—
84C23×Dic7—42no—
85C23×Dic7C2×C418yes—
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2314yes—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2314yes—
96C22×Dic14—42no—
97C22×Dic14—42no—
98C22×Dic14C2×C418yescomplemented
99C22×Dic14C2314yes—
100C2×C7×C22⋊C4C2×C418yes—
101C2×C7×C22⋊C4Q818yescomplemented
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C42×C7—24no—
105C2×C42×C7—42no—
106C2×C42×C7C2314yes—
107C2×C42×C7C2314yes—
108C2×C22⋊Dic7—24no—
109C2×C22⋊Dic7C2×C418yes—
110C2×C22⋊Dic7C2314yes—
111C2×C22⋊Dic7C2314yes—
112C2×C4⋊Dic7—24no—
113C2×C4⋊Dic7—42no—
114C2×C4⋊Dic7C2×C418yescomplemented
115C2×C4⋊Dic7C2314yes—
116C2×C4⋊Dic7C2314yes—
117C2×C4⋊Dic7C2314yes—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—42no—
120C2×Dic7⋊C4C2×C418yescomplemented
121C2×Dic7⋊C4C2×C418yescomplemented
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×C4×Dic7—24no—
127C2×C4×Dic7—42no—
128C2×C4×Dic7—42no—
129C2×C4×Dic7—42no—
130C2×C4×Dic7C2314yes—
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
133C2×C4×Dic7C2314yes—
134#6441C2×C4164yescomplemented
135C7×#95C2314yes—
136C7×#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C22×C22⋊Q8—71no—
150#2368—716no—
151C2×#391—71no—
152C2×#391—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×#387—71no—
156C2×#387—71no—
157C2×#385—71no—
158C2×#385—71no—
159C2×C4×C4⋊C4—71no—
160C2×C4×C4⋊C4—71no—
161C2×C4×C22⋊C4—71no—
162C2×C4×C22⋊C4—71no—
163C2×C4×C22⋊C4D711yescharacteristic
164C22×#95—71no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7C22×C414yes—
170C24×C7C2×Q814yes—
171C24×C7#4114yes—
172C24×C7C2412yes—
173C24×C7C2411yescharacteristic
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—28no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—28no—
189C22×C4×C7—44no—
190C22×C4×C7—416no—
191C22×C4×C7C22×C414yes—
192C22×C4×C7C22×C414yes—
193C22×C4×C7C2×Q814yes—
194C22×C4×C7C2×Q814yes—
195C22×C4×C7#4114yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—28no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—28no—
223C22×Dic7—416no—
224C22×Dic7—44no—
225C22×Dic7—44no—
226C22×Dic7—44no—
227C22×Dic7—416no—
228C22×Dic7C22×C414yes—
229C22×Dic7C22×C414yes—
230C22×Dic7C22×C414yes—
231C22×Dic7C22×C414yes—
232C22×Dic7C22×C4116yes—
233C22×Dic7#4114yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2412yes—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C2×Dic14—416no—
243C2×Dic14—44no—
244C2×Dic14—44no—
245C2×Dic14C22×C4116yescomplemented
246C7×C22⋊C4C22×C4116yes—
247C7×C22⋊C4C2×Q8116yescomplemented
248C42×C7—28no—
249C42×C7—44no—
250C22⋊Dic7—28no—
251C22⋊Dic7C22×C4116yes—
252C4⋊Dic7—28no—
253C4⋊Dic7—44no—
254C4⋊Dic7C22×C4116yescomplemented
255Dic7⋊C4—28no—
256Dic7⋊C4—44no—
257Dic7⋊C4C22×C4116yescomplemented
258Dic7⋊C4C22×C4116yescomplemented
259C4×Dic7—28no—
260C4×Dic7—44no—
261C4×Dic7—44no—
262C4×Dic7—44no—
263C23×Q8—71no—
264C24×C4—71no—
265C24×C4—71no—
266C24×C4C2×D711yescharacteristic
267C2×C22⋊Q8—716no—
268C2×C22⋊Q8—78no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4—71no—
272C22×C4⋊C4—71no—
273C22×C4⋊C4—71no—
274C22×C4⋊C4—71no—
275C22×C4⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4—71no—
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C42—71no—
281C22×C42—71no—
282C22×C42—71no—
283C22×C42—71no—
284C22×C42C2×D711yescharacteristic
285C22×C42C2×D711yescharacteristic
286#391—78no—
287#391—78no—
288#387—78no—
289#387—78no—
290#387—78no—
291#387—78no—
292#385—78no—
293#385—78no—
294C4×C4⋊C4—78no—
295C4×C4⋊C4—78no—
296C4×C22⋊C4—78no—
297C4×C22⋊C4—78no—
298C4×C22⋊C4C2×D718yes—
299C2×#95—78no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95C2×D711yescharacteristic
313C2×#95C2×D711yescharacteristic
314C23×C7—28no—
315C23×C7—28no—
316C23×C7—28no—
317C23×C7—28no—
318C23×C7—28no—
319C23×C7—28no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7C4×Q8116yes—
325C23×C7C23×C414yes—
326C23×C7C23×C412yes—
327C23×C7C22×Q814yes—
328C23×C7C22×Q812yes—
329C23×C7C2×#4114yes—
330C23×C7C2×#4112yes—
331C23×C7C2×#4112yes—
332C23×C7C2×#4112yes—
333C23×C7H(5,𝔽2)12yes—
334C23×C7H(5,𝔽2)12yes—
335C23×C7C2511yescharacteristic
336C2×C4×C7—28no—
337C2×C4×C7—28no—
338C2×C4×C7—28no—
339C2×C4×C7—28no—
340C2×C4×C7—28no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—416no—
355C2×C4×C7—44no—
356C2×C4×C7C23×C414yes—
357C2×C4×C7C23×C414yes—
358C2×C4×C7C22×Q814yes—
359C2×C4×C7C22×Q814yes—
360C2×C4×C7C2×#4114yes—
361C2×Dic7—28no—
362C2×Dic7—28no—
363C2×Dic7—28no—
364C2×Dic7—28no—
365C2×Dic7—28no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—416no—
386C2×Dic7—416no—
387C2×Dic7—44no—
388C2×Dic7—44no—
389C2×Dic7—44no—
390C2×Dic7C23×C414yes—
391C2×Dic7C23×C414yes—
392C2×Dic7C23×C414yes—
393C2×Dic7C23×C414yes—
394C2×Dic7C2×#4114yes—
395Dic14—416no—
396C25C22×D711yescharacteristic
397C22×Q8—78no—
398C22×Q8—74no—
399C22×Q8—282no—
400C22×Q8—282no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—42no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—78no—
410C23×C4—74no—
411C23×C4—71no—
412C23×C4—71no—
413C23×C4—71no—
414C23×C4—74no—
415C23×C4—144no—
416C23×C4—144no—
417C23×C4—282no—
418C23×C4—282no—
419C23×C4—282no—
420C23×C4C22×D711yescharacteristic
421C23×C4C22×D714yes—
422C23×C4C22×D711yescharacteristic
423C23×C4C22×D711yescharacteristic
424C23×C4C22×D711yescharacteristic
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C22⋊Q8—764no—
428C2×C4⋊C4—78no—
429C2×C4⋊C4—78no—
430C2×C4⋊C4—78no—
431C2×C4⋊C4—74no—
432C2×C4⋊C4—74no—
433C2×C4⋊C4—74no—
434C2×C4⋊C4—74no—
435C2×C4⋊C4—74no—
436C2×C4⋊C4—74no—
437C2×C4⋊C4—74no—
438C2×C4⋊C4—144no—
439C2×C4⋊C4—144no—
440C2×C4⋊C4—282no—
441C2×C4⋊C4—282no—
442C2×C22⋊C4—78no—
443C2×C22⋊C4—74no—
444C2×C22⋊C4—74no—
445C2×C22⋊C4—144no—
446C2×C22⋊C4Dic1418yescomplemented
447C2×C22⋊C4C4×D718yes—
448C2×C22⋊C4C22×D714yes—
449C2×C22⋊C4C22×D714yes—
450C2×C42—24no—
451C2×C42—42no—
452C2×C42—74no—
453C2×C42—74no—
454C2×C42—74no—
455C2×C42—74no—
456C2×C42—144no—
457C2×C42—282no—
458C2×C42—282no—
459C2×C42—282no—
460C2×C42C22×D714yes—
461C2×C42C22×D714yes—
462#95—74no—
463#95—74no—
464#95—74no—
465#95—74no—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95—74no—
471#95—74no—
472#95—74no—
473#95—74no—
474#95C22×D714yes—
475#95C22×D714yes—
476C22×C7—232no—
477C22×C7—24no—
478C22×C7—24no—
479C22×C7—24no—
480C22×C7—24no—
481C22×C7—24no—
482C22×C7—24no—
483C22×C7C2×C4×Q818yes—
484C22×C7C2×C4×Q814yes—
485C22×C7C4×#4114yes—
486C22×C7#51814yes—
487C22×C7#55114yes—
488C22×C7#55114yes—
489C22×C7#55414yes—
490C22×C7#55414yes—
491C22×C7C24×C411yescharacteristic
492C22×C7C23×Q811yescharacteristic
493C22×C7C22×#4111yescharacteristic
494C22×C7C22×#4111yescharacteristic
495C22×C7C22×#4111yescharacteristic
496C22×C7C2×H(5,𝔽2)11yescharacteristic
497C22×C7C2×H(5,𝔽2)11yescharacteristic
498C4×C7—24no—
499C4×C7—24no—
500C4×C7—24no—
501C4×C7—24no—
502C4×C7—24no—
503C4×C7—42no—
504Dic7—24no—
505Dic7—24no—
506Dic7—24no—
507Dic7—24no—
508Dic7—24no—
509Dic7—42no—
510Dic7—42no—
511Dic7—42no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24C2×Dic1414yes—
517C24C2×C4×D714yes—
518C24#115714yes—
519C24C23×D712yes—
520C24C23×D711yescharacteristic
521C2×Q8—716no—
522C2×Q8—2816no—
523C2×Q8—284no—
524C2×Q8—284no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—44no—
541C22×C4—416no—
542C22×C4—74no—
543C22×C4—74no—
544C22×C4—74no—
545C22×C4—74no—
546C22×C4—74no—
547C22×C4—72no—
548C22×C4—72no—
549C22×C4—72no—
550C22×C4—72no—
551C22×C4—72no—
552C22×C4—716no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—148no—
557C22×C4—142no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—148no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—2816no—
578C22×C4—284no—
579C22×C4—284no—
580C22×C4—284no—
581C22×C4—2816no—
582C22×C4C2×Dic1414yes—
583C22×C4C2×Dic1414yes—
584C22×C4C2×C4×D714yes—
585C22×C4C2×C4×D714yes—
586C22×C4#115914yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D712yes—
590C22×C4C23×D712yes—
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C4⋊C4—716no—
594C4⋊C4—716no—
595C4⋊C4—716no—
596C4⋊C4—148no—
597C4⋊C4—148no—
598C4⋊C4—284no—
599C4⋊C4—284no—
600C22⋊C4—716no—
601C22⋊C4—148no—
602C22⋊C4C2×Dic14116yescomplemented
603C22⋊C4C2×C4×D7116yes—
604C42—28no—
605C42—44no—
606C42—148no—
607C42—284no—
608C42—284no—
609C42—284no—
610C2×C7—28no—
611C2×C7#236818yescomplemented
612C2×C7C22×C4×Q811yescharacteristic
613C2×C7C2×C4×#4111yescharacteristic
614C2×C7C2×#51811yescharacteristic
615C2×C7C2×#55111yescharacteristic
616C2×C7C2×#55111yescharacteristic
617C2×C7C2×#55411yescharacteristic
618C2×C7C2×#55411yescharacteristic
619C23—28no—
620C23—28no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23C4×Dic14116yes—
630C23C22×Dic1414yes—
631C23C22×Dic1412yes—
632C23C22×C4×D714yes—
633C23C22×C4×D712yes—
634C23C2×#115714yes—
635C23C2×#115712yes—
636C23C2×#115912yes—
637C23#654812yes—
638C23D7×#4112yes—
639C23#655312yes—
640C23C24×D711yescharacteristic
641Q8—2816no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—416no—
661C2×C4—44no—
662C2×C4—74no—
663C2×C4—74no—
664C2×C4—74no—
665C2×C4—74no—
666C2×C4—74no—
667C2×C4—148no—
668C2×C4—148no—
669C2×C4—148no—
670C2×C4—148no—
671C2×C4—148no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—142no—
677C2×C4—142no—
678C2×C4—142no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—2816no—
692C2×C4—2816no—
693C2×C4—284no—
694C2×C4—284no—
695C2×C4—284no—
696C2×C4C22×Dic1414yes—
697C2×C4C22×Dic1414yes—
698C2×C4C22×C4×D714yes—
699C2×C4C22×C4×D714yes—
700C2×C4C2×#115914yes—
701C7C2×#236811yescharacteristic, complemented, Sylow
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—232no—
709C22C2×C4×Dic1418yes—
710C22C2×C4×Dic1414yes—
711C22#9018614yes—
712C22#9021814yes—
713C22C4×#115914yes—
714C22#9023014yes—
715C22#9023414yes—
716C22#9023614yes—
717C22C23×Dic1411yescharacteristic
718C22C23×C4×D711yescharacteristic
719C22C22×#115711yescharacteristic
720C22C22×#115911yescharacteristic
721C22C2×#654811yescharacteristic
722C22C2×D7×#4111yescharacteristic
723C22C2×#655311yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—144no—
731C4—144no—
732C4—144no—
733C4—144no—
734C4—144no—
735C4—282no—
736C4—282no—
737C4—282no—
738C2—28no—
739C2#1173091918yesdirect product factor
740C2C22×C4×Dic1411yescharacteristic
741C2C2×#9018611yescharacteristic
742C2C2×#9021811yescharacteristic
743C2C2×C4×#115911yescharacteristic
744C2C2×#9023411yescharacteristic
745C2C2×#9023011yescharacteristic
746C2C2×#9023611yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2368
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C2×#89701C2semidirect
9. C2×#89705C2semidirect
10. C2×C4×C4⋊Dic7C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11730919C2direct (N × H)
13. C2×#89418C2semidirect
14. C2×#89427C2semidirect
15. C2×#89427C2semidirect
16. C2×#89426C2semidirect
38. C2×#6441C4semidirect
60. C4×C4⋊Dic7C22semidirect
61. #89705C22semidirect
62. C4×Dic7⋊C4C22semidirect
63. #89701C22semidirect
64. #89427C22semidirect
65. #89427C22semidirect
66. #89426C22semidirect
67. #89418C22semidirect
98. C22×Dic14C2×C4semidirect
101. C2×C7×C22⋊C4Q8semidirect
114. C2×C4⋊Dic7C2×C4semidirect
120. C2×Dic7⋊C4C2×C4semidirect
121. C2×Dic7⋊C4C2×C4semidirect
134. #6441C2×C4semidirect
245. C2×Dic14C22×C4semidirect
247. C7×C22⋊C4C2×Q8semidirect
254. C4⋊Dic7C22×C4semidirect
257. Dic7⋊C4C22×C4semidirect
258. Dic7⋊C4C22×C4semidirect
446. C2×C22⋊C4Dic14semidirect
602. C22⋊C4C2×Dic14semidirect
611. C2×C7#2368semidirect
701. C7C2×#2368semidirect
739. C2#11730919direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64412
C2×C4×C7×C22⋊C42
C2×#899822
C22×C7⋊#952
C2×#897222
C2×C22⋊C4×Dic72
C2×#897012
C2×#897052
C2×C4×C4⋊Dic72
C2×C4×Dic7⋊C42
#117309192
C2×#894182
C2×#894272
C2×#894262
C2×#23687