Finite Group Databasebeta

← C2×#11734786 #13520422

Subgroups — C2×#11734786 #13520422

Order 1792.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic, complemented
3C2×#89752C211yesmaximal, characteristic, complemented
4C2×#89752C211yesmaximal, characteristic, complemented
5C2×#89762C211yesmaximal, characteristic, complemented
6C2×#89762C211yesmaximal, characteristic, complemented
7C2×#89750C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic
9C2×#89731C211yesmaximal, characteristic
10C2×#89724C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic
12C2×#89717C211yesmaximal, characteristic, complemented
13C2×#89716C211yesmaximal, characteristic, complemented
14#11734786C2116yesmaximal, direct product factor
15C2×#89447C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C7×#396C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89764C2218yescomplemented
54#89762C2218yescomplemented
55#89762C2218yescomplemented
56#89752C2218yescomplemented
57#89752C2218yescomplemented
58#89750C2218yescomplemented
59#89731C2218yes—
60#89731C2218yes—
61#89729C2218yes—
62#89724C2218yescomplemented
63#89717C2218yescomplemented
64#89716C2218yescomplemented
65#89447C2218yescomplemented
66#89421C2218yescomplemented
67C2×#2651—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C24×D7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C22×C22⋊D7—24no—
77C22×C22⋊D7—42no—
78C22×C22⋊D7—42no—
79C22×C22⋊D7C2314yes—
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C2×C7×C4⋊C4—42no—
88C2×C7×C4⋊C4—42no—
89C2×C7×C4⋊C4—42no—
90C2×C7×C4⋊C4C2314yes—
91C2×C7×C4⋊C4C2314yes—
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4C2314yes—
97C2×C7×C22⋊C4C2314yes—
98C2×C7×C22⋊C4C2314yes—
99C2×C22⋊Dic7—24no—
100C2×C22⋊Dic7—24no—
101C2×C22⋊Dic7—42no—
102C2×C22⋊Dic7C2314yes—
103C2×C22⋊Dic7C2314yes—
104C2×C22⋊Dic7C2314yes—
105C2×(C2×D7)⋊C4—24no—
106C2×(C2×D7)⋊C4—24no—
107C2×(C2×D7)⋊C4—42no—
108C2×(C2×D7)⋊C4—42no—
109C2×(C2×D7)⋊C4—42no—
110C2×(C2×D7)⋊C4—42no—
111C2×(C2×D7)⋊C4C2314yes—
112C2×(C2×D7)⋊C4C2314yes—
113C2×(C2×D7)⋊C4C2314yes—
114C2×(C2×D7)⋊C4C2314yes—
115C2×(C2×D7)⋊C4C2314yes—
116C2×(C2×D7)⋊C4C2314yes—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—42no—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×C4×Dic7—24no—
130C2×C4×Dic7—42no—
131C2×C4×Dic7—42no—
132C2×C4×Dic7C2314yes—
133C2×C4×Dic7C2314yes—
134C2×C4×Dic7C2314yes—
135C7×#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145#2651—716no—
146C2×#399—71no—
147C2×#398—71no—
148C2×#398—71no—
149C2×#397—71no—
150C2×#397—71no—
151C2×#396D711yescharacteristic, complemented
152C2×#394—71no—
153C2×#394—71no—
154C2×#390—71no—
155C2×#388—71no—
156C2×#388—71no—
157C2×#388—71no—
158C2×#388—71no—
159C2×#387—71no—
160C2×C4×C4⋊C4—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7C2412yes—
169C24×C7C2411yescharacteristic
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7—22no—
175C23×D7—22no—
176C23×D7—22no—
177C23×D7C2412yes—
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—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C2×C22⋊D7—28no—
203C2×C22⋊D7—44no—
204C2×C22⋊D7—44no—
205C2×C22⋊D7—416no—
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—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7#4114yes—
225C22×Dic7#4114yes—
226C22×Dic7#4114yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C7×C4⋊C4—44no—
235C7×C4⋊C4—44no—
236C7×C4⋊C4—44no—
237C7×C22⋊C4—44no—
238C7×C22⋊C4—44no—
239C7×C22⋊C4—44no—
240C22⋊Dic7—28no—
241C22⋊Dic7—28no—
242C22⋊Dic7—44no—
243(C2×D7)⋊C4—28no—
244(C2×D7)⋊C4—28no—
245(C2×D7)⋊C4—44no—
246(C2×D7)⋊C4—44no—
247(C2×D7)⋊C4—44no—
248(C2×D7)⋊C4—44no—
249Dic7⋊C4—28no—
250Dic7⋊C4—28no—
251Dic7⋊C4—28no—
252Dic7⋊C4—44no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255C4×Dic7—28no—
256C4×Dic7—44no—
257C4×Dic7—44no—
258C23×D4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4C2×D711yescharacteristic
266C22×C4⋊C4C2×D711yescharacteristic
267C22×C4⋊C4C2×D711yescharacteristic
268C22×C22⋊C4—71no—
269C22×C22⋊C4—71no—
270C22×C22⋊C4—71no—
271C22×C22⋊C4—71no—
272C22×C22⋊C4—71no—
273C22×C22⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4—71no—
276C22×C22⋊C4—71no—
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C22⋊C4C2×D711yescharacteristic
279C22×C22⋊C4C2×D711yescharacteristic
280C22×C42—71no—
281C22×C42—71no—
282C22×C42—71no—
283#399—78no—
284#398—78no—
285#398—78no—
286#397—78no—
287#397—78no—
288#396C2×D718yescomplemented
289#394—78no—
290#394—78no—
291#390—78no—
292#388—78no—
293#388—78no—
294#388—78no—
295#388—78no—
296#387—78no—
297C4×C4⋊C4—78no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95—71no—
305C2×#95—71no—
306C2×#95—71no—
307C2×#95C2×D711yescharacteristic
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—44no—
316C23×C7—44no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7—44no—
321C23×C7—44no—
322C23×C7C2×#4112yes—
323C23×C7C2×#4112yes—
324C23×C7C2×#4112yes—
325C23×C7H(5,𝔽2)12yes—
326C23×C7H(5,𝔽2)12yes—
327C23×C7H(5,𝔽2)12yes—
328C23×C72−1+412yes—
329C23×C7C2511yescharacteristic
330C22×D7—22no—
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—22no—
334C22×D7—22no—
335C22×D7—22no—
336C22×D7—22no—
337C22×D7—44no—
338C22×D7—44no—
339C22×D7—44no—
340C22×D7—44no—
341C22×D7—44no—
342C22×D7—44no—
343C22×D7—44no—
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—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7—44no—
365C2×C4×C7—44no—
366C2×C4×C7—44no—
367C2×C4×C7—44no—
368C22⋊D7—416no—
369C2×Dic7—28no—
370C2×Dic7—28no—
371C2×Dic7—28no—
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—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—44no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7C2×#4114yes—
395C2×Dic7C2×#4114yes—
396C2×Dic7C2×#4114yes—
397C25—71no—
398C25C22×D711yescharacteristic
399C22×D4—74no—
400C22×D4—144no—
401C22×D4—282no—
402C22×D4—282no—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—74no—
420C2×C4⋊C4—74no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—74no—
423C2×C4⋊C4—74no—
424C2×C4⋊C4—74no—
425C2×C4⋊C4—144no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—282no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4—282no—
431C2×C4⋊C4C22×D714yes—
432C2×C4⋊C4C22×D714yes—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—74no—
441C2×C22⋊C4—74no—
442C2×C22⋊C4—74no—
443C2×C22⋊C4—74no—
444C2×C22⋊C4—74no—
445C2×C22⋊C4—74no—
446C2×C22⋊C4—144no—
447C2×C22⋊C4—144no—
448C2×C22⋊C4—144no—
449C2×C22⋊C4—144no—
450C2×C22⋊C4—282no—
451C2×C22⋊C4—282no—
452C2×C22⋊C4—282no—
453C2×C22⋊C4—282no—
454C2×C22⋊C4—282no—
455C2×C22⋊C4C22×D714yes—
456C2×C22⋊C4C22×D714yes—
457C2×C22⋊C4C22×D714yes—
458C2×C42—74no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—144no—
462C2×C42—282no—
463C2×C42—282no—
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#95C22×D714yes—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—88no—
482C22×C7#52914yes—
483C22×C7#53814yes—
484C22×C7#53914yes—
485C22×C7#54014yes—
486C22×C7#54014yes—
487C22×C7#54214yes—
488C22×C7#54214yes—
489C22×C7C22×#4111yescharacteristic
490C22×C7C22×#4111yescharacteristic
491C22×C7C22×#4111yescharacteristic
492C22×C7C2×H(5,𝔽2)11yescharacteristic
493C22×C7C2×H(5,𝔽2)11yescharacteristic
494C22×C7C2×H(5,𝔽2)11yescharacteristic
495C22×C7C2×2−1+411yescharacteristic
496C2×D7—42no—
497C2×D7—42no—
498C2×D7—42no—
499C2×D7—42no—
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—88no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509C4×C7—42no—
510Dic7—24no—
511Dic7—24no—
512Dic7—24no—
513Dic7—42no—
514Dic7—42no—
515Dic7—42no—
516Dic7—42no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—72no—
525C24—142no—
526C24—142no—
527C24—142no—
528C24—142no—
529C24—142no—
530C24—142no—
531C24—142no—
532C24C23×D712yes—
533C24C23×D711yescharacteristic
534C2×D4—148no—
535C2×D4—284no—
536C2×D4—284no—
537C2×D4—2816no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—74no—
557C22×C4—74no—
558C22×C4—74no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—72no—
563C22×C4—72no—
564C22×C4—72no—
565C22×C4—72no—
566C22×C4—142no—
567C22×C4—142no—
568C22×C4—142no—
569C22×C4—142no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—142no—
573C22×C4—142no—
574C22×C4—142no—
575C22×C4—142no—
576C22×C4—142no—
577C22×C4—142no—
578C22×C4—142no—
579C22×C4—142no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4C23×D712yes—
585C22×C4C23×D712yes—
586C22×C4C23×D712yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D712yes—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—148no—
594C4⋊C4—148no—
595C4⋊C4—148no—
596C4⋊C4—284no—
597C4⋊C4—284no—
598C4⋊C4—284no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—148no—
603C22⋊C4—148no—
604C22⋊C4—148no—
605C22⋊C4—148no—
606C22⋊C4—284no—
607C22⋊C4—284no—
608C22⋊C4—284no—
609C22⋊C4—284no—
610C22⋊C4—284no—
611C42—148no—
612C42—284no—
613C42—284no—
614C2×C7—82no—
615C2×C7#265118yescomplemented
616C2×C7C2×#52911yescharacteristic
617C2×C7C2×#53811yescharacteristic
618C2×C7C2×#53911yescharacteristic
619C2×C7C2×#54011yescharacteristic
620C2×C7C2×#54011yescharacteristic
621C2×C7C2×#54211yescharacteristic
622C2×C7C2×#54211yescharacteristic
623D7—82no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—142no—
642C23—142no—
643C23—142no—
644C23—142no—
645C23—284no—
646C23—284no—
647C23—284no—
648C23—284no—
649C23—284no—
650C23—284no—
651C23—284no—
652C23#654812yes—
653C23#654812yes—
654C23#654812yes—
655C23#655112yes—
656C23D7×#4112yes—
657C23D7×#4112yes—
658C23D7×#4112yes—
659C23C24×D711yescharacteristic
660D4—2816no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—74no—
686C2×C4—74no—
687C2×C4—74no—
688C2×C4—148no—
689C2×C4—148no—
690C2×C4—148no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—142no—
708C2×C4—142no—
709C2×C4—284no—
710C2×C4—284no—
711C2×C4—284no—
712C2×C4—284no—
713C7C2×#265111yescharacteristic, complemented, Sylow
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—88no—
722C22—282no—
723C22—282no—
724C22—282no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—568no—
730C22#9030414yes—
731C22#9030614yes—
732C22#9030614yes—
733C22#9032914yes—
734C22#9033114yes—
735C22#9033114yes—
736C22#9039714yes—
737C22C2×#654811yescharacteristic
738C22C2×#654811yescharacteristic
739C22C2×#654811yescharacteristic
740C22C2×#655111yescharacteristic
741C22C2×D7×#4111yescharacteristic
742C22C2×D7×#4111yescharacteristic
743C22C2×D7×#4111yescharacteristic
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—144no—
751C4—144no—
752C4—144no—
753C4—282no—
754C4—282no—
755C4—282no—
756C4—282no—
757C2—82no—
758C2—562no—
759C2#1173478618yesdirect product factor
760C2C2×#9030611yescharacteristic
761C2C2×#9030611yescharacteristic
762C2C2×#9030411yescharacteristic
763C2C2×#9033111yescharacteristic
764C2C2×#9033111yescharacteristic
765C2C2×#9032911yescharacteristic
766C2C2×#9039711yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#396D7
hypocenterC7C2×#2651
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C2×C7×#396C2semidirect
2. C2×#89764C2semidirect
3. C2×#89752C2semidirect
4. C2×#89752C2semidirect
5. C2×#89762C2semidirect
6. C2×#89762C2semidirect
7. C2×#89750C2semidirect
10. C2×#89724C2semidirect
12. C2×#89717C2semidirect
13. C2×#89716C2semidirect
14. #11734786C2direct (N × H)
15. C2×#89447C2semidirect
16. C2×#89421C2semidirect
42. C7×#396C22semidirect
53. #89764C22semidirect
54. #89762C22semidirect
55. #89762C22semidirect
56. #89752C22semidirect
57. #89752C22semidirect
58. #89750C22semidirect
62. #89724C22semidirect
63. #89717C22semidirect
64. #89716C22semidirect
65. #89447C22semidirect
66. #89421C22semidirect
151. C2×#396D7semidirect
288. #396C2×D7semidirect
615. C2×C7#2651semidirect
713. C7C2×#2651semidirect
759. C2#11734786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×#897642
C2×#897522
C2×#897622
C2×#897502
C2×#897312
C2×#897242
C2×#897292
C2×#897172
C2×#897162
#117347862
C2×#894472
C2×#894212
C2×#26517