Finite Group Databasebeta

← C2×#11734436 #13520424

Subgroups — C2×#11734436 #13520424

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×#394C211yesmaximal, characteristic
2C2×#89994C211yesmaximal, characteristic
3C2×#89993C211yesmaximal, characteristic
4C2×#89756C211yesmaximal, characteristic, complemented
5C2×#89753C211yesmaximal, characteristic, complemented
6C2×#89721C211yesmaximal, characteristic, complemented
7C2×#89724C211yesmaximal, characteristic, complemented
8C2×#89724C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89717C211yesmaximal, characteristic, complemented
11C2×#89717C211yesmaximal, characteristic, complemented
12C2×#89717C211yesmaximal, characteristic, complemented
13C2×#89716C211yesmaximal, characteristic, complemented
14#11734436C2116yesmaximal, direct product factor
15C2×#89429C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
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×#394C2218yes—
43C2×C7×#95C2211yescharacteristic
44#89994C2218yes—
45#89993C2218yes—
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89756C2218yescomplemented
56#89753C2218yescomplemented
57#89724C2218yescomplemented
58#89724C2218yescomplemented
59#89721C2218yescomplemented
60#89720C2218yescomplemented
61#89717C2218yescomplemented
62#89717C2218yescomplemented
63#89717C2218yescomplemented
64#89716C2218yescomplemented
65#89429C2218yescomplemented
66#89421C2218yescomplemented
67C2×#2651—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C22×C7×D4—24no—
71C22×C7×D4—42no—
72C22×C7×D4—42no—
73C22×C7×D4C2314yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C2×C7×C4⋊C4—24no—
88C2×C7×C4⋊C4C2314yes—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4—42no—
92C2×C7×C22⋊C4—42no—
93C2×C7×C22⋊C4C2314yes—
94C2×C7×C22⋊C4C2314yes—
95C2×C7×C22⋊C4C2314yes—
96C2×C7×C22⋊C4C2314yes—
97C2×C22⋊Dic7—24no—
98C2×C22⋊Dic7—24no—
99C2×C22⋊Dic7—24no—
100C2×C22⋊Dic7—24no—
101C2×C22⋊Dic7—42no—
102C2×C22⋊Dic7—42no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7—42no—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×C22⋊Dic7C2314yes—
110C2×C22⋊Dic7C2314yes—
111C2×C22⋊Dic7C2314yes—
112C2×C22⋊Dic7C2314yes—
113C2×C4⋊Dic7—42no—
114C2×C4⋊Dic7—42no—
115C2×C4⋊Dic7C2314yes—
116C2×C4⋊Dic7C2314yes—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—42no—
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×#396—71no—
152C2×#394—71no—
153C2×#394D711yescharacteristic
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×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7C2412yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C2×C7×D4—28no—
179C2×C7×D4—44no—
180C2×C7×D4—44no—
181C2×C7×D4—416no—
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×C7#4114yes—
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—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×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C7×C4⋊C4—28no—
235C7×C22⋊C4—44no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4—44no—
238C7×C22⋊C4—44no—
239C22⋊Dic7—28no—
240C22⋊Dic7—28no—
241C22⋊Dic7—28no—
242C22⋊Dic7—28no—
243C22⋊Dic7—44no—
244C22⋊Dic7—44no—
245C22⋊Dic7—44no—
246C22⋊Dic7—44no—
247C4⋊Dic7—44no—
248C4⋊Dic7—44no—
249Dic7⋊C4—28no—
250Dic7⋊C4—28no—
251Dic7⋊C4—44no—
252Dic7⋊C4—44no—
253Dic7⋊C4—44no—
254Dic7⋊C4—44no—
255C4×Dic7—28no—
256C4×Dic7—44no—
257C4×Dic7—44no—
258C23×D4C2×D711yescharacteristic
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⋊C4—71no—
266C22×C4⋊C4—71no—
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⋊C4C2×D711yescharacteristic
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#396—78no—
289#394—78no—
290#394C2×D718yes—
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—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—44no—
323C23×C7—44no—
324C23×C7—44no—
325C23×C7—44no—
326C23×C7—44no—
327C23×C7—44no—
328C23×C7—44no—
329C23×C7—44no—
330C23×C7—44no—
331C23×C7—44no—
332C23×C7—44no—
333C23×C7—44no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7C2×#4112yes—
337C23×C7C2×#4112yes—
338C23×C7C2×#4112yes—
339C23×C7H(5,𝔽2)12yes—
340C23×C7H(5,𝔽2)12yes—
341C23×C7H(5,𝔽2)12yes—
342C23×C72−1+412yes—
343C23×C7C2511yescharacteristic
344C7×D4—416no—
345C2×C4×C7—28no—
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—44no—
361C2×C4×C7—44no—
362C2×C4×C7—44no—
363C2×C4×C7—44no—
364C2×C4×C7C2×#4114yes—
365C2×Dic7—28no—
366C2×Dic7—28no—
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—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—44no—
390C2×Dic7—44no—
391C2×Dic7—44no—
392C2×Dic7—44no—
393C2×Dic7—44no—
394C2×Dic7—44no—
395C2×Dic7C2×#4114yes—
396C2×Dic7C2×#4114yes—
397C25C22×D711yescharacteristic
398C25C22×D711yescharacteristic
399C22×D4—24no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4C22×D714yes—
403C23×C4—71no—
404C23×C4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413C23×C4C22×D711yescharacteristic
414C23×C4C22×D711yescharacteristic
415C23×C4C22×D711yescharacteristic
416C2×C4⋊C4—24no—
417C2×C4⋊C4—74no—
418C2×C4⋊C4—74no—
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—282no—
428C2×C4⋊C4—282no—
429C2×C4⋊C4—282no—
430C2×C4⋊C4—282no—
431C2×C4⋊C4—282no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
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⋊C4C22×D714yes—
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—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—88no—
489C22×C7—88no—
490C22×C7#52914yes—
491C22×C7#53814yes—
492C22×C7#53914yes—
493C22×C7#54014yes—
494C22×C7#54014yes—
495C22×C7#54214yes—
496C22×C7#54214yes—
497C22×C7C22×#4111yescharacteristic
498C22×C7C22×#4111yescharacteristic
499C22×C7C22×#4111yescharacteristic
500C22×C7C2×H(5,𝔽2)11yescharacteristic
501C22×C7C2×H(5,𝔽2)11yescharacteristic
502C22×C7C2×H(5,𝔽2)11yescharacteristic
503C22×C7C2×2−1+411yescharacteristic
504C4×C7—24no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—42no—
509Dic7—24no—
510Dic7—24no—
511Dic7—42no—
512Dic7—42no—
513Dic7—42no—
514Dic7—42no—
515Dic7—42no—
516Dic7—42no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24C23×D712yes—
532C24C23×D712yes—
533C24C23×D711yescharacteristic
534C2×D4—28no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—416no—
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—74no—
553C22×C4—74no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—72no—
557C22×C4—72no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—72no—
561C22×C4—72no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—142no—
565C22×C4—142no—
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×C4#115914yes—
585C22×C4C23×D712yes—
586C22×C4C23×D712yes—
587C22×C4C23×D712yes—
588C22×C4C23×D712yes—
589C22×C4C23×D712yes—
590C4⋊C4—28no—
591C4⋊C4—148no—
592C4⋊C4—148no—
593C4⋊C4—284no—
594C4⋊C4—284no—
595C4⋊C4—284no—
596C4⋊C4—284no—
597C4⋊C4—284no—
598C4⋊C4—284no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—148no—
604C22⋊C4—148no—
605C22⋊C4—148no—
606C22⋊C4—148no—
607C22⋊C4—284no—
608C22⋊C4—284no—
609C22⋊C4—284no—
610C22⋊C4—284no—
611C42—148no—
612C42—284no—
613C42—284no—
614C2×C7—82no—
615C2×C7—82no—
616C2×C7#265118yescomplemented
617C2×C7C2×#52911yescharacteristic
618C2×C7C2×#53811yescharacteristic
619C2×C7C2×#53911yescharacteristic
620C2×C7C2×#54011yescharacteristic
621C2×C7C2×#54011yescharacteristic
622C2×C7C2×#54211yescharacteristic
623C2×C7C2×#54211yescharacteristic
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23C2×#115912yes—
653C23#654812yes—
654C23#654812yes—
655C23#654812yes—
656C23D7×#4112yes—
657C23D7×#4112yes—
658C23#655412yes—
659C23C24×D711yescharacteristic
660D4—416no—
661C2×C4—28no—
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—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—74no—
681C2×C4—74no—
682C2×C4—148no—
683C2×C4—148no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
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—284no—
707C2×C4—284no—
708C2×C4—284no—
709C2×C4—284no—
710C2×C4—284no—
711C2×C4—284no—
712C2×C4C2×#115914yes—
713C7C2×#265111yescharacteristic, complemented, Sylow
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22#9028414yes—
731C22#9029414yes—
732C22#9030614yes—
733C22#9030614yes—
734C22#9035114yes—
735C22#9035314yes—
736C22#9037114yes—
737C22C22×#115911yescharacteristic
738C22C2×#654811yescharacteristic
739C22C2×#654811yescharacteristic
740C22C2×#654811yescharacteristic
741C22C2×D7×#4111yescharacteristic
742C22C2×D7×#4111yescharacteristic
743C22C2×#655411yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—144no—
750C4—144no—
751C4—282no—
752C4—282no—
753C4—282no—
754C4—282no—
755C4—282no—
756C4—282no—
757C2—82no—
758C2—82no—
759C2#1173443618yesdirect product factor
760C2C2×#9028411yescharacteristic
761C2C2×#9030611yescharacteristic
762C2C2×#9030611yescharacteristic
763C2C2×#9029411yescharacteristic
764C2C2×#9035311yescharacteristic
765C2C2×#9035111yescharacteristic
766C2C2×#9037111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#394D7
hypocenterC7C2×#2651
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
4. C2×#89756C2semidirect
5. C2×#89753C2semidirect
6. C2×#89721C2semidirect
7. C2×#89724C2semidirect
8. C2×#89724C2semidirect
9. C2×#89720C2semidirect
10. C2×#89717C2semidirect
11. C2×#89717C2semidirect
12. C2×#89717C2semidirect
13. C2×#89716C2semidirect
14. #11734436C2direct (N × H)
15. C2×#89429C2semidirect
16. C2×#89421C2semidirect
55. #89756C22semidirect
56. #89753C22semidirect
57. #89724C22semidirect
58. #89724C22semidirect
59. #89721C22semidirect
60. #89720C22semidirect
61. #89717C22semidirect
62. #89717C22semidirect
63. #89717C22semidirect
64. #89716C22semidirect
65. #89429C22semidirect
66. #89421C22semidirect
616. C2×C7#2651semidirect
713. C7C2×#2651semidirect
759. C2#11734436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×#899942
C2×#899932
C2×#897562
C2×#897532
C2×#897212
C2×#897242
C2×#897202
C2×#897172
C2×#897162
#117344362
C2×#894292
C2×#894212
C2×#26517