Finite Group Databasebeta

← C2×#11734985 #13520866

Subgroups — C2×#11734985 #13520866

Order 1792.

2590 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6441C211yesmaximal, characteristic
2C22×#6440C211yesmaximal, characteristic
3C2×C7×#397C211yesmaximal, characteristic
4C2×#89756C211yesmaximal, characteristic, complemented
5C2×#89744C211yesmaximal, characteristic, complemented
6C2×#89725C211yesmaximal, characteristic
7C2×#89724C211yesmaximal, characteristic
8C2×#89724C211yesmaximal, characteristic
9C2×#89714C211yesmaximal, characteristic
10#11734985C2116yesmaximal, direct product factor
11C2×#89432C211yesmaximal, characteristic, complemented
12C2×#89430C211yesmaximal, characteristic, complemented
13C2×#89429C211yesmaximal, characteristic, complemented
14C2×#89418C211yesmaximal, characteristic, complemented
15C2×#89418C211yesmaximal, characteristic, complemented
16C2×#89419C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C2×#6441—28no—
39C2×#6441C2218yes—
40C2×#6440—28no—
41C2×#6440C2218yes—
42C7×#397C2218yes—
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
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57#89756C2218yescomplemented
58#89744C2218yescomplemented
59#89725C2218yes—
60#89724C2218yes—
61#89724C2218yes—
62#89714C2218yes—
63#89432C2218yescomplemented
64#89430C2218yescomplemented
65#89429C2218yescomplemented
66#89419C2218yescomplemented
67#89418C2218yescomplemented
68#89418C2218yescomplemented
69C2×#2625—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×Dic7—24no—
78C23×Dic7—24no—
79C23×Dic7D418yes—
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2314yes—
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C22×Dic14—24no—
90C22×Dic14—24no—
91C22×Dic14—24no—
92C22×Dic14C2314yes—
93C2×C7×C4⋊C4—42no—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
101C2×C22⋊Dic7—24no—
102C2×C22⋊Dic7—24no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7C2314yes—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—42no—
109C2×C4⋊Dic7C2314yes—
110C2×C4⋊Dic7C2314yes—
111C2×Dic7⋊C4—24no—
112C2×Dic7⋊C4—24no—
113C2×Dic7⋊C4—24no—
114C2×Dic7⋊C4—24no—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—42no—
118C2×Dic7⋊C4—42no—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×C4×Dic7—24no—
128C2×C4×Dic7—24no—
129C2×C4×Dic7C2314yes—
130C2×C4×Dic7C2314yes—
131#6441—232no—
132#6440—232no—
133C7×#95C2314yes—
134C7×#95C2314yes—
135C7×#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C22×C22⋊Q8—71no—
148C22×#117—71no—
149#2625—716no—
150C2×#400—71no—
151C2×#400—71no—
152C2×#398—71no—
153C2×#398—71no—
154C2×#397—71no—
155C2×#397—71no—
156C2×#397—71no—
157C2×#397D711yescharacteristic
158C2×#391—71no—
159C2×#391—71no—
160C2×#389—71no—
161C2×#389—71no—
162C2×#380—71no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7C2×D414yes—
170C24×C7C2412yes—
171C24×C7C2411yescharacteristic
172C22×C4×C7—22no—
173C22×C4×C7—22no—
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—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—232no—
199C22×Dic7—28no—
200C22×Dic7—28no—
201C22×Dic7—22no—
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×Dic7C2×D4116yes—
220C22×Dic7C2×D414yes—
221C22×Dic7C2×D414yes—
222C22×Dic7#4114yes—
223C22×Dic7#4114yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C2×Dic14—28no—
233C2×Dic14—28no—
234C2×Dic14—28no—
235C2×Dic14—416no—
236C7×C4⋊C4—44no—
237C7×C22⋊C4—28no—
238C7×C22⋊C4—28no—
239C7×C22⋊C4—44no—
240C22⋊Dic7—28no—
241C22⋊Dic7—28no—
242C22⋊Dic7—44no—
243C4⋊Dic7—28no—
244C4⋊Dic7—44no—
245Dic7⋊C4—28no—
246Dic7⋊C4—28no—
247Dic7⋊C4—28no—
248Dic7⋊C4—28no—
249Dic7⋊C4—28no—
250Dic7⋊C4—28no—
251Dic7⋊C4—44no—
252Dic7⋊C4—44no—
253C4×Dic7—28no—
254C4×Dic7—28no—
255C23×Q8—71no—
256C24×C4—71no—
257C2×C22⋊Q8—78no—
258C2×C22⋊Q8—148no—
259C2×#117—78no—
260C2×#117—148no—
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⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C4⋊C4—71no—
270C22×C4⋊C4—71no—
271C22×C4⋊C4C2×D711yescharacteristic
272C22×C22⋊C4—71no—
273C22×C22⋊C4—71no—
274C22×C22⋊C4—71no—
275C22×C22⋊C4C2×D711yescharacteristic
276C22×C22⋊C4C2×D711yescharacteristic
277C22×C22⋊C4C2×D711yescharacteristic
278C22×C42—71no—
279C22×C42—71no—
280#400—78no—
281#400—78no—
282#398—78no—
283#398—78no—
284#397—78no—
285#397—78no—
286#397—78no—
287#397C2×D718yes—
288#391—78no—
289#391—78no—
290#389—78no—
291#389—78no—
292#380—78no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95—71no—
304C2×#95C2×D711yescharacteristic
305C2×#95C2×D711yescharacteristic
306C2×#95C2×D711yescharacteristic
307C23×C7—28no—
308C23×C7—28no—
309C23×C7—28no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—44no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7C22×D414yes—
321C23×C7C22×D412yes—
322C23×C7C2×#4112yes—
323C23×C7C2×#4112yes—
324C23×C7H(5,𝔽2)12yes—
325C23×C72−1+412yes—
326C23×C72−1+412yes—
327C23×C72−1+412yes—
328C23×C7C2511yescharacteristic
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
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—44no—
348C2×C4×C7—44no—
349C2×C4×C7—44no—
350C2×C4×C7—44no—
351C2×C4×C7—44no—
352C2×C4×C7—44no—
353C2×Dic7—28no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—232no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
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—44no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7—44no—
379C2×Dic7—44no—
380C2×Dic7—44no—
381C2×Dic7#123116yes—
382C2×Dic7C22×D414yes—
383C2×Dic7C22×D414yes—
384C2×Dic7C2×#4114yes—
385C2×Dic7C2×#4114yes—
386Dic14—416no—
387C25C22×D711yescharacteristic
388C22×Q8—74no—
389C22×Q8—144no—
390C22×Q8—144no—
391C22×Q8—144no—
392C23×C4—71no—
393C23×C4—78no—
394C23×C4—74no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4—71no—
398C23×C4—71no—
399C23×C4—71no—
400C23×C4—71no—
401C23×C4—71no—
402C23×C4—144no—
403C23×C4—144no—
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C23×C4C22×D711yescharacteristic
407C23×C4C22×D711yescharacteristic
408C23×C4C22×D711yescharacteristic
409C23×C4C22×D711yescharacteristic
410C22⋊Q8—1432no—
411#117—1432no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—74no—
415C2×C4⋊C4—74no—
416C2×C4⋊C4—74no—
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—144no—
424C2×C4⋊C4—144no—
425C2×C4⋊C4—144no—
426C2×C4⋊C4—144no—
427C2×C4⋊C4—144no—
428C2×C4⋊C4—144no—
429C2×C4⋊C4—144no—
430C2×C4⋊C4—282no—
431C2×C4⋊C4—282no—
432C2×C4⋊C4—282no—
433C2×C4⋊C4C22×D714yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—74no—
438C2×C22⋊C4—74no—
439C2×C22⋊C4—74no—
440C2×C22⋊C4—144no—
441C2×C22⋊C4—144no—
442C2×C22⋊C4—282no—
443C2×C22⋊C4C22×D714yes—
444C2×C22⋊C4C22×D714yes—
445C2×C22⋊C4C22×D714yes—
446C2×C42—74no—
447C2×C42—74no—
448C2×C42—144no—
449C2×C42—144no—
450#95—74no—
451#95—74no—
452#95—74no—
453#95—74no—
454#95—74no—
455#95—74no—
456#95—74no—
457#95—74no—
458#95—74no—
459#95—74no—
460#95—74no—
461#95C22×D714yes—
462#95C22×D714yes—
463#95C22×D714yes—
464C22×C7—24no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—416no—
468C22×C7—42no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7C2×#12314yes—
473C22×C7#53614yes—
474C22×C7#53714yes—
475C22×C7#54114yes—
476C22×C7#54114yes—
477C22×C7#54214yes—
478C22×C7#54214yes—
479C22×C7C23×D411yescharacteristic
480C22×C7C22×#4111yescharacteristic
481C22×C7C22×#4111yescharacteristic
482C22×C7C2×H(5,𝔽2)11yescharacteristic
483C22×C7C2×2−1+411yescharacteristic
484C22×C7C2×2−1+411yescharacteristic
485C22×C7C2×2−1+411yescharacteristic
486C4×C7—42no—
487C4×C7—42no—
488C4×C7—42no—
489C4×C7—42no—
490C4×C7—42no—
491C4×C7—42no—
492Dic7—24no—
493Dic7—42no—
494Dic7—42no—
495Dic7—42no—
496Dic7—42no—
497Dic7—42no—
498Dic7—42no—
499Dic7C2×#12318yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24D4×D714yes—
507C24C23×D712yes—
508C24C23×D711yescharacteristic
509C2×Q8—148no—
510C2×Q8—148no—
511C2×Q8—148no—
512C2×Q8—2816no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—74no—
532C22×C4—74no—
533C22×C4—74no—
534C22×C4—72no—
535C22×C4—74no—
536C22×C4—716no—
537C22×C4—72no—
538C22×C4—72no—
539C22×C4—72no—
540C22×C4—72no—
541C22×C4—72no—
542C22×C4—72no—
543C22×C4—72no—
544C22×C4—1432no—
545C22×C4—148no—
546C22×C4—148no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
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×C4C23×D712yes—
568C22×C4C23×D712yes—
569C22×C4C23×D712yes—
570C22×C4C23×D712yes—
571C22×C4C23×D712yes—
572C22×C4C23×D712yes—
573C4⋊C4—44no—
574C4⋊C4—148no—
575C4⋊C4—148no—
576C4⋊C4—148no—
577C4⋊C4—148no—
578C4⋊C4—148no—
579C4⋊C4—148no—
580C4⋊C4—148no—
581C4⋊C4—284no—
582C4⋊C4—284no—
583C4⋊C4—284no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—44no—
587C22⋊C4—148no—
588C22⋊C4—148no—
589C22⋊C4—284no—
590C42—148no—
591C42—148no—
592C2×C7—44no—
593C2×C7#262518yescomplemented
594C2×C7C22×#12311yescharacteristic
595C2×C7C2×#53611yescharacteristic
596C2×C7C2×#53711yescharacteristic
597C2×C7C2×#54111yescharacteristic
598C2×C7C2×#54111yescharacteristic
599C2×C7C2×#54211yescharacteristic
600C2×C7C2×#54211yescharacteristic
601C23—28no—
602C23—28no—
603C23—28no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23C2×D4×D714yes—
615C23C2×D4×D712yes—
616C23#654812yes—
617C23D7×#4112yes—
618C23D7×#4112yes—
619C23#655412yes—
620C23#655412yes—
621C23#655412yes—
622C23C24×D711yescharacteristic
623Q8—2816no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—716no—
649C2×C4—74no—
650C2×C4—74no—
651C2×C4—74no—
652C2×C4—74no—
653C2×C4—1432no—
654C2×C4—148no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—284no—
676C2×C4—284no—
677C2×C4—284no—
678C2×C4—284no—
679C2×C4—284no—
680C2×C4—284no—
681C7C2×#262511yescharacteristic, complemented, Sylow
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—416no—
690C22#9028814yes—
691C22#9033914yes—
692C22D7×#12314yes—
693C22#9035314yes—
694C22#9036014yes—
695C22#9039214yes—
696C22#9039214yes—
697C22C22×D4×D711yescharacteristic
698C22C2×#654811yescharacteristic
699C22C2×D7×#4111yescharacteristic
700C22C2×D7×#4111yescharacteristic
701C22C2×#655411yescharacteristic
702C22C2×#655411yescharacteristic
703C22C2×#655411yescharacteristic
704C4—42no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—78no—
711C4—144no—
712C4—282no—
713C4—282no—
714C4—282no—
715C4—282no—
716C4—282no—
717C4—282no—
718C2—44no—
719C2#1173498518yesdirect product factor
720C2C2×#9028811yescharacteristic
721C2C2×#9033911yescharacteristic
722C2C2×#9035311yescharacteristic
723C2C2×D7×#12311yescharacteristic
724C2C2×#9036011yescharacteristic
725C2C2×#9039211yescharacteristic
726C2C2×#9039211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#397C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#397D7
hypocenterC7C2×#2625
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
4. C2×#89756C2semidirect
5. C2×#89744C2semidirect
10. #11734985C2direct (N × H)
11. C2×#89432C2semidirect
12. C2×#89430C2semidirect
13. C2×#89429C2semidirect
14. C2×#89418C2semidirect
15. C2×#89418C2semidirect
16. C2×#89419C2semidirect
57. #89756C22semidirect
58. #89744C22semidirect
63. #89432C22semidirect
64. #89430C22semidirect
65. #89429C22semidirect
66. #89419C22semidirect
67. #89418C22semidirect
68. #89418C22semidirect
593. C2×C7#2625semidirect
681. C7C2×#2625semidirect
719. C2#11734985direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64412
C22×#64402
C2×C7×#3972
C2×#897562
C2×#897442
C2×#897252
C2×#897242
C2×#897142
#117349852
C2×#894322
C2×#894302
C2×#894292
C2×#894182
C2×#894192
C2×#26257