Finite Group Databasebeta

← C2×#11732429 #13522285

Subgroups — C2×#11732429 #13522285

Order 1792.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6452C211yesmaximal, characteristic, complemented
2C22×#6435C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×#89764C211yesmaximal, characteristic
5C2×#89766C211yesmaximal, characteristic
6C2×#89748C211yesmaximal, characteristic, complemented
7C2×#89700C211yesmaximal, characteristic, complemented
8#11732429C2116yesmaximal, direct product factor
9C2×#89449C211yesmaximal, characteristic
10C2×#89448C211yesmaximal, characteristic
11C2×#89439C211yesmaximal, characteristic
12C2×#89419C211yesmaximal, characteristic, complemented
13C2×#89419C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89426C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic
17C23×C4×D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C22×Dic7⋊C4C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C22×C4×Dic7C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C2×#6452—28no—
45C2×#6452C2218yescomplemented
46C2×#6435—28no—
47C2×#6435C2218yes—
48C7×#387C2218yescomplemented
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#89766C2218yes—
58#89764C2218yes—
59#89748C2218yescomplemented
60#89700C2218yescomplemented
61#89449C2218yes—
62#89448C2218yes—
63#89439C2218yes—
64#89438C2218yes—
65#89426C2218yescomplemented
66#89419C2218yescomplemented
67#89419C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2441—71nomaximal, Sylow
70C24×D7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C22×C4×D7—24no—
86C22×C4×D7—24no—
87C22×C4×D7Q818yes—
88C22×C4×D7C2314yes—
89C2×C7×C4⋊C4—24no—
90C2×C7×C4⋊C4—24no—
91C2×C7×C4⋊C4C2314yes—
92C2×C7×C4⋊C4C2314yes—
93C2×C42×C7—24no—
94C2×C42×C7C2314yes—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—24no—
97C2×(C2×D7)⋊C4—24no—
98C2×(C2×D7)⋊C4—24no—
99C2×(C2×D7)⋊C4—42no—
100C2×(C2×D7)⋊C4—42no—
101C2×(C2×D7)⋊C4C2314yes—
102C2×(C2×D7)⋊C4C2314yes—
103C2×(C2×D7)⋊C4C2314yes—
104C2×(C2×D7)⋊C4C2314yes—
105C2×(C2×D7)⋊C4C2314yes—
106C2×(C2×D7)⋊C4C2314yes—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—24no—
109C2×C4⋊Dic7—24no—
110C2×C4⋊Dic7—42no—
111C2×C4⋊Dic7C2314yes—
112C2×C4⋊Dic7C2314yes—
113C2×C4⋊Dic7C2314yes—
114C2×C4⋊Dic7C2314yes—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4—24no—
119C2×Dic7⋊C4—24no—
120C2×Dic7⋊C4—24no—
121C2×Dic7⋊C4—42no—
122C2×Dic7⋊C4—42no—
123C2×Dic7⋊C4—42no—
124C2×Dic7⋊C4D418yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C2×Dic7⋊C4C2314yes—
128C2×Dic7⋊C4C2314yes—
129C2×Dic7⋊C4C2314yes—
130C2×Dic7⋊C4C2314yes—
131C2×Dic7⋊C4C2314yes—
132C2×Dic7⋊C4C2314yes—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—24no—
137C2×C4×Dic7—24no—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140C2×C4×Dic7C2314yes—
141#6452—232no—
142#6435—232no—
143C7×#95C2314yes—
144C7×#95C2314yes—
145C7×#95C2314yes—
146C7×#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C22×#125—71no—
152C22×#117—71no—
153#2441—716no—
154C2×#399—71no—
155C2×#399—71no—
156C2×#396—71no—
157C2×#396—71no—
158C2×#389—71no—
159C2×#389—71no—
160C2×#389—71no—
161C2×#389—71no—
162C2×#387—71no—
163C2×#387D711yescharacteristic, complemented
164C2×#384—71no—
165C2×#380—71no—
166C2×C4×C22⋊C4—71no—
167C24×C7C2411yescharacteristic
168C23×D7—22no—
169C23×D7—22no—
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—22no—
174C23×D7C2×Q814yes—
175C23×D7C2412yes—
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×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7C2×D414yes—
195C22×C4×C7C2×Q814yes—
196C22×C4×C7#4114yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×C4×C7C2412yes—
201C22×C4×C7C2412yes—
202C22×C4×C7C2412yes—
203C22×C4×C7C2412yes—
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×Dic7C2×D414yes—
221C22×Dic7C2×D414yes—
222C22×Dic7C2×Q814yes—
223C22×Dic7#4114yes—
224C22×Dic7#4114yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C2×C4×D7—232no—
233C2×C4×D7—28no—
234C2×C4×D7—28no—
235C2×C4×D7C2×Q8116yes—
236C7×C4⋊C4—28no—
237C7×C4⋊C4—28no—
238C42×C7—28no—
239(C2×D7)⋊C4—28no—
240(C2×D7)⋊C4—28no—
241(C2×D7)⋊C4—28no—
242(C2×D7)⋊C4—28no—
243(C2×D7)⋊C4—44no—
244(C2×D7)⋊C4—44no—
245C4⋊Dic7—28no—
246C4⋊Dic7—28no—
247C4⋊Dic7—28no—
248C4⋊Dic7—44no—
249Dic7⋊C4—28no—
250Dic7⋊C4—28no—
251Dic7⋊C4—28no—
252Dic7⋊C4—28no—
253Dic7⋊C4—28no—
254Dic7⋊C4—28no—
255Dic7⋊C4—44no—
256Dic7⋊C4—44no—
257Dic7⋊C4—44no—
258Dic7⋊C4C2×D4116yes—
259C4×Dic7—28no—
260C4×Dic7—28no—
261C4×Dic7—28no—
262C24×C4—71no—
263C2×#125—78no—
264C2×#125—148no—
265C2×#117—78no—
266C2×#117—148no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
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×C4⋊C4—71no—
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4C2×D711yescharacteristic
282C22×C4⋊C4C2×D711yescharacteristic
283C22×C22⋊C4—71no—
284C22×C22⋊C4—71no—
285C22×C22⋊C4—71no—
286C22×C22⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C42—71no—
290C22×C42—71no—
291C22×C42—71no—
292C22×C42C2×D711yescharacteristic
293#399—78no—
294#399—78no—
295#396—78no—
296#396—78no—
297#389—78no—
298#389—78no—
299#389—78no—
300#389—78no—
301#387—78no—
302#387C2×D718yescomplemented
303#384—78no—
304#380—78no—
305C4×C22⋊C4—78no—
306C2×#95—71no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
310C2×#95C2×D711yescharacteristic
311C2×#95C2×D711yescharacteristic
312C2×#95C2×D711yescharacteristic
313C2×#95C2×D711yescharacteristic
314C23×C7C22×D412yes—
315C23×C7C22×Q812yes—
316C23×C7C2×#4112yes—
317C23×C7C2×#4112yes—
318C23×C7C2×#4112yes—
319C23×C7H(5,𝔽2)12yes—
320C23×C72−1+412yes—
321C23×C7C2511yescharacteristic
322C22×D7—28no—
323C22×D7—28no—
324C22×D7—28no—
325C22×D7—22no—
326C22×D7—22no—
327C22×D7—22no—
328C22×D7—22no—
329C22×D7—22no—
330C22×D7—22no—
331C22×D7—44no—
332C22×D7—44no—
333C22×D7—44no—
334C22×D7—44no—
335C22×D7C22×Q814yes—
336C2×C4×C7—28no—
337C2×C4×C7—28no—
338C2×C4×C7—28no—
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—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—44no—
358C2×C4×C7—44no—
359C2×C4×C7—44no—
360C2×C4×C7—44no—
361C2×C4×C7C22×D414yes—
362C2×C4×C7C22×Q814yes—
363C2×C4×C7C2×#4114yes—
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—44no—
383C2×Dic7—44no—
384C2×Dic7—44no—
385C2×Dic7—44no—
386C2×Dic7C22⋊Q8116yes—
387C2×Dic7C22×D414yes—
388C2×Dic7C22×D414yes—
389C2×Dic7C22×Q814yes—
390C2×Dic7C2×#4114yes—
391C2×Dic7C2×#4114yes—
392C4×D7—232no—
393C25—71no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4—78no—
398C23×C4—74no—
399C23×C4—71no—
400C23×C4—71no—
401C23×C4—71no—
402C23×C4—71no—
403C23×C4—144no—
404C23×C4—144no—
405C23×C4C22×D711yescharacteristic
406C23×C4C22×D711yescharacteristic
407C23×C4C22×D711yescharacteristic
408C23×C4C22×D711yescharacteristic
409C23×C4C22×D711yescharacteristic
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412#125—1432no—
413#117—1432no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—78no—
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—74no—
426C2×C4⋊C4—74no—
427C2×C4⋊C4—74no—
428C2×C4⋊C4—74no—
429C2×C4⋊C4—74no—
430C2×C4⋊C4—74no—
431C2×C4⋊C4—144no—
432C2×C4⋊C4—144no—
433C2×C4⋊C4—144no—
434C2×C4⋊C4—144no—
435C2×C4⋊C4—144no—
436C2×C4⋊C4—144no—
437C2×C4⋊C4—144no—
438C2×C4⋊C4—144no—
439C2×C4⋊C4—144no—
440C2×C4⋊C4—282no—
441C2×C4⋊C4—282no—
442C2×C4⋊C4—282no—
443C2×C4⋊C4—282no—
444C2×C4⋊C4C22×D714yes—
445C2×C4⋊C4C22×D714yes—
446C2×C22⋊C4—74no—
447C2×C22⋊C4—74no—
448C2×C22⋊C4—74no—
449C2×C22⋊C4—74no—
450C2×C22⋊C4—74no—
451C2×C22⋊C4—74no—
452C2×C22⋊C4—144no—
453C2×C22⋊C4—144no—
454C2×C22⋊C4—144no—
455C2×C22⋊C4—144no—
456C2×C22⋊C4—282no—
457C2×C22⋊C4—282no—
458C2×C42—24no—
459C2×C42—74no—
460C2×C42—74no—
461C2×C42—74no—
462C2×C42—144no—
463C2×C42—144no—
464C2×C42—144no—
465C2×C42C22×D714yes—
466#95—74no—
467#95—74no—
468#95—74no—
469#95—74no—
470#95C22×D714yes—
471#95C22×D714yes—
472#95C22×D714yes—
473#95C22×D714yes—
474C22×C7C2×C22⋊Q814yes—
475C22×C7#53314yes—
476C22×C7#54414yes—
477C22×C7#54714yes—
478C22×C7#55014yes—
479C22×C7#55214yes—
480C22×C7#55314yes—
481C22×C7C23×D411yescharacteristic
482C22×C7C23×Q811yescharacteristic
483C22×C7C22×#4111yescharacteristic
484C22×C7C22×#4111yescharacteristic
485C22×C7C22×#4111yescharacteristic
486C22×C7C2×H(5,𝔽2)11yescharacteristic
487C22×C7C2×2−1+411yescharacteristic
488C2×D7—24no—
489C2×D7—24no—
490C2×D7—24no—
491C2×D7—42no—
492C2×D7—416no—
493C2×D7—42no—
494C2×D7—42no—
495C2×D7—42no—
496C4×C7—24no—
497C4×C7—24no—
498C4×C7—24no—
499C4×C7—42no—
500C4×C7—42no—
501C4×C7—42no—
502C4×C7—42no—
503Dic7—24no—
504Dic7—24no—
505Dic7—42no—
506Dic7—42no—
507Dic7—42no—
508Dic7—42no—
509Dic7C2×C22⋊Q818yes—
510C24—74no—
511C24—72no—
512C24—142no—
513C24—142no—
514C24—142no—
515C24—142no—
516C24—142no—
517C24—142no—
518C24C23×D711yescharacteristic
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—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—74no—
538C22×C4—74no—
539C22×C4—74no—
540C22×C4—72no—
541C22×C4—74no—
542C22×C4—74no—
543C22×C4—72no—
544C22×C4—72no—
545C22×C4—716no—
546C22×C4—72no—
547C22×C4—72no—
548C22×C4—72no—
549C22×C4—72no—
550C22×C4—148no—
551C22×C4—1432no—
552C22×C4—148no—
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×C4—142no—
568C22×C4—142no—
569C22×C4#115714yes—
570C22×C4D4×D714yes—
571C22×C4Q8×D714yes—
572C22×C4C23×D712yes—
573C22×C4C23×D712yes—
574C22×C4C23×D712yes—
575C22×C4C23×D712yes—
576C22×C4C23×D712yes—
577C22×C4C23×D712yes—
578C22×C4C23×D712yes—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—716no—
582C4⋊C4—148no—
583C4⋊C4—148no—
584C4⋊C4—148no—
585C4⋊C4—148no—
586C4⋊C4—148no—
587C4⋊C4—148no—
588C4⋊C4—148no—
589C4⋊C4—148no—
590C4⋊C4—148no—
591C4⋊C4—284no—
592C4⋊C4—284no—
593C4⋊C4—284no—
594C4⋊C4—284no—
595C22⋊C4—148no—
596C22⋊C4—148no—
597C22⋊C4—148no—
598C22⋊C4—148no—
599C22⋊C4—284no—
600C22⋊C4—284no—
601C42—28no—
602C42—148no—
603C42—148no—
604C42—148no—
605C2×C7#244118yescomplemented
606C2×C7C22×C22⋊Q811yescharacteristic
607C2×C7C2×#53311yescharacteristic
608C2×C7C2×#54411yescharacteristic
609C2×C7C2×#54711yescharacteristic
610C2×C7C2×#55011yescharacteristic
611C2×C7C2×#55211yescharacteristic
612C2×C7C2×#55311yescharacteristic
613D7—44no—
614C23—74no—
615C23—148no—
616C23—148no—
617C23—148no—
618C23—142no—
619C23—142no—
620C23—142no—
621C23—142no—
622C23—142no—
623C23—142no—
624C23—284no—
625C23—284no—
626C23—284no—
627C23—284no—
628C23C2×#115712yes—
629C23C2×D4×D712yes—
630C23C2×Q8×D712yes—
631C23D7×#4112yes—
632C23D7×#4112yes—
633C23#655312yes—
634C23#655412yes—
635C23C24×D711yescharacteristic
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
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—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—716no—
662C2×C4—74no—
663C2×C4—74no—
664C2×C4—74no—
665C2×C4—74no—
666C2×C4—74no—
667C2×C4—1432no—
668C2×C4—148no—
669C2×C4—148no—
670C2×C4—142no—
671C2×C4—142no—
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—284no—
687C2×C4—284no—
688C2×C4—284no—
689C2×C4—284no—
690C2×C4C2×#115714yes—
691C2×C4C2×D4×D714yes—
692C2×C4C2×Q8×D714yes—
693C7C2×#244111yescharacteristic, complemented, Sylow
694C22—144no—
695C22—144no—
696C22—144no—
697C22—282no—
698C22—282no—
699C22—282no—
700C22—282no—
701C22—2816no—
702C22#9022214yes—
703C22#9024414yes—
704C22#9026914yes—
705C22D7×C22⋊Q814yes—
706C22#9034614yes—
707C22#9038014yes—
708C22#9040014yes—
709C22C22×#115711yescharacteristic
710C22C22×D4×D711yescharacteristic
711C22C22×Q8×D711yescharacteristic
712C22C2×D7×#4111yescharacteristic
713C22C2×D7×#4111yescharacteristic
714C22C2×#655311yescharacteristic
715C22C2×#655411yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—78no—
724C4—144no—
725C4—144no—
726C4—282no—
727C4—282no—
728C4—282no—
729C4—282no—
730C2—284no—
731C2#1173242918yesdirect product factor
732C2C2×#9022211yescharacteristic
733C2C2×#9024411yescharacteristic
734C2C2×#9026911yescharacteristic
735C2C2×D7×C22⋊Q811yescharacteristic
736C2C2×#9034611yescharacteristic
737C2C2×#9038011yescharacteristic
738C2C2×#9040011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#387C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#387D7
hypocenterC7C2×#2441
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#6452C2semidirect
3. C2×C7×#387C2semidirect
6. C2×#89748C2semidirect
7. C2×#89700C2semidirect
8. #11732429C2direct (N × H)
12. C2×#89419C2semidirect
13. C2×#89419C2semidirect
14. C2×#89419C2semidirect
15. C2×#89426C2semidirect
45. C2×#6452C22semidirect
48. C7×#387C22semidirect
59. #89748C22semidirect
60. #89700C22semidirect
65. #89426C22semidirect
66. #89419C22semidirect
67. #89419C22semidirect
68. #89419C22semidirect
163. C2×#387D7semidirect
302. #387C2×D7semidirect
605. C2×C7#2441semidirect
693. C7C2×#2441semidirect
731. C2#11732429direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64522
C22×#64352
C2×C7×#3872
C2×#897642
C2×#897662
C2×#897482
C2×#897002
#117324292
C2×#894492
C2×#894482
C2×#894392
C2×#894192
C2×#894262
C2×#894382
C2×#24417